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ОС","\u002Fcsharp\u002Fsystem-programming-windows\u002Fwindows-hooks-services","01.csharp\u002F07.system-programming-windows\u002F20.windows-hooks-services",{"title":376,"path":377,"stem":378},"Системне Програмування C# (Windows) — 07.system-programming-windows","\u002Fcsharp\u002Fsystem-programming-windows\u002Fimplementation_plan","01.csharp\u002F07.system-programming-windows\u002Fimplementation_plan",{"title":380,"icon":132,"path":381,"stem":382,"children":383,"page":59},"Io","\u002Fcsharp\u002Fio","01.csharp\u002F08.io",[384,388,392,396,400],{"title":385,"path":386,"stem":387},"8.1.1. Основи роботи з файловою системою","\u002Fcsharp\u002Fio\u002Ffile-system-basics","01.csharp\u002F08.io\u002F01.file-system-basics",{"title":389,"path":390,"stem":391},"8.1.2. Потоки (Streams) та Серіалізація Даних","\u002Fcsharp\u002Fio\u002Fstreams-serialization","01.csharp\u002F08.io\u002F02.streams-serialization",{"title":393,"path":394,"stem":395},"8.2.1. JSON Serialization з System.Text.Json","\u002Fcsharp\u002Fio\u002Fjson-serialization","01.csharp\u002F08.io\u002F03.json-serialization",{"title":397,"path":398,"stem":399},"8.2.2. XML Serialization та LINQ to XML","\u002Fcsharp\u002Fio\u002Fxml-serialization","01.csharp\u002F08.io\u002F04.xml-serialization",{"title":401,"path":402,"stem":403},"8.2.3. Binary Serialization: MessagePack та Protocol Buffers","\u002Fcsharp\u002Fio\u002Fbinary-serialization","01.csharp\u002F08.io\u002F05.binary-serialization",{"title":405,"icon":132,"path":406,"stem":407,"children":408,"page":59},"Ado Net","\u002Fcsharp\u002Fado-net","01.csharp\u002F09.ado-net",[409,413,417,421,425,429,433,437,441,445,449,453],{"title":410,"path":411,"stem":412},"9.1. Введення в ADO.NET","\u002Fcsharp\u002Fado-net\u002Fintroduction-to-adonet","01.csharp\u002F09.ado-net\u002F01.introduction-to-adonet",{"title":414,"path":415,"stem":416},"9.2. Клас DbConnection — з'єднання з базою даних","\u002Fcsharp\u002Fado-net\u002Fconnection","01.csharp\u002F09.ado-net\u002F02.connection",{"title":418,"path":419,"stem":420},"9.3. Клас DbCommand — виконання SQL-запитів","\u002Fcsharp\u002Fado-net\u002Fcommand-and-queries","01.csharp\u002F09.ado-net\u002F03.command-and-queries",{"title":422,"path":423,"stem":424},"9.4. Клас DbDataReader — ефективне читання даних","\u002Fcsharp\u002Fado-net\u002Fdatareader","01.csharp\u002F09.ado-net\u002F04.datareader",{"title":426,"path":427,"stem":428},"9.5. Параметризовані запити та захист від SQL Injection","\u002Fcsharp\u002Fado-net\u002Fparameters-and-sql-injection","01.csharp\u002F09.ado-net\u002F05.parameters-and-sql-injection",{"title":430,"path":431,"stem":432},"9.6. Транзакції в ADO.NET","\u002Fcsharp\u002Fado-net\u002Ftransactions","01.csharp\u002F09.ado-net\u002F06.transactions",{"title":434,"path":435,"stem":436},"9.7. DbProviderFactory — провайдер-незалежний код","\u002Fcsharp\u002Fado-net\u002Fprovider-factory","01.csharp\u002F09.ado-net\u002F07.provider-factory",{"title":438,"path":439,"stem":440},"9.8. Асинхронний доступ до даних","\u002Fcsharp\u002Fado-net\u002Fasync-data-access","01.csharp\u002F09.ado-net\u002F08.async-data-access",{"title":442,"path":443,"stem":444},"9.9. Від'єднаний режим: DataSet, DataTable, DataRow","\u002Fcsharp\u002Fado-net\u002Fdisconnected-mode-dataset","01.csharp\u002F09.ado-net\u002F09.disconnected-mode-dataset",{"title":446,"path":447,"stem":448},"9.10. DataAdapter — міст між DataSet та базою даних","\u002Fcsharp\u002Fado-net\u002Fdata-adapter","01.csharp\u002F09.ado-net\u002F10.data-adapter",{"title":450,"path":451,"stem":452},"9.11. Data Mapper та Repository: Архітектура доступу до даних","\u002Fcsharp\u002Fado-net\u002Fdata-mapper-repository","01.csharp\u002F09.ado-net\u002F11.data-mapper-repository",{"title":454,"path":455,"stem":456},"9.12. Identity Map, Unit of Work та Specification Pattern","\u002Fcsharp\u002Fado-net\u002Fadvanced-patterns","01.csharp\u002F09.ado-net\u002F12.advanced-patterns",{"title":458,"icon":255,"path":459,"stem":460,"children":461,"page":59},"Ef Core","\u002Fcsharp\u002Fef-core","01.csharp\u002F10.ef-core",[462,466,470,474,478,482,486,490,494,498,502,506,510,514,518,522,526,532,538,542,546,550,554,558,562,566,570,574,578,582,586,590,594,598,602,606,610,614,618,622,626,630,634,638,642,646],{"title":463,"path":464,"stem":465},"Що таке ORM? Від SQL до об'єктів","\u002Fcsharp\u002Fef-core\u002Fwhat-is-orm","01.csharp\u002F10.ef-core\u002F01.what-is-orm",{"title":467,"path":468,"stem":469},"Перший проєкт — від нуля до CRUD","\u002Fcsharp\u002Fef-core\u002Ffirst-project","01.csharp\u002F10.ef-core\u002F02.first-project",{"title":471,"path":472,"stem":473},"DbContext — Серце EF Core","\u002Fcsharp\u002Fef-core\u002Fdbcontext-deep-dive","01.csharp\u002F10.ef-core\u002F03.dbcontext-deep-dive",{"title":475,"path":476,"stem":477},"Провайдери баз даних — Архітектура та Вибір СУБД","\u002Fcsharp\u002Fef-core\u002Fdatabase-providers","01.csharp\u002F10.ef-core\u002F04.database-providers",{"title":479,"path":480,"stem":481},"Конвенції EF Core — Магія без конфігурації","\u002Fcsharp\u002Fef-core\u002Fconventions","01.csharp\u002F10.ef-core\u002F05.conventions",{"title":483,"path":484,"stem":485},"Fluent API та Data Annotations — Явна конфігурація моделі","\u002Fcsharp\u002Fef-core\u002Ffluent-api-vs-annotations","01.csharp\u002F10.ef-core\u002F06.fluent-api-vs-annotations",{"title":487,"path":488,"stem":489},"Зв'язки — One-to-One та One-to-Many","\u002Fcsharp\u002Fef-core\u002Frelationships-basics","01.csharp\u002F10.ef-core\u002F07.relationships-basics",{"title":491,"path":492,"stem":493},"Зв'язки Advanced — Many-to-Many та Складні Сценарії","\u002Fcsharp\u002Fef-core\u002Frelationships-advanced","01.csharp\u002F10.ef-core\u002F08.relationships-advanced",{"title":495,"path":496,"stem":497},"Властивості — Типи, Конвертери, Компаратори (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part1","01.csharp\u002F10.ef-core\u002F09.property-configuration-part1",{"title":499,"path":500,"stem":501},"Властивості — Value Comparers, Generators, Shadow Properties (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part2","01.csharp\u002F10.ef-core\u002F09.property-configuration-part2",{"title":503,"path":504,"stem":505},"Складні типи — Owned Types та Complex Types (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part1","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part1",{"title":507,"path":508,"stem":509},"Складні типи — Complex Types, Keyless Entities, Порівняння (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part2","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part2",{"title":511,"path":512,"stem":513},"JSON Columns — Складні дані у JSON (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part1","01.csharp\u002F10.ef-core\u002F11.json-columns-part1",{"title":515,"path":516,"stem":517},"JSON Columns — Value Comparers, Індекси, Провайдери (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part2","01.csharp\u002F10.ef-core\u002F11.json-columns-part2",{"title":519,"path":520,"stem":521},"Успадкування — Абстрактні класи та TPH (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finheritance-part1","01.csharp\u002F10.ef-core\u002F12.inheritance-part1",{"title":523,"path":524,"stem":525},"Успадкування — TPT, TPC та Порівняння Стратегій (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finheritance-part2","01.csharp\u002F10.ef-core\u002F12.inheritance-part2",{"title":527,"path":528,"stem":529,"children":530},"Індекси, Обмеження та Схема (Частина 1)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part1","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part1",[531],{"title":527,"path":528,"stem":529},{"title":533,"path":534,"stem":535,"children":536},"Індекси, Обмеження та Схема (Частина 2)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part2","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part2",[537],{"title":533,"path":534,"stem":535},{"title":539,"path":540,"stem":541},"Seed Data — Початкові Дані (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fseeding-part1","01.csharp\u002F10.ef-core\u002F14.seeding-part1",{"title":543,"path":544,"stem":545},"Seed Data — SQL-скрипти, Bogus та Стратегії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fseeding-part2","01.csharp\u002F10.ef-core\u002F14.seeding-part2",{"title":547,"path":548,"stem":549},"Global Query Filters — Глобальні Фільтри (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part1","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part1",{"title":551,"path":552,"stem":553},"Global Query Filters — Підводні камені та Інтеграція (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part2","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part2",{"title":555,"path":556,"stem":557},"LINQ-запити в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part1","01.csharp\u002F10.ef-core\u002F16.linq-queries-part1",{"title":559,"path":560,"stem":561},"LINQ-запити в EF Core (Частина 2)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part2","01.csharp\u002F10.ef-core\u002F16.linq-queries-part2",{"title":563,"path":564,"stem":565},"Завантаження Пов'язаних Даних (Частина 1)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part1","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part1",{"title":567,"path":568,"stem":569},"Завантаження Пов'язаних Даних (Частина 2)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part2","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part2",{"title":571,"path":572,"stem":573},"Raw SQL, Views та Stored Procedures (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part1","01.csharp\u002F10.ef-core\u002F18.raw-sql-part1",{"title":575,"path":576,"stem":577},"Raw SQL — Stored Procedures, DbFunction та Bulk Operations (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part2","01.csharp\u002F10.ef-core\u002F18.raw-sql-part2",{"title":579,"path":580,"stem":581},"Продвинуті Запити — Compiled Queries, Bulk та Оптимізація (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part1","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part1",{"title":583,"path":584,"stem":585},"Продвинуті Запити — Query Tags, Bulk та Interceptors (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part2","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part2",{"title":587,"path":588,"stem":589},"Change Tracker — Відстеження Змін (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part1","01.csharp\u002F10.ef-core\u002F20.change-tracking-part1",{"title":591,"path":592,"stem":593},"Change Tracker — Графи Об'єктів та Disconnected (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part2","01.csharp\u002F10.ef-core\u002F20.change-tracking-part2",{"title":595,"path":596,"stem":597},"Збереження Даних та Транзакції (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part1","01.csharp\u002F10.ef-core\u002F21.saving-data-part1",{"title":599,"path":600,"stem":601},"Збереження Даних — Concurrency та Outbox (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part2","01.csharp\u002F10.ef-core\u002F21.saving-data-part2",{"title":603,"path":604,"stem":605},"Конкурентність та Блокування (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part1","01.csharp\u002F10.ef-core\u002F22.concurrency-part1",{"title":607,"path":608,"stem":609},"Конкурентність — Дедлоки та Queue Processing (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part2","01.csharp\u002F10.ef-core\u002F22.concurrency-part2",{"title":611,"path":612,"stem":613},"Міграції в EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part1","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part1",{"title":615,"path":616,"stem":617},"Міграції в EF Core — Основи (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part2","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part2",{"title":619,"path":620,"stem":621},"Міграції — Просунуті Сценарії (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part1","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part1",{"title":623,"path":624,"stem":625},"Міграції — Просунуті Сценарії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part2","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part2",{"title":627,"path":628,"stem":629},"Управління Схемою та Database-First (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part1","01.csharp\u002F10.ef-core\u002F25.schema-management-part1",{"title":631,"path":632,"stem":633},"Управління Схемою та Database-First (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part2","01.csharp\u002F10.ef-core\u002F25.schema-management-part2",{"title":635,"path":636,"stem":637},"Продуктивність EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fperformance-fundamentals-part1","01.csharp\u002F10.ef-core\u002F26.performance-fundamentals-part1",{"title":639,"path":640,"stem":641},"Interceptors в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part1","01.csharp\u002F10.ef-core\u002F29.interceptors-part1",{"title":643,"path":644,"stem":645},"Interceptors в EF Core — Connection, Transaction та Materialization (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part2","01.csharp\u002F10.ef-core\u002F29.interceptors-part2",{"title":647,"path":648,"stem":649},"План вивчення Entity Framework Core — Повний курс","\u002Fcsharp\u002Fef-core\u002Fimplementation_plan","01.csharp\u002F10.ef-core\u002Fimplementation_plan",{"title":651,"icon":652,"path":653,"stem":654,"children":655,"page":59},"ASP.NET","i-devicon-dotnetcore","\u002Fcsharp\u002Faspnet","01.csharp\u002F11.aspnet",[656,730,791,869,927,941,967,1057,1111,1182,1212,1289,1346],{"title":657,"icon":658,"path":659,"stem":660,"children":661,"page":59},"Minimal API","i-lucide-network","\u002Fcsharp\u002Faspnet\u002Fminimal-api","01.csharp\u002F11.aspnet\u002F01.minimal-api",[662,666,670,674,678,682,686,690,694,698,702,706,710,714,718,722,726],{"title":663,"path":664,"stem":665},"Вступ до ASP.NET та еволюція фреймворку","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fintroduction","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F01.introduction",{"title":667,"path":668,"stem":669},"Перший додаток на ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Ffirst-application","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F02.first-application",{"title":671,"path":672,"stem":673},"WebApplication, Builder та Dependency Injection","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fwebapplication-builder","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F03.webapplication-builder",{"title":675,"path":676,"stem":677},"Конвеєр запитів та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frequest-pipeline-middleware","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F04.request-pipeline-middleware",{"title":679,"path":680,"stem":681},"Маршрутизація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F05.routing-basics",{"title":683,"path":684,"stem":685},"Маршрутизація в ASP.NET Core: Розширені можливості","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F06.routing-advanced",{"title":687,"path":688,"stem":689},"Статичні файли в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-files","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F07.static-files",{"title":691,"path":692,"stem":693},"Статичні Активи: MapStaticAssets (ASP.NET Core 9.0)","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-assets","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F08.static-assets",{"title":695,"path":696,"stem":697},"Конфігурація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-fundamentals","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F09.configuration-fundamentals",{"title":699,"path":700,"stem":701},"Конфігурація: Паттерн Options","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-options","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F10.configuration-options",{"title":703,"path":704,"stem":705},"Логування в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F11.logging-basics",{"title":707,"path":708,"stem":709},"Логування: Serilog та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F12.logging-advanced",{"title":711,"path":712,"stem":713},"Управління станом: HttpContext.Items та Cookies","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstate-management","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F13.state-management",{"title":715,"path":716,"stem":717},"Стан сесії: Sessions","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fsession-state","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F14.session-state",{"title":719,"path":720,"stem":721},"Структура проєкту: від хаосу до архітектури","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fproject-structure","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F15.project-structure",{"title":723,"path":724,"stem":725},"Scalar у Minimal API: повний проєкт і Fluent OpenAPI","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fscalar-openapi-fluent","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F16.scalar-openapi-fluent",{"title":727,"path":728,"stem":729},"Swagger \u002F Swashbuckle у Minimal API: окремий класичний шлях","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fswagger-swashbuckle","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F17.swagger-swashbuckle",{"title":731,"icon":658,"path":732,"stem":733,"children":734,"page":59},"API","\u002Fcsharp\u002Faspnet\u002Fapi","01.csharp\u002F11.aspnet\u002F02.api",[735,739,743,747,751,755,759,763,767,771,775,779,783,787],{"title":736,"path":737,"stem":738},"Що таке API. Клієнт-серверна архітектура","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fwhat-is-api","01.csharp\u002F11.aspnet\u002F02.api\u002F01.what-is-api",{"title":740,"path":741,"stem":742},"Формати даних: JSON, XML, TOML та бінарні формати","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fdata-formats","01.csharp\u002F11.aspnet\u002F02.api\u002F02.data-formats",{"title":744,"path":745,"stem":746},"Парадигми API та концепція REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-paradigms-rest","01.csharp\u002F11.aspnet\u002F02.api\u002F03.api-paradigms-rest",{"title":748,"path":749,"stem":750},"HTTP-методи, статус-коди та заголовки","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fhttp-methods-status-codes","01.csharp\u002F11.aspnet\u002F02.api\u002F04.http-methods-status-codes",{"title":752,"path":753,"stem":754},"Організація HTTP API за принципами REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Frest-organizing","01.csharp\u002F11.aspnet\u002F02.api\u002F05.rest-organizing",{"title":756,"path":757,"stem":758},"Номенклатура URL та CRUD-операції","\u002Fcsharp\u002Faspnet\u002Fapi\u002Furl-nomenclature-crud","01.csharp\u002F11.aspnet\u002F02.api\u002F06.url-nomenclature-crud",{"title":760,"path":761,"stem":762},"Правила дизайну: іменування та стандарти","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-naming","01.csharp\u002F11.aspnet\u002F02.api\u002F07.api-design-naming",{"title":764,"path":765,"stem":766},"Валідація, ліміти та обробка помилок","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-validation","01.csharp\u002F11.aspnet\u002F02.api\u002F08.api-design-validation",{"title":768,"path":769,"stem":770},"Обробка помилок у Minimal API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Ferror-handling-http","01.csharp\u002F11.aspnet\u002F02.api\u002F09.error-handling-http",{"title":772,"path":773,"stem":774},"Ідемпотентність та синхронізація стану","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fidempotency-sync","01.csharp\u002F11.aspnet\u002F02.api\u002F10.idempotency-sync",{"title":776,"path":777,"stem":778},"Пагінація та організація списків","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fpagination-lists","01.csharp\u002F11.aspnet\u002F02.api\u002F11.pagination-lists",{"title":780,"path":781,"stem":782},"Безпека API, кешування та інтернаціоналізація","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fsecurity-auth","01.csharp\u002F11.aspnet\u002F02.api\u002F12.security-auth",{"title":784,"path":785,"stem":786},"Процес проєктування API та документування","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-process","01.csharp\u002F11.aspnet\u002F02.api\u002F13.api-design-process",{"title":788,"path":789,"stem":790},"OpenAPI: контракт, специфікація та документація API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fopenapi","01.csharp\u002F11.aspnet\u002F02.api\u002F14.openapi",{"title":792,"icon":793,"path":794,"stem":795,"children":796,"page":59},"Auth","i-lucide-shield-check","\u002Fcsharp\u002Faspnet\u002Fauth","01.csharp\u002F11.aspnet\u002F03.auth",[797,801,805,809,813,817,821,825,829,833,837,841,845,849,853,857,861,865],{"title":798,"path":799,"stem":800},"Основи аутентифікації та авторизації","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauth-fundamentals","01.csharp\u002F11.aspnet\u002F03.auth\u002F01.auth-fundamentals",{"title":802,"path":803,"stem":804},"JWT-аутентифікація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fjwt-authentication","01.csharp\u002F11.aspnet\u002F03.auth\u002F02.jwt-authentication",{"title":806,"path":807,"stem":808},"Авторизація: ролі, політики та resource-based доступ","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauthorization-policies","01.csharp\u002F11.aspnet\u002F03.auth\u002F03.authorization-policies",{"title":810,"path":811,"stem":812},"Cookie-аутентифікація та ASP.NET Core Identity","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcookie-auth-identity","01.csharp\u002F11.aspnet\u002F03.auth\u002F04.cookie-auth-identity",{"title":814,"path":815,"stem":816},"JWT + Refresh Tokens (HttpOnly Cookie)","\u002Fcsharp\u002Faspnet\u002Fauth\u002F04b.identity-auth-jwt","01.csharp\u002F11.aspnet\u002F03.auth\u002F04b.identity-auth-jwt",{"title":818,"path":819,"stem":820},"Identity: Підтвердження Email та Скидання Пароля","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-email-confirmation","01.csharp\u002F11.aspnet\u002F03.auth\u002F05.identity-email-confirmation",{"title":822,"path":823,"stem":824},"Identity: Двофакторна Аутентифікація (2FA)","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-two-factor","01.csharp\u002F11.aspnet\u002F03.auth\u002F06.identity-two-factor",{"title":826,"path":827,"stem":828},"Identity: Внутрішня Архітектура та Кастомізація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-internals","01.csharp\u002F11.aspnet\u002F03.auth\u002F07.identity-internals",{"title":830,"path":831,"stem":832},"OAuth 2.0 та зовнішні провайдери","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-external-providers","01.csharp\u002F11.aspnet\u002F03.auth\u002F08.oauth-external-providers",{"title":834,"path":835,"stem":836},"Безпека на практиці: CORS, HTTPS та захист від атак","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fsecurity-hardening","01.csharp\u002F11.aspnet\u002F03.auth\u002F09.security-hardening",{"title":838,"path":839,"stem":840},"Теорія OAuth 2.0: Поняття, Аналогії та Флоу","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-theory","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oauth-theory",{"title":842,"path":843,"stem":844},"OIDC, OAuth 2.0 та Keycloak в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foidc-keycloak","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oidc-keycloak",{"title":846,"path":847,"stem":848},"API Keys аутентифікація в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fapi-keys","01.csharp\u002F11.aspnet\u002F03.auth\u002F11.api-keys",{"title":850,"path":851,"stem":852},"Rate Limiting та Throttling в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frate-limiting","01.csharp\u002F11.aspnet\u002F03.auth\u002F12.rate-limiting",{"title":854,"path":855,"stem":856},"Refresh Token Rotation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frefresh-token-rotation","01.csharp\u002F11.aspnet\u002F03.auth\u002F13.refresh-token-rotation",{"title":858,"path":859,"stem":860},"Certificate Authentication та mTLS в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcertificate-auth","01.csharp\u002F11.aspnet\u002F03.auth\u002F14.certificate-auth",{"title":862,"path":863,"stem":864},"RBAC, ABAC та ReBAC в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frbac-abac-rebac","01.csharp\u002F11.aspnet\u002F03.auth\u002F15.rbac-abac-rebac",{"title":866,"path":867,"stem":868},"Multi-tenancy та ізоляція даних в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fmulti-tenancy","01.csharp\u002F11.aspnet\u002F03.auth\u002F16.multi-tenancy",{"title":870,"icon":871,"path":872,"stem":873,"children":874,"page":59},"Нотифікації","i-lucide-bell","\u002Fcsharp\u002Faspnet\u002Fnotifications","01.csharp\u002F11.aspnet\u002F04.notifications",[875,879,883,887,891,895,899,903,907,911,915,919,923],{"title":876,"path":877,"stem":878},"In-App нотифікації через базу даних","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fin-app-database-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F01.in-app-database-notifications",{"title":880,"path":881,"stem":882},"Polling: Регулярний запит оновлень","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fpolling","01.csharp\u002F11.aspnet\u002F04.notifications\u002F02.polling",{"title":884,"path":885,"stem":886},"Server-Sent Events: Однострімовий push від сервера","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fserver-sent-events","01.csharp\u002F11.aspnet\u002F04.notifications\u002F03.server-sent-events",{"title":888,"path":889,"stem":890},"WebSockets: Двостороннє з'єднання в реальному часі","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fwebsockets","01.csharp\u002F11.aspnet\u002F04.notifications\u002F04.websockets",{"title":892,"path":893,"stem":894},"SignalR: Абстракція над транспортами реального часу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fsignalr","01.csharp\u002F11.aspnet\u002F04.notifications\u002F05.signalr",{"title":896,"path":897,"stem":898},"Background Services: Фонові задачі в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fbackground-services","01.csharp\u002F11.aspnet\u002F04.notifications\u002F06.background-services",{"title":900,"path":901,"stem":902},"Web Push нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fweb-push","01.csharp\u002F11.aspnet\u002F04.notifications\u002F07.web-push",{"title":904,"path":905,"stem":906},"Email нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Femail-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F08.email-notifications",{"title":908,"path":909,"stem":910},"Порівняння підходів: Як вибрати правильну технологію нотифікацій","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fchoosing-the-right-approach","01.csharp\u002F11.aspnet\u002F04.notifications\u002F09.choosing-the-right-approach",{"title":912,"path":913,"stem":914},"Hangfire: Надійне планування фонових задач","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire","01.csharp\u002F11.aspnet\u002F04.notifications\u002F10.hangfire",{"title":916,"path":917,"stem":918},"Практика: Конвертація зображень у WebP через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-image-webp","01.csharp\u002F11.aspnet\u002F04.notifications\u002F11.hangfire-image-webp",{"title":920,"path":921,"stem":922},"Практика: Підготовка відео до HLS-стрімінгу через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-video-hls","01.csharp\u002F11.aspnet\u002F04.notifications\u002F12.hangfire-video-hls",{"title":924,"path":925,"stem":926},"Telegram-нотифікації: від одного повідомлення до масових розсилок і мульти-канального підходу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Ftelegram-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F13.telegram-notifications",{"title":928,"icon":929,"path":930,"stem":931,"children":932,"page":59},"Інтернаціоналізація","i-lucide-languages","\u002Fcsharp\u002Faspnet\u002Fi18n","01.csharp\u002F11.aspnet\u002F05.i18n",[933,937],{"title":934,"path":935,"stem":936},"Інтернаціоналізація (i18n) у Minimal API: від A до Я","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Finternationalization","01.csharp\u002F11.aspnet\u002F05.i18n\u002F01.internationalization",{"title":938,"path":939,"stem":940},"Humanizer: людиномовні рядки у .NET","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Fhumanizer","01.csharp\u002F11.aspnet\u002F05.i18n\u002F02.humanizer",{"title":942,"icon":943,"path":944,"stem":945,"children":946,"page":59},"Кешування","i-lucide-layers","\u002Fcsharp\u002Faspnet\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching",[947,951,955,959,963],{"title":948,"path":949,"stem":950},"Огляд кешування: чотири рівні і коли що обирати","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching\u002F01.caching",{"title":952,"path":953,"stem":954},"IMemoryCache: кеш в оперативній пам'яті","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fmemory-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F02.memory-cache",{"title":956,"path":957,"stem":958},"IDistributedCache і Redis: розподілений кеш","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fdistributed-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F03.distributed-cache",{"title":960,"path":961,"stem":962},"Response Cache: HTTP-кешування через Cache-Control","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fresponse-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F04.response-cache",{"title":964,"path":965,"stem":966},"Output Cache: серверний кеш HTTP-відповідей (.NET 7+)","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Foutput-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F05.output-cache",{"title":968,"icon":969,"path":970,"stem":971,"children":972,"page":59},"Тестування","i-lucide-test-tube","\u002Fcsharp\u002Faspnet\u002Ftesting","01.csharp\u002F11.aspnet\u002F07.testing",[973,977,981,985,989,993,997,1001,1005,1009,1013,1017,1021,1025,1029,1033,1037,1041,1045,1049,1053],{"title":974,"path":975,"stem":976},"Що таке тестування? Від інтуїції до науки","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-is-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F01.what-is-testing",{"title":978,"path":979,"stem":980},"Піраміда тестування — Стратегія, а не Догма","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-pyramid","01.csharp\u002F11.aspnet\u002F07.testing\u002F02.testing-pyramid",{"title":982,"path":983,"stem":984},"Дві Школи Тестування — Лондон проти Детройту","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-schools","01.csharp\u002F11.aspnet\u002F07.testing\u002F03.testing-schools",{"title":986,"path":987,"stem":988},"TDD та BDD — Тести як Дизайн-інструмент","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftdd-and-bdd","01.csharp\u002F11.aspnet\u002F07.testing\u002F04.tdd-and-bdd",{"title":990,"path":991,"stem":992},"Що саме тестувати — Техніки аналізу та Циклomatична складність","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-to-test","01.csharp\u002F11.aspnet\u002F07.testing\u002F05.what-to-test",{"title":994,"path":995,"stem":996},"Тестові Фреймворки — Навіщо вони і що всередині","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftest-frameworks","01.csharp\u002F11.aspnet\u002F07.testing\u002F06.test-frameworks",{"title":998,"path":999,"stem":1000},"xUnit — Факти, Теорії та Lifecycle тестів","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-basics","01.csharp\u002F11.aspnet\u002F07.testing\u002F07.xunit-basics",{"title":1002,"path":1003,"stem":1004},"xUnit Advanced — Fixtures, Кастомізація та Розширення","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F08.xunit-advanced",{"title":1006,"path":1007,"stem":1008},"Moq — Глибоке занурення в мокування","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fmocking-with-moq","01.csharp\u002F11.aspnet\u002F07.testing\u002F09.mocking-with-moq",{"title":1010,"path":1011,"stem":1012},"Тестування Баз Даних — EF Core, SQLite та Testcontainers","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fdatabase-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F10.database-testing",{"title":1014,"path":1015,"stem":1016},"Integration Testing — Частина 1 [Теорія та WebApplicationFactory]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F11.integration-testing",{"title":1018,"path":1019,"stem":1020},"Інтеграційне тестування — Практика","\u002Fcsharp\u002Faspnet\u002Ftesting\u002F11a.integration-testing-practice","01.csharp\u002F11.aspnet\u002F07.testing\u002F11a.integration-testing-practice",{"title":1022,"path":1023,"stem":1024},"Integration Testing — Частина 2 [Просунуті Сценарії та Testcontainers]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F12.integration-testing-advanced",{"title":1026,"path":1027,"stem":1028},"Професійний Postman: Колекції, Змінні та GitHub Інтеграція","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fpostman-professional","01.csharp\u002F11.aspnet\u002F07.testing\u002F13.postman-professional",{"title":1030,"path":1031,"stem":1032},"HttpClient у Тестах Частина 1: Архітектура та MockHttpMessageHandler","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fhttpclient-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F14.httpclient-testing",{"title":1034,"path":1035,"stem":1036},"HttpClient у Тестах Частина 2: WireMock.Net та Resilience","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwiremock-net","01.csharp\u002F11.aspnet\u002F07.testing\u002F15.wiremock-net",{"title":1038,"path":1039,"stem":1040},"Патерни та Анти-патерни Тестування: Test Smells","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-patterns","01.csharp\u002F11.aspnet\u002F07.testing\u002F16.testing-patterns",{"title":1042,"path":1043,"stem":1044},"Просунуті інструменти: Time, Snapshots та Властивості","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fadvanced-testing-tools","01.csharp\u002F11.aspnet\u002F07.testing\u002F17.advanced-testing-tools",{"title":1046,"path":1047,"stem":1048},"Тестування Архітектури з NetArchTest","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Farchitecture-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F18.architecture-testing",{"title":1050,"path":1051,"stem":1052},"Тестування Продуктивності: BenchmarkDotNet, NBomber та k6","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fperformance-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F19.performance-testing",{"title":1054,"path":1055,"stem":1056},"Залишок плану для курсу \"Тестування ASP.NET Minimal API\"","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fremaining_plan","01.csharp\u002F11.aspnet\u002F07.testing\u002Fremaining_plan",{"title":1058,"icon":1059,"path":1060,"stem":1061,"children":1062,"page":59},"Платежі","i-lucide-credit-card","\u002Fcsharp\u002Faspnet\u002Fpayments","01.csharp\u002F11.aspnet\u002F08.payments",[1063,1067,1071,1075,1079,1083,1087,1091,1095,1099,1103,1107],{"title":1064,"path":1065,"stem":1066},"Основи платіжної інфраструктури","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-fundamentals","01.csharp\u002F11.aspnet\u002F08.payments\u002F01.payment-fundamentals",{"title":1068,"path":1069,"stem":1070},"Методи оплати в Україні","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-methods-ukraine","01.csharp\u002F11.aspnet\u002F08.payments\u002F02.payment-methods-ukraine",{"title":1072,"path":1073,"stem":1074},"PCI DSS та безпека платежів","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpci-dss-security","01.csharp\u002F11.aspnet\u002F08.payments\u002F03.pci-dss-security",{"title":1076,"path":1077,"stem":1078},"Архітектура платіжної підсистеми","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-architecture","01.csharp\u002F11.aspnet\u002F08.payments\u002F04.payment-architecture",{"title":1080,"path":1081,"stem":1082},"Інтеграція LiqPay (ПриватБанк)","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fliqpay-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F05.liqpay-integration",{"title":1084,"path":1085,"stem":1086},"Інтеграція Monobank Acquiring API","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fmonobank-acquiring","01.csharp\u002F11.aspnet\u002F08.payments\u002F06.monobank-acquiring",{"title":1088,"path":1089,"stem":1090},"Інтеграція Stripe","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fstripe-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F07.stripe-integration",{"title":1092,"path":1093,"stem":1094},"Webhooks — глибоке занурення","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fwebhooks-deep-dive","01.csharp\u002F11.aspnet\u002F08.payments\u002F08.webhooks-deep-dive",{"title":1096,"path":1097,"stem":1098},"Підписки та рекурентні платежі","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fsubscriptions-recurring","01.csharp\u002F11.aspnet\u002F08.payments\u002F09.subscriptions-recurring",{"title":1100,"path":1101,"stem":1102},"Повернення коштів та диспути","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Frefunds-disputes","01.csharp\u002F11.aspnet\u002F08.payments\u002F10.refunds-disputes",{"title":1104,"path":1105,"stem":1106},"Тестування платіжних інтеграцій","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Ftesting-payments","01.csharp\u002F11.aspnet\u002F08.payments\u002F11.testing-payments",{"title":1108,"path":1109,"stem":1110},"Чекліст виходу в Production","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fproduction-checklist","01.csharp\u002F11.aspnet\u002F08.payments\u002F12.production-checklist",{"title":1112,"icon":1113,"items":1114,"path":1127,"stem":1128,"children":1129,"page":59},"Популярні бібліотеки","lucide:box",[1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126],"01.fluent-validation","02.mapster","03.erroror-result-pattern","04.serilog","05.mediatr","06.polly","07.health-checks","08.feature-management","09.fluent-email","10.quest-pdf","11.bogus","12.humanizer-guard","\u002Fcsharp\u002Faspnet\u002Flibraries","01.csharp\u002F11.aspnet\u002F09.libraries",[1130,1134,1138,1142,1146,1150,1154,1158,1162,1166,1170,1174,1178],{"title":1131,"path":1132,"stem":1133},"Валідація з FluentValidation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-validation","01.csharp\u002F11.aspnet\u002F09.libraries\u002F01.fluent-validation",{"title":1135,"path":1136,"stem":1137},"Маппінг об","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmapster","01.csharp\u002F11.aspnet\u002F09.libraries\u002F02.mapster",{"title":1139,"path":1140,"stem":1141},"Обробка помилок з ErrorOr та Result Pattern в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ferroror-result-pattern","01.csharp\u002F11.aspnet\u002F09.libraries\u002F03.erroror-result-pattern",{"title":1143,"path":1144,"stem":1145},"Структуроване логування з Serilog в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fserilog","01.csharp\u002F11.aspnet\u002F09.libraries\u002F04.serilog",{"title":1147,"path":1148,"stem":1149},"CQRS та Mediator з MediatR в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmediatr","01.csharp\u002F11.aspnet\u002F09.libraries\u002F05.mediatr",{"title":1151,"path":1152,"stem":1153},"Відмовостійкість з Polly в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fpolly","01.csharp\u002F11.aspnet\u002F09.libraries\u002F06.polly",{"title":1155,"path":1156,"stem":1157},"Health Checks в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F09.libraries\u002F07.health-checks",{"title":1159,"path":1160,"stem":1161},"Feature Management та Feature Flags в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffeature-management","01.csharp\u002F11.aspnet\u002F09.libraries\u002F08.feature-management",{"title":1163,"path":1164,"stem":1165},"Відправка Email з FluentEmail в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-email","01.csharp\u002F11.aspnet\u002F09.libraries\u002F09.fluent-email",{"title":1167,"path":1168,"stem":1169},"Генерація PDF з QuestPDF в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fquest-pdf","01.csharp\u002F11.aspnet\u002F09.libraries\u002F10.quest-pdf",{"title":1171,"path":1172,"stem":1173},"Генерація тестових даних з Bogus в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fbogus","01.csharp\u002F11.aspnet\u002F09.libraries\u002F11.bogus",{"title":1175,"path":1176,"stem":1177},"Humanizer та Guard Clauses в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhumanizer-guard","01.csharp\u002F11.aspnet\u002F09.libraries\u002F12.humanizer-guard",{"title":1179,"path":1180,"stem":1181},"План модуля 10.libraries — Популярні бібліотеки ASP.NET","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fplan","01.csharp\u002F11.aspnet\u002F09.libraries\u002Fplan",{"title":1183,"icon":1184,"path":1185,"stem":1186,"children":1187,"page":59},"Razor Pages","i-lucide-layout-template","\u002Fcsharp\u002Faspnet\u002Frazor-pages","01.csharp\u002F11.aspnet\u002F10.razor-pages",[1188,1192,1196,1200,1204,1208],{"title":1189,"path":1190,"stem":1191},"Від Minimal API до Razor Pages: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ffrom-minimal-api","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F01.from-minimal-api",{"title":1193,"path":1194,"stem":1195},"PageModel: логіка сторінки Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fpage-model","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F02.page-model",{"title":1197,"path":1198,"stem":1199},"Razor синтаксис: шаблонізатор у .cshtml","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Frazor-syntax","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F03.razor-syntax",{"title":1201,"path":1202,"stem":1203},"Tag Helpers: типізований HTML","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ftag-helpers","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F04.tag-helpers",{"title":1205,"path":1206,"stem":1207},"Форми і валідація: повний цикл обробки даних","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fforms-validation","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F05.forms-validation",{"title":1209,"path":1210,"stem":1211},"Практичний проєкт: TaskManager на Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fproject-task-manager","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F06.project-task-manager",{"title":1213,"path":1214,"stem":1215,"children":1216,"page":59},"ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc","01.csharp\u002F11.aspnet\u002F11.mvc",[1217,1221,1225,1229,1233,1237,1241,1245,1249,1253,1257,1261,1265,1269,1273,1277,1281,1285],{"title":1218,"path":1219,"stem":1220},"Патерн MVC: архітектура, що змінила веб","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-pattern","01.csharp\u002F11.aspnet\u002F11.mvc\u002F01.mvc-pattern",{"title":1222,"path":1223,"stem":1224},"Від Razor Pages до MVC: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffrom-razor-pages","01.csharp\u002F11.aspnet\u002F11.mvc\u002F02.from-razor-pages",{"title":1226,"path":1227,"stem":1228},"Controllers та Actions: серце MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fcontrollers-actions","01.csharp\u002F11.aspnet\u002F11.mvc\u002F03.controllers-actions",{"title":1230,"path":1231,"stem":1232},"Маршрутизація в MVC: Convention vs Attribute Routing","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Frouting-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F04.routing-mvc",{"title":1234,"path":1235,"stem":1236},"Model Binding: від HTTP до C#","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmodel-binding","01.csharp\u002F11.aspnet\u002F11.mvc\u002F05.model-binding",{"title":1238,"path":1239,"stem":1240},"Views, ViewData, ViewBag, TempData і ViewModel","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fviews-viewdata-tempdata","01.csharp\u002F11.aspnet\u002F11.mvc\u002F06.views-viewdata-tempdata",{"title":1242,"path":1243,"stem":1244},"Filters: аспектно-орієнтоване програмування в MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffilters","01.csharp\u002F11.aspnet\u002F11.mvc\u002F07.filters",{"title":1246,"path":1247,"stem":1248},"Areas: структурування великих застосунків","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fareas","01.csharp\u002F11.aspnet\u002F11.mvc\u002F08.areas",{"title":1250,"path":1251,"stem":1252},"View Components: повторювані незалежні блоки UI","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fview-components","01.csharp\u002F11.aspnet\u002F11.mvc\u002F09.view-components",{"title":1254,"path":1255,"stem":1256},"Display та Editor Templates","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fdisplay-editor-templates","01.csharp\u002F11.aspnet\u002F11.mvc\u002F10.display-editor-templates",{"title":1258,"path":1259,"stem":1260},"Валідація: IValidatableObject та FluentValidation","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fvalidation-advanced","01.csharp\u002F11.aspnet\u002F11.mvc\u002F11.validation-advanced",{"title":1262,"path":1263,"stem":1264},"HTMX: інтерактивність через HTML-атрибути","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx","01.csharp\u002F11.aspnet\u002F11.mvc\u002F12.htmx",{"title":1266,"path":1267,"stem":1268},"HTMX у ASP.NET Core MVC: серверна інтеграція","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fajax-htmx-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F13.ajax-htmx-mvc",{"title":1270,"path":1271,"stem":1272},"Практичний проєкт: Каталог товарів з HTMX","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F14.htmx-project",{"title":1274,"path":1275,"stem":1276},"Завантаження та обробка файлів","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffile-upload","01.csharp\u002F11.aspnet\u002F11.mvc\u002F15.file-upload",{"title":1278,"path":1279,"stem":1280},"Глобалізація та Локалізація MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fglobalization-localization","01.csharp\u002F11.aspnet\u002F11.mvc\u002F16.globalization-localization",{"title":1282,"path":1283,"stem":1284},"Підсумковий проєкт: Блог-платформа","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F17.mvc-project",{"title":1286,"path":1287,"stem":1288},"План курсу: ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fplan","01.csharp\u002F11.aspnet\u002F11.mvc\u002Fplan",{"title":1290,"path":1291,"stem":1292,"children":1293,"page":59},"Web Api","\u002Fcsharp\u002Faspnet\u002Fweb-api","01.csharp\u002F11.aspnet\u002F12.web-api",[1294,1298,1302,1306,1310,1314,1318,1322,1326,1330,1334,1338,1342],{"title":1295,"path":1296,"stem":1297},"Від Minimal API до Controller-based API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffrom-minimal-api-to-controllers","01.csharp\u002F11.aspnet\u002F12.web-api\u002F01.from-minimal-api-to-controllers",{"title":1299,"path":1300,"stem":1301},"ControllerBase, ActionResult\u003CT> та Response Types","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontroller-base-actionresult","01.csharp\u002F11.aspnet\u002F12.web-api\u002F02.controller-base-actionresult",{"title":1303,"path":1304,"stem":1305},"Content Negotiation - JSON, XML та власні форматери","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontent-negotiation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F03.content-negotiation",{"title":1307,"path":1308,"stem":1309},"Версіонування API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-versioning","01.csharp\u002F11.aspnet\u002F12.web-api\u002F04.api-versioning",{"title":1311,"path":1312,"stem":1313},"ProblemDetails та структурована обробка помилок","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fproblemdetails-error-handling","01.csharp\u002F11.aspnet\u002F12.web-api\u002F05.problemdetails-error-handling",{"title":1315,"path":1316,"stem":1317},"Фільтри у Web API контексті","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffilters-for-api","01.csharp\u002F11.aspnet\u002F12.web-api\u002F06.filters-for-api",{"title":1319,"path":1320,"stem":1321},"Пагінація, фільтрація та сортування","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fpagination-filtering-sorting","01.csharp\u002F11.aspnet\u002F12.web-api\u002F07.pagination-filtering-sorting",{"title":1323,"path":1324,"stem":1325},"HATEOAS та Resource Expansion","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhateoas-resource-expansion","01.csharp\u002F11.aspnet\u002F12.web-api\u002F08.hateoas-resource-expansion",{"title":1327,"path":1328,"stem":1329},"Гібридна архітектура - Minimal API + Controllers","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fminimal-api-vs-controllers-hybrid","01.csharp\u002F11.aspnet\u002F12.web-api\u002F09.minimal-api-vs-controllers-hybrid",{"title":1331,"path":1332,"stem":1333},"Документація API - Swashbuckle, NSwag та генерація клієнтів","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-documentation-generation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F10.api-documentation-generation",{"title":1335,"path":1336,"stem":1337},"Health Checks та моніторинг API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhealth-checks-monitoring","01.csharp\u002F11.aspnet\u002F12.web-api\u002F11.health-checks-monitoring",{"title":1339,"path":1340,"stem":1341},"Підсумковий проєкт - Production-Ready REST API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fweb-api-project","01.csharp\u002F11.aspnet\u002F12.web-api\u002F12.web-api-project",{"title":1343,"path":1344,"stem":1345},"План курсу: ASP.NET Core Web API (Controllers)","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fplan","01.csharp\u002F11.aspnet\u002F12.web-api\u002Fplan",{"title":1347,"icon":1348,"path":1349,"stem":1350,"children":1351,"page":59},"Моніторинг","i-lucide-activity","\u002Fcsharp\u002Faspnet\u002Fmonitoring","01.csharp\u002F11.aspnet\u002F13.monitoring",[1352,1356,1360],{"title":1353,"path":1354,"stem":1355},"Спостережуваність: від console.log до production-систем","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fobservability-intro","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F01.observability-intro",{"title":1357,"path":1358,"stem":1359},"Health Checks: перший рівень observability","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F02.health-checks",{"title":1361,"path":1362,"stem":1363},"Вбудовані метрики .NET 10 та System.Diagnostics.Metrics","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fdotnet-metrics","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F03.dotnet-metrics",{"title":1365,"icon":1366,"path":1367,"stem":1368,"children":1369,"page":59},"Desktop UI","i-lucide-app-window","\u002Fcsharp\u002Fdesktop-ui","01.csharp\u002F12.desktop-ui",[1370,1374,1378,1382,1386,1390,1394,1398,1402,1406,1410,1414,1418,1422,1426,1430,1434,1438,1442,1446,1450,1454,1458,1462,1466,1470,1474,1478,1482,1486,1490,1494,1498,1502,1506,1510,1514,1518,1522,1526,1530,1534,1538,1542,1546,1550,1554,1558,1562,1566,1570,1574,1578,1582,1586,1590,1594,1598,1602,1606,1610,1614,1618,1622,1626,1630,1634,1638,1642,1646,1650],{"title":1371,"path":1372,"stem":1373},"Що таке десктопна розробка?","\u002Fcsharp\u002Fdesktop-ui\u002Fwhat-is-desktop-dev","01.csharp\u002F12.desktop-ui\u002F01.what-is-desktop-dev",{"title":1375,"path":1376,"stem":1377},"Архітектура WPF — як влаштований графічний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-architecture","01.csharp\u002F12.desktop-ui\u002F02.wpf-architecture",{"title":1379,"path":1380,"stem":1381},"Перший WPF-проєкт — від нуля до вікна","\u002Fcsharp\u002Fdesktop-ui\u002Ffirst-wpf-app","01.csharp\u002F12.desktop-ui\u002F03.first-wpf-app",{"title":1383,"path":1384,"stem":1385},"Перший Avalonia-проєкт: WPF для всіх платформ","\u002Fcsharp\u002Fdesktop-ui\u002F03a.first-avalonia-app","01.csharp\u002F12.desktop-ui\u002F03a.first-avalonia-app",{"title":1387,"path":1388,"stem":1389},"XAML: декларативний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-basics","01.csharp\u002F12.desktop-ui\u002F04.xaml-basics",{"title":1391,"path":1392,"stem":1393},"Fluent UI у WPF — сучасний дизайн Windows 11","\u002Fcsharp\u002Fdesktop-ui\u002F04a.wpf-fluent-ui","01.csharp\u002F12.desktop-ui\u002F04a.wpf-fluent-ui",{"title":1395,"path":1396,"stem":1397},"WPF UI — сучасна бібліотека Fluent контролів","\u002Fcsharp\u002Fdesktop-ui\u002F04b.wpf-ui-library","01.csharp\u002F12.desktop-ui\u002F04b.wpf-ui-library",{"title":1399,"path":1400,"stem":1401},"HandyControl — велика бібліотека UI контролів для WPF","\u002Fcsharp\u002Fdesktop-ui\u002F04c.handycontrol-library","01.csharp\u002F12.desktop-ui\u002F04c.handycontrol-library",{"title":1403,"path":1404,"stem":1405},"Простори імен та ресурси XAML","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-namespaces-resources","01.csharp\u002F12.desktop-ui\u002F05.xaml-namespaces-resources",{"title":1407,"path":1408,"stem":1409},"XAML в Avalonia: ключові відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F05a.avalonia-xaml-differences","01.csharp\u002F12.desktop-ui\u002F05a.avalonia-xaml-differences",{"title":1411,"path":1412,"stem":1413},"Розширення розмітки XAML (Markup Extensions)","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-markup-extensions","01.csharp\u002F12.desktop-ui\u002F06.xaml-markup-extensions",{"title":1415,"path":1416,"stem":1417},"Панелі Layout: StackPanel, WrapPanel, DockPanel","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part1","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part1",{"title":1419,"path":1420,"stem":1421},"Grid, Canvas, UniformGrid","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part2","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part2",{"title":1423,"path":1424,"stem":1425},"Просунуті техніки Layout","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-advanced","01.csharp\u002F12.desktop-ui\u002F08.layout-advanced",{"title":1427,"path":1428,"stem":1429},"Адаптивний Layout та найкращі практики","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-responsive","01.csharp\u002F12.desktop-ui\u002F09.layout-responsive",{"title":1431,"path":1432,"stem":1433},"Layout в Avalonia: відмінності та нові можливості","\u002Fcsharp\u002Fdesktop-ui\u002F09a.layout-avalonia","01.csharp\u002F12.desktop-ui\u002F09a.layout-avalonia",{"title":1435,"path":1436,"stem":1437},"Button, Image, ProgressBar та інші базові контроли","\u002Fcsharp\u002Fdesktop-ui\u002Fbasic-controls","01.csharp\u002F12.desktop-ui\u002F10.basic-controls",{"title":1439,"path":1440,"stem":1441},"Контроли в Avalonia: відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F10a.controls-avalonia","01.csharp\u002F12.desktop-ui\u002F10a.controls-avalonia",{"title":1443,"path":1444,"stem":1445},"Текстові контроли — TextBlock, TextBox, RichTextBox","\u002Fcsharp\u002Fdesktop-ui\u002Ftext-controls","01.csharp\u002F12.desktop-ui\u002F11.text-controls",{"title":1447,"path":1448,"stem":1449},"Контроли вибору — CheckBox, RadioButton, ComboBox, ListBox, DatePicker","\u002Fcsharp\u002Fdesktop-ui\u002Fselection-controls","01.csharp\u002F12.desktop-ui\u002F12.selection-controls",{"title":1451,"path":1452,"stem":1453},"Content Model — GroupBox, Expander, TabControl, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fcontent-controls","01.csharp\u002F12.desktop-ui\u002F13.content-controls",{"title":1455,"path":1456,"stem":1457},"UI\u002FUX принципи десктопних застосунків","\u002Fcsharp\u002Fdesktop-ui\u002F13a.ui-ux-principles","01.csharp\u002F12.desktop-ui\u002F13a.ui-ux-principles",{"title":1459,"path":1460,"stem":1461},"Dependency Properties — Концепція та Value Resolution","\u002Fcsharp\u002Fdesktop-ui\u002Fdependency-properties-part1","01.csharp\u002F12.desktop-ui\u002F14.dependency-properties-part1",{"title":1463,"path":1464,"stem":1465},"Avalonia Property System — StyledProperty та DirectProperty","\u002Fcsharp\u002Fdesktop-ui\u002F14a.avalonia-property-system","01.csharp\u002F12.desktop-ui\u002F14a.avalonia-property-system",{"title":1467,"path":1468,"stem":1469},"Attached Properties — Властивості без меж","\u002Fcsharp\u002Fdesktop-ui\u002Fattached-properties","01.csharp\u002F12.desktop-ui\u002F15.attached-properties",{"title":1471,"path":1472,"stem":1473},"Routed Events — Маршрутизація подій у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Frouted-events","01.csharp\u002F12.desktop-ui\u002F16.routed-events",{"title":1475,"path":1476,"stem":1477},"Data Binding — Від Code-Behind до Декларативності","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part1","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part1",{"title":1479,"path":1480,"stem":1481},"INotifyPropertyChanged — Живе оновлення UI","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part2","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part2",{"title":1483,"path":1484,"stem":1485},"Compiled Bindings в Avalonia — Безпека на етапі компіляції","\u002Fcsharp\u002Fdesktop-ui\u002F17a.avalonia-compiled-bindings","01.csharp\u002F12.desktop-ui\u002F17a.avalonia-compiled-bindings",{"title":1487,"path":1488,"stem":1489},"Просунутий Data Binding — ElementName, RelativeSource, MultiBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-advanced","01.csharp\u002F12.desktop-ui\u002F18.data-binding-advanced",{"title":1491,"path":1492,"stem":1493},"Value Converters — Перетворення типів даних у Data Binding","\u002Fcsharp\u002Fdesktop-ui\u002Fvalue-converters","01.csharp\u002F12.desktop-ui\u002F19.value-converters",{"title":1495,"path":1496,"stem":1497},"Data Templates — Візуалізація об'єктів у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-templates","01.csharp\u002F12.desktop-ui\u002F20.data-templates",{"title":1499,"path":1500,"stem":1501},"Collections Binding Part 1 — ObservableCollection та ItemsControl","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part1","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part1",{"title":1503,"path":1504,"stem":1505},"Collections Binding Part 2 — ICollectionView, Filtering, Sorting та Virtualization","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part2","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part2",{"title":1507,"path":1508,"stem":1509},"MVVM Pattern — Від Spaghetti Code до архітектури","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-pattern","01.csharp\u002F12.desktop-ui\u002F22.mvvm-pattern",{"title":1511,"path":1512,"stem":1513},"ViewModel Implementation — Від BaseViewModel до валідації","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-implementation","01.csharp\u002F12.desktop-ui\u002F23.viewmodel-implementation",{"title":1515,"path":1516,"stem":1517},"Commands — Від event handlers до декларативних команд","\u002Fcsharp\u002Fdesktop-ui\u002Fcommands","01.csharp\u002F12.desktop-ui\u002F24.commands",{"title":1519,"path":1520,"stem":1521},"MVVM Toolkit — MVVM без boilerplate через Source Generators","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-toolkit","01.csharp\u002F12.desktop-ui\u002F25.mvvm-toolkit",{"title":1523,"path":1524,"stem":1525},"Messenger Pattern — Комунікація між ViewModel без прямих посилань","\u002Fcsharp\u002Fdesktop-ui\u002Fmessenger-pattern","01.csharp\u002F12.desktop-ui\u002F26.messenger-pattern",{"title":1527,"path":1528,"stem":1529},"Стилі WPF — CSS для десктопу","\u002Fcsharp\u002Fdesktop-ui\u002Fstyles-basics","01.csharp\u002F12.desktop-ui\u002F27.styles-basics",{"title":1531,"path":1532,"stem":1533},"CSS-like стилі Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F27a.avalonia-css-styling","01.csharp\u002F12.desktop-ui\u002F27a.avalonia-css-styling",{"title":1535,"path":1536,"stem":1537},"Control Templates — Частина 1. Концепція та TemplateBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part1","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part1",{"title":1539,"path":1540,"stem":1541},"Control Templates — Частина 2. Named Parts та ContentPresenter","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part2","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part2",{"title":1543,"path":1544,"stem":1545},"Control Themes в Avalonia — нова ера стилізації","\u002Fcsharp\u002Fdesktop-ui\u002F28a.avalonia-control-themes","01.csharp\u002F12.desktop-ui\u002F28a.avalonia-control-themes",{"title":1547,"path":1548,"stem":1549},"Triggers та Visual State Manager у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Ftriggers-visual-states","01.csharp\u002F12.desktop-ui\u002F29.triggers-visual-states",{"title":1551,"path":1552,"stem":1553},"Pseudo-classes в Avalonia — замість WPF Triggers","\u002Fcsharp\u002Fdesktop-ui\u002F29a.avalonia-pseudo-classes","01.csharp\u002F12.desktop-ui\u002F29a.avalonia-pseudo-classes",{"title":1555,"path":1556,"stem":1557},"Теми та ресурсні словники у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fresources-themes","01.csharp\u002F12.desktop-ui\u002F30.resources-themes",{"title":1559,"path":1560,"stem":1561},"Avalonia Themes — Fluent Design та система тематизації","\u002Fcsharp\u002Fdesktop-ui\u002F30a.avalonia-themes-fluent","01.csharp\u002F12.desktop-ui\u002F30a.avalonia-themes-fluent",{"title":1563,"path":1564,"stem":1565},"Контроли колекцій — глибоке занурення","\u002Fcsharp\u002Fdesktop-ui\u002Fcollection-controls","01.csharp\u002F12.desktop-ui\u002F31.collection-controls",{"title":1567,"path":1568,"stem":1569},"DataGrid — колонки та базове відображення","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part1","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part1",{"title":1571,"path":1572,"stem":1573},"DataGrid — сортування, фільтрація, редагування","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part2","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part2",{"title":1575,"path":1576,"stem":1577},"TreeView та GridView","\u002Fcsharp\u002Fdesktop-ui\u002Ftreeview-listview","01.csharp\u002F12.desktop-ui\u002F33.treeview-listview",{"title":1579,"path":1580,"stem":1581},"Меню, Toolbar, ContextMenu, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fmenus-toolbars","01.csharp\u002F12.desktop-ui\u002F34.menus-toolbars",{"title":1583,"path":1584,"stem":1585},"Навігація та керування вікнами. Частина 1: вікна та сторінки","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part1","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part1",{"title":1587,"path":1588,"stem":1589},"Навігація та керування вікнами. Частина 2: MVVM-навігація","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part2","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part2",{"title":1591,"path":1592,"stem":1593},"Avalonia — Навігація та діалоги","\u002Fcsharp\u002Fdesktop-ui\u002F35a.avalonia-navigation-dialogs","01.csharp\u002F12.desktop-ui\u002F35a.avalonia-navigation-dialogs",{"title":1595,"path":1596,"stem":1597},"Діалоги та File Pickers у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdialogs-file-pickers","01.csharp\u002F12.desktop-ui\u002F36.dialogs-file-pickers",{"title":1599,"path":1600,"stem":1601},"UserControl: компонентний підхід у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fuser-controls","01.csharp\u002F12.desktop-ui\u002F37.user-controls",{"title":1603,"path":1604,"stem":1605},"Custom Controls: Lookless Controls у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fcustom-controls","01.csharp\u002F12.desktop-ui\u002F38.custom-controls",{"title":1607,"path":1608,"stem":1609},"Avalonia TemplatedControl — Lookless Controls","\u002Fcsharp\u002Fdesktop-ui\u002F38a.avalonia-templated-controls","01.csharp\u002F12.desktop-ui\u002F38a.avalonia-templated-controls",{"title":1611,"path":1612,"stem":1613},"Анімації у WPF: Storyboard та Easing Functions","\u002Fcsharp\u002Fdesktop-ui\u002Fanimations-transitions","01.csharp\u002F12.desktop-ui\u002F39.animations-transitions",{"title":1615,"path":1616,"stem":1617},"Анімації в Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F39a.avalonia-animations","01.csharp\u002F12.desktop-ui\u002F39a.avalonia-animations",{"title":1619,"path":1620,"stem":1621},"2D Графіка та Мультимедіа у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fmedia-graphics","01.csharp\u002F12.desktop-ui\u002F40.media-graphics",{"title":1623,"path":1624,"stem":1625},"Dependency Injection у WPF та Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Fdi-integration","01.csharp\u002F12.desktop-ui\u002F41.di-integration",{"title":1627,"path":1628,"stem":1629},"SQLite та EF Core у десктопних додатках","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part1","01.csharp\u002F12.desktop-ui\u002F42.data-persistence-part1",{"title":1631,"path":1632,"stem":1633},"Repository Pattern та Unit of Work","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part2","01.csharp\u002F12.desktop-ui\u002F43.data-persistence-part2",{"title":1635,"path":1636,"stem":1637},"Тестування ViewModels","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-testing","01.csharp\u002F12.desktop-ui\u002F44.viewmodel-testing",{"title":1639,"path":1640,"stem":1641},"Avalonia Headless Testing — тестування UI без вікон","\u002Fcsharp\u002Fdesktop-ui\u002F44a.avalonia-headless-testing","01.csharp\u002F12.desktop-ui\u002F44a.avalonia-headless-testing",{"title":1643,"path":1644,"stem":1645},"Кросплатформна розробка з Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-cross-platform","01.csharp\u002F12.desktop-ui\u002F45.avalonia-cross-platform",{"title":1647,"path":1648,"stem":1649},"Пакування та розгортання Avalonia додатків","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F46.avalonia-packaging-deployment",{"title":1651,"path":1652,"stem":1653},"Розгортання WPF застосунків","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F47.wpf-packaging-deployment",{"title":1655,"icon":658,"path":1656,"stem":1657,"children":1658,"page":59},"Network Programming","\u002Fcsharp\u002Fnetwork-programming","01.csharp\u002F13.network-programming",[1659,1663,1667,1671,1675,1679,1683,1687,1691,1695,1699],{"title":1660,"path":1661,"stem":1662},"Основи комп'ютерних мереж","\u002Fcsharp\u002Fnetwork-programming\u002Ffoundations","01.csharp\u002F13.network-programming\u002F01.foundations",{"title":1664,"path":1665,"stem":1666},"Модель OSI та стек TCP\u002FIP","\u002Fcsharp\u002Fnetwork-programming\u002Fosi-model","01.csharp\u002F13.network-programming\u002F02.osi-model",{"title":1668,"path":1669,"stem":1670},"IP-протокол та адресація","\u002Fcsharp\u002Fnetwork-programming\u002Fip-addressing","01.csharp\u002F13.network-programming\u002F03.ip-addressing",{"title":1672,"path":1673,"stem":1674},"UDP — протокол без з'єднання","\u002Fcsharp\u002Fnetwork-programming\u002Fudp","01.csharp\u002F13.network-programming\u002F05.udp",{"title":1676,"path":1677,"stem":1678},"UDP Broadcast та Multicast","\u002Fcsharp\u002Fnetwork-programming\u002Fudp-broadcast-multicast","01.csharp\u002F13.network-programming\u002F06.udp-broadcast-multicast",{"title":1680,"path":1681,"stem":1682},"HTTP — протокол вебу","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-fundamentals","01.csharp\u002F13.network-programming\u002F07.http-fundamentals",{"title":1684,"path":1685,"stem":1686},"HttpListener — вбудований HTTP-сервер .NET","\u002Fcsharp\u002Fnetwork-programming\u002F07a.http-listener","01.csharp\u002F13.network-programming\u002F07a.http-listener",{"title":1688,"path":1689,"stem":1690},"HTTP Advanced — cookies, аутентифікація та HTTPS","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-advanced","01.csharp\u002F13.network-programming\u002F08.http-advanced",{"title":1692,"path":1693,"stem":1694},"SMTP та протоколи електронної пошти","\u002Fcsharp\u002Fnetwork-programming\u002Fsmtp","01.csharp\u002F13.network-programming\u002F09.smtp",{"title":1696,"path":1697,"stem":1698},"WebSocket — повнодуплексний протокол реального часу","\u002Fcsharp\u002Fnetwork-programming\u002Fwebsockets","01.csharp\u002F13.network-programming\u002F10.websockets",{"title":1700,"path":1701,"stem":1702},"TLS\u002FSSL — криптографічний захист мережевих з'єднань","\u002Fcsharp\u002Fnetwork-programming\u002Ftls-ssl","01.csharp\u002F13.network-programming\u002F11.tls-ssl",{"title":1704,"path":1705,"stem":1706},"C# & .NET: The Ultimate Roadmap","\u002Fcsharp\u002Froadmap","01.csharp\u002Froadmap",{"title":1708,"icon":1709,"path":1710,"stem":1711,"children":1712,"page":59},"C++","i-devicon-cplusplus","\u002Fcpp","02.cpp",[1713,1717,1721,1725,1729,1733,1737,1741,1745,1748,1752,1756,1760,1764,1768,1772,1776,1780,1784,1788,1792,1796,1800,1804,1808,1812,1816,1820,1824,1828,1832,1836,1840,1844,1848,1852,1856,1860,1864,1868,1872,1876,1880,1884,1888,1892,1896,1900,1904,1908,1912,1916,1920,1924,1928,1932,1936,1940,1944,1948,1952,1956,1960,1964,1968,1972,1976,1980,1984,1988,1992,1996,2000,2004,2008,2012,2016,2020,2024,2028,2032,2036,2040,2044,2048,2052,2056,2060,2064,2068,2072,2076,2080],{"title":1714,"path":1715,"stem":1716},"Вступ у програмування та алгоритми","\u002Fcpp\u002Fintro-algorithms","02.cpp\u002F01.intro-algorithms",{"title":1718,"path":1719,"stem":1720},"Code Style: угоди про оформлення коду","\u002Fcpp\u002Fcode-style","02.cpp\u002F02.code-style",{"title":1722,"path":1723,"stem":1724},"Середовище розробки та перший проєкт","\u002Fcpp\u002Fide-setup","02.cpp\u002F03.ide-setup",{"title":1726,"path":1727,"stem":1728},"Вивід даних на екран","\u002Fcpp\u002Fdata-output","02.cpp\u002F04.data-output",{"title":1730,"path":1731,"stem":1732},"Типи даних, змінні та константи","\u002Fcpp\u002Fdata-types-variables","02.cpp\u002F05.data-types-variables",{"title":1734,"path":1735,"stem":1736},"Ввід даних з клавіатури","\u002Fcpp\u002Fdata-input","02.cpp\u002F06.data-input",{"title":1738,"path":1739,"stem":1740},"Оператори, перетворення типів та логічні операції","\u002Fcpp\u002Foperators-type-conversion","02.cpp\u002F07.operators-type-conversion",{"title":1742,"path":1743,"stem":1744},"Цикли","\u002Fcpp\u002Floops","02.cpp\u002F08.loops",{"title":32,"path":1746,"stem":1747},"\u002Fcpp\u002Farrays","02.cpp\u002F09.arrays",{"title":1749,"path":1750,"stem":1751},"Алгоритми сортування та аналіз складності","\u002Fcpp\u002Fsorting","02.cpp\u002F10.sorting",{"title":1753,"path":1754,"stem":1755},"Алгоритми пошуку","\u002Fcpp\u002Fsearching","02.cpp\u002F11.searching",{"title":1757,"path":1758,"stem":1759},"Функції: основи","\u002Fcpp\u002Ffunctions-basics","02.cpp\u002F12.functions-basics",{"title":1761,"path":1762,"stem":1763},"Функції: прототипи, область видимості та додаткові можливості","\u002Fcpp\u002Ffunctions-scope","02.cpp\u002F13.functions-scope",{"title":1765,"path":1766,"stem":1767},"Функції: перевантаження та шаблони","\u002Fcpp\u002Ffunctions-overloading-templates","02.cpp\u002F14.functions-overloading-templates",{"title":1769,"path":1770,"stem":1771},"Вказівники: основи","\u002Fcpp\u002Fpointers-basics","02.cpp\u002F15.pointers-basics",{"title":1773,"path":1774,"stem":1775},"Посилання (References)","\u002Fcpp\u002Freferences","02.cpp\u002F16.references",{"title":1777,"path":1778,"stem":1779},"Вказівники, const і масиви","\u002Fcpp\u002Fpointers-const-arrays","02.cpp\u002F17.pointers-const-arrays",{"title":1781,"path":1782,"stem":1783},"Адресна арифметика","\u002Fcpp\u002Fpointer-arithmetic","02.cpp\u002F18.pointer-arithmetic",{"title":1785,"path":1786,"stem":1787},"Динамічна пам'ять","\u002Fcpp\u002Fdynamic-memory","02.cpp\u002F19.dynamic-memory",{"title":1789,"path":1790,"stem":1791},"Вказівники типу void","\u002Fcpp\u002Fvoid-pointers","02.cpp\u002F20.void-pointers",{"title":1793,"path":1794,"stem":1795},"Вказівники на вказівники","\u002Fcpp\u002Fpointers-to-pointers","02.cpp\u002F21.pointers-to-pointers",{"title":1797,"path":1798,"stem":1799},"Оператор доступу до членів через вказівник (->)","\u002Fcpp\u002Fmember-access-operator","02.cpp\u002F22.member-access-operator",{"title":1801,"path":1802,"stem":1803},"Цикл for-each (Range-based for)","\u002Fcpp\u002Fforeach-loop","02.cpp\u002F23.foreach-loop",{"title":1805,"path":1806,"stem":1807},"Вказівники на функції","\u002Fcpp\u002Ffunction-pointers","02.cpp\u002F24.function-pointers",{"title":1809,"path":1810,"stem":1811},"Лямбда-вирази","\u002Fcpp\u002Flambdas","02.cpp\u002F25.lambdas",{"title":1813,"path":1814,"stem":1815},"Лямбда-захоплення","\u002Fcpp\u002Flambda-captures","02.cpp\u002F26.lambda-captures",{"title":1817,"path":1818,"stem":1819},"Еліпсис","\u002Fcpp\u002Fellipsis","02.cpp\u002F27.ellipsis",{"title":1821,"path":1822,"stem":1823},"Безпечні альтернативи еліпсису","\u002Fcpp\u002F27a.ellipsis","02.cpp\u002F27a.ellipsis",{"title":1825,"path":1826,"stem":1827},"Аргументи командного рядка","\u002Fcpp\u002Fcommand-line-arguments","02.cpp\u002F28.command-line-arguments",{"title":1829,"path":1830,"stem":1831},"Перерахування (enum)","\u002Fcpp\u002Fenum","02.cpp\u002F29.enum",{"title":1833,"path":1834,"stem":1835},"Класи-перерахування (enum class)","\u002Fcpp\u002Fenum-class","02.cpp\u002F30.enum-class",{"title":1837,"path":1838,"stem":1839},"Псевдоніми типів (typedef і using)","\u002Fcpp\u002Ftype-aliases","02.cpp\u002F31.type-aliases",{"title":1841,"path":1842,"stem":1843},"Системи числення та двійкова арифметика","\u002Fcpp\u002Fnumber-systems","02.cpp\u002F32.number-systems",{"title":1845,"path":1846,"stem":1847},"Структури (struct): агрегування даних","\u002Fcpp\u002Fstruct","02.cpp\u002F33.struct",{"title":1849,"path":1850,"stem":1851},"Структури у функціях","\u002Fcpp\u002Fstruct-functions","02.cpp\u002F34.struct-functions",{"title":1853,"path":1854,"stem":1855},"Масиви структур і вкладені структури","\u002Fcpp\u002Fstruct-arrays","02.cpp\u002F35.struct-arrays",{"title":1857,"path":1858,"stem":1859},"Патерни struct та межі застосування","\u002Fcpp\u002Fstruct-patterns","02.cpp\u002F36.struct-patterns",{"title":1861,"path":1862,"stem":1863},"Символи та таблиця ASCII","\u002Fcpp\u002Fascii-characters","02.cpp\u002F37.ascii-characters",{"title":1865,"path":1866,"stem":1867},"Unicode та кодування UTF","\u002Fcpp\u002Funicode-utf","02.cpp\u002F38.unicode-utf",{"title":1869,"path":1870,"stem":1871},"C-style рядки","\u002Fcpp\u002Fc-strings","02.cpp\u002F39.c-strings",{"title":1873,"path":1874,"stem":1875},"Вступ до std::string","\u002Fcpp\u002Fstd-string-intro","02.cpp\u002F40.std-string-intro",{"title":1877,"path":1878,"stem":1879},"Довжина, ємність та доступ до символів std::string","\u002Fcpp\u002Fstd-string-capacity-access","02.cpp\u002F41.std-string-capacity-access",{"title":1881,"path":1882,"stem":1883},"Модифікація std::string: присвоювання, додавання, вставка, видалення та заміна","\u002Fcpp\u002Fstd-string-modification","02.cpp\u002F42.std-string-modification",{"title":1885,"path":1886,"stem":1887},"Пошук у std::string: find, npos та практичні патерни","\u002Fcpp\u002Fstd-string-search","02.cpp\u002F43.std-string-search",{"title":1889,"path":1890,"stem":1891},"std::string_view: невласницький погляд на рядок без копіювання","\u002Fcpp\u002Fstd-string-view","02.cpp\u002F44.std-string-view",{"title":1893,"path":1894,"stem":1895},"Об'єднання (union): один блок пам'яті, кілька інтерпретацій","\u002Fcpp\u002Funion","02.cpp\u002F45.union",{"title":1897,"path":1898,"stem":1899},"Організація коду: файли, препроцесор, простори імен","\u002Fcpp\u002Fmultifile-programs","02.cpp\u002F46.multifile-programs",{"title":1901,"path":1902,"stem":1903},"Робота з файлами: C-стиль (stdio.h)","\u002Fcpp\u002Fc-style-files","02.cpp\u002F47.c-style-files",{"title":1905,"path":1906,"stem":1907},"Робота з файлами: C++-стиль (fstream)","\u002Fcpp\u002Fcpp-style-files","02.cpp\u002F48.cpp-style-files",{"title":1909,"path":1910,"stem":1911},"Введення в ООП: від процедур до об'єктів","\u002Fcpp\u002Foop-intro","02.cpp\u002F49.oop-intro",{"title":1913,"path":1914,"stem":1915},"Класи, об'єкти та методи","\u002Fcpp\u002Fclasses-objects-methods","02.cpp\u002F50.classes-objects-methods",{"title":1917,"path":1918,"stem":1919},"Специфікатори доступу та інкапсуляція","\u002Fcpp\u002Faccess-specifiers-encapsulation","02.cpp\u002F51.access-specifiers-encapsulation",{"title":1921,"path":1922,"stem":1923},"Конструктори: гарантована ініціалізація об'єктів","\u002Fcpp\u002Fconstructors","02.cpp\u002F52.constructors",{"title":1925,"path":1926,"stem":1927},"Списки ініціалізації та делегуючі конструктори","\u002Fcpp\u002Finit-lists-delegating","02.cpp\u002F53.init-lists-delegating",{"title":1929,"path":1930,"stem":1931},"Деструктори та ідіома RAII","\u002Fcpp\u002Fdestructors-raii","02.cpp\u002F54.destructors-raii",{"title":1933,"path":1934,"stem":1935},"Прихований покажчик this","\u002Fcpp\u002Fthis-pointer","02.cpp\u002F55.this-pointer",{"title":1937,"path":1938,"stem":1939},"Розподіл класу на заголовковий файл та файл реалізації","\u002Fcpp\u002Fclass-header-source","02.cpp\u002F56.class-header-source",{"title":1941,"path":1942,"stem":1943},"Класи та const","\u002Fcpp\u002Fconst-classes","02.cpp\u002F57.const-classes",{"title":1945,"path":1946,"stem":1947},"Статичні члени класу","\u002Fcpp\u002Fstatic-members","02.cpp\u002F58.static-members",{"title":1949,"path":1950,"stem":1951},"Конструктор копіювання та запобігання копіюванню","\u002Fcpp\u002Fcopy-constructor","02.cpp\u002F59.copy-constructor",{"title":1953,"path":1954,"stem":1955},"Дружні функції та класи","\u002Fcpp\u002Ffriend-functions-classes","02.cpp\u002F60.friend-functions-classes",{"title":1957,"path":1958,"stem":1959},"Анонімні об'єкти та вкладені типи","\u002Fcpp\u002Fanonymous-objects-nested-types","02.cpp\u002F61.anonymous-objects-nested-types",{"title":1961,"path":1962,"stem":1963},"Вимірювання часу виконання: RAII-таймер","\u002Fcpp\u002Ftiming-raii-timer","02.cpp\u002F62.timing-raii-timer",{"title":1965,"path":1966,"stem":1967},"Перевантаження операторів: основи та арифметика","\u002Fcpp\u002Foperator-overloading-basics","02.cpp\u002F63.operator-overloading-basics",{"title":1969,"path":1970,"stem":1971},"Перевантаження операторів: методи класу та спеціальні оператори","\u002Fcpp\u002Foperator-overloading-methods","02.cpp\u002F64.operator-overloading-methods",{"title":1973,"path":1974,"stem":1975},"Приведення типів, explicit та delete","\u002Fcpp\u002Ftypecast-explicit-delete","02.cpp\u002F65.typecast-explicit-delete",{"title":1977,"path":1978,"stem":1979},"Глибоке копіювання та оператор присвоювання","\u002Fcpp\u002Fdeep-copy-assignment","02.cpp\u002F66.deep-copy-assignment",{"title":1981,"path":1982,"stem":1983},"Зв'язки між об'єктами: композиція та агрегація","\u002Fcpp\u002Fcomposition-aggregation","02.cpp\u002F67.composition-aggregation",{"title":1985,"path":1986,"stem":1987},"Асоціація та залежність між об","\u002Fcpp\u002Fassociation-dependency","02.cpp\u002F68.association-dependency",{"title":1989,"path":1990,"stem":1991},"Контейнерні класи та `std::initializer_list`","\u002Fcpp\u002Fcontainer-classes-initializer-list","02.cpp\u002F69.container-classes-initializer-list",{"title":1993,"path":1994,"stem":1995},"Вступ до наслідування: базові поняття та відношення «is-a»","\u002Fcpp\u002Finheritance-intro","02.cpp\u002F70.inheritance-intro",{"title":1997,"path":1998,"stem":1999},"Конструктори, деструктори та порядок ініціалізації в ієрархіях","\u002Fcpp\u002Finheritance-constructors-destructors","02.cpp\u002F71.inheritance-constructors-destructors",{"title":2001,"path":2002,"stem":2003},"Специфікатор `protected` та види наслідування","\u002Fcpp\u002Finheritance-access-specifiers","02.cpp\u002F72.inheritance-access-specifiers",{"title":2005,"path":2006,"stem":2007},"Перевизначення методів та приховування імен","\u002Fcpp\u002Fmethod-overriding-hiding","02.cpp\u002F73.method-overriding-hiding",{"title":2009,"path":2010,"stem":2011},"Множинне наслідування та проблема ромба","\u002Fcpp\u002Fmultiple-inheritance-diamond","02.cpp\u002F74.multiple-inheritance-diamond",{"title":2013,"path":2014,"stem":2015},"Вказівники на базовий клас та віртуальні функції","\u002Fcpp\u002Fvirtual-functions-polymorphism","02.cpp\u002F75.virtual-functions-polymorphism",{"title":2017,"path":2018,"stem":2019},"Специфікатори override, final та віртуальні деструктори","\u002Fcpp\u002Foverride-final-virtual-destructors","02.cpp\u002F76.override-final-virtual-destructors",{"title":2021,"path":2022,"stem":2023},"Внутрішні механізми поліморфізму: vtable, vptr та зв'язування","\u002Fcpp\u002Fvirtual-table-binding","02.cpp\u002F77.virtual-table-binding",{"title":2025,"path":2026,"stem":2027},"Абстрактні класи та чисті віртуальні функції","\u002Fcpp\u002Fabstract-classes-interfaces","02.cpp\u002F78.abstract-classes-interfaces",{"title":2029,"path":2030,"stem":2031},"Зрізка об'єктів, віртуальне наслідування та поліморфний вивід","\u002Fcpp\u002Fslicing-virtual-base-io","02.cpp\u002F79.slicing-virtual-base-io",{"title":2033,"path":2034,"stem":2035},"Динамічне приведення типів (`dynamic_cast`) та RTTI","\u002Fcpp\u002Fdynamic-cast-rtti","02.cpp\u002F80.dynamic-cast-rtti",{"title":2037,"path":2038,"stem":2039},"Шаблони функцій: узагальнене програмування","\u002Fcpp\u002Ffunction-templates","02.cpp\u002F81.function-templates",{"title":2041,"path":2042,"stem":2043},"Шаблони класів та NTTP-параметри","\u002Fcpp\u002Fclass-templates-nttp","02.cpp\u002F82.class-templates-nttp",{"title":2045,"path":2046,"stem":2047},"Повна (явна) спеціалізація шаблонів","\u002Fcpp\u002Ffull-template-specialization","02.cpp\u002F83.full-template-specialization",{"title":2049,"path":2050,"stem":2051},"Часткова спеціалізація шаблонів класів","\u002Fcpp\u002Fpartial-template-specialization","02.cpp\u002F84.partial-template-specialization",{"title":2053,"path":2054,"stem":2055},"Механізм винятків: try, catch, throw та розкручування стеку","\u002Fcpp\u002Fexceptions-basics","02.cpp\u002F85.exceptions-basics",{"title":2057,"path":2058,"stem":2059},"Ієрархія std::exception та власні класи винятків","\u002Fcpp\u002Fexception-hierarchy-custom","02.cpp\u002F86.exception-hierarchy-custom",{"title":2061,"path":2062,"stem":2063},"Повторне генерування винятків та функціональний try-блок","\u002Fcpp\u002Frethrow-function-try","02.cpp\u002F87.rethrow-function-try",{"title":2065,"path":2066,"stem":2067},"Безпека винятків, noexcept та деструктори","\u002Fcpp\u002Fsafety-noexcept","02.cpp\u002F88.safety-noexcept",{"title":2069,"path":2070,"stem":2071},"Стаття 89 — Власні структури даних: стек та черга","\u002Fcpp\u002Fcustom-stack-queue","02.cpp\u002F89.custom-stack-queue",{"title":2073,"path":2074,"stem":2075},"Стаття 90 — Власні структури даних: однозв'язаний список","\u002Fcpp\u002Flinked-list","02.cpp\u002F90.linked-list",{"title":2077,"path":2078,"stem":2079},"Стаття 91 — Власні структури даних: бінарне дерево пошуку","\u002Fcpp\u002Fbinary-search-tree","02.cpp\u002F91.binary-search-tree",{"title":2081,"path":2082,"stem":2083},"Стаття 92 — Власні структури даних: хеш-таблиця","\u002Fcpp\u002Fhash-table","02.cpp\u002F92.hash-table",{"title":2085,"icon":2086,"path":2087,"stem":2088,"children":2089,"page":59},"JavaScript","i-devicon-javascript","\u002Fjavascript","03.javascript",[2090,2116,2170,2192,2496,2534,2552],{"title":2091,"icon":2092,"path":2093,"stem":2094,"children":2095,"page":59},"Events","i-lucide-mouse-pointer-click","\u002Fjavascript\u002Fevents","03.javascript\u002F01.events",[2096,2100,2104,2108,2112],{"title":2097,"path":2098,"stem":2099},"Вступ до подій браузера","\u002Fjavascript\u002Fevents\u002Fintro","03.javascript\u002F01.events\u002F01.intro",{"title":2101,"path":2102,"stem":2103},"Бульбашковий механізм (Bubbling) та занурення (Capturing)","\u002Fjavascript\u002Fevents\u002Fbubbling-capturing","03.javascript\u002F01.events\u002F02.bubbling-capturing",{"title":2105,"path":2106,"stem":2107},"Делегування подій (Event Delegation)","\u002Fjavascript\u002Fevents\u002Fdelegate-events","03.javascript\u002F01.events\u002F03.delegate-events",{"title":2109,"path":2110,"stem":2111},"Типові дії браузера та preventDefault()","\u002Fjavascript\u002Fevents\u002Fprevent-default","03.javascript\u002F01.events\u002F04.prevent-default",{"title":2113,"path":2114,"stem":2115},"Запуск користувацьких подій (Custom Events)","\u002Fjavascript\u002Fevents\u002Fcustom-events","03.javascript\u002F01.events\u002F05.custom-events",{"title":2117,"icon":2118,"path":2119,"stem":2120,"children":2121,"page":59},"Network","i-lucide-globe","\u002Fjavascript\u002Fnetwork","03.javascript\u002F02.network",[2122,2126,2130,2134,2138,2142,2146,2150,2154,2158,2162,2166],{"title":2123,"path":2124,"stem":2125},"Fetch API - Сучасний підхід до HTTP-запитів","\u002Fjavascript\u002Fnetwork\u002F01-fetch-api","03.javascript\u002F02.network\u002F01-fetch-api",{"title":2127,"path":2128,"stem":2129},"FormData - Робота з формами та файлами","\u002Fjavascript\u002Fnetwork\u002F02-formdata","03.javascript\u002F02.network\u002F02-formdata",{"title":2131,"path":2132,"stem":2133},"Відстеження прогресу завантаження","\u002Fjavascript\u002Fnetwork\u002F03-download-progress","03.javascript\u002F02.network\u002F03-download-progress",{"title":2135,"path":2136,"stem":2137},"Переривання fetch-запитів","\u002Fjavascript\u002Fnetwork\u002F04-abort-requests","03.javascript\u002F02.network\u002F04-abort-requests",{"title":2139,"path":2140,"stem":2141},"CORS - Запити між різними джерелами","\u002Fjavascript\u002Fnetwork\u002F05-cors","03.javascript\u002F02.network\u002F05-cors",{"title":2143,"path":2144,"stem":2145},"Fetch API - Повний довідник опцій","\u002Fjavascript\u002Fnetwork\u002F06-fetch-options","03.javascript\u002F02.network\u002F06-fetch-options",{"title":2147,"path":2148,"stem":2149},"URL Objects - Робота з посиланнями","\u002Fjavascript\u002Fnetwork\u002F07-url-objects","03.javascript\u002F02.network\u002F07-url-objects",{"title":2151,"path":2152,"stem":2153},"XMLHttpRequest - AJAX та низькорівневі запити","\u002Fjavascript\u002Fnetwork\u002F08-xmlhttprequest","03.javascript\u002F02.network\u002F08-xmlhttprequest",{"title":2155,"path":2156,"stem":2157},"Відновлюване завантаження файлів","\u002Fjavascript\u002Fnetwork\u002F09-resumable-upload","03.javascript\u002F02.network\u002F09-resumable-upload",{"title":2159,"path":2160,"stem":2161},"Cookies, document.cookie та світ після \"Cookiepocalypse\"","\u002Fjavascript\u002Fnetwork\u002F10-cookies","03.javascript\u002F02.network\u002F10-cookies",{"title":2163,"path":2164,"stem":2165},"js-cookie: Керування Cookies без Болю","\u002Fjavascript\u002Fnetwork\u002F11-js-cookie","03.javascript\u002F02.network\u002F11-js-cookie",{"title":2167,"path":2168,"stem":2169},"Axios: Потужний HTTP-клієнт для JavaScript","\u002Fjavascript\u002Fnetwork\u002F12-axios","03.javascript\u002F02.network\u002F12-axios",{"title":2171,"icon":2172,"path":2173,"stem":2174,"children":2175,"page":59},"Bom","i-lucide-monitor","\u002Fjavascript\u002Fbom","03.javascript\u002F03.bom",[2176,2180,2184,2188],{"title":2177,"path":2178,"stem":2179},"LocalStorage, SessionStorage та patterns збереження даних","\u002Fjavascript\u002Fbom\u002F01-localstorage","03.javascript\u002F03.bom\u002F01-localstorage",{"title":2181,"path":2182,"stem":2183},"Location Object - Керування адресою сторінки","\u002Fjavascript\u002Fbom\u002F02-location-object","03.javascript\u002F03.bom\u002F02-location-object",{"title":2185,"path":2186,"stem":2187},"History API - Керування історією браузера","\u002Fjavascript\u002Fbom\u002F03-history-api","03.javascript\u002F03.bom\u002F03-history-api",{"title":2189,"path":2190,"stem":2191},"Navigator Object - Ідентифікація та Можливості Пристрою","\u002Fjavascript\u002Fbom\u002F04-navigator-object","03.javascript\u002F03.bom\u002F04-navigator-object",{"title":2193,"icon":2194,"path":2195,"stem":2196,"children":2197},"React","i-devicon-react","\u002Fjavascript\u002Freact","03.javascript\u002F04.react\u002Findex",[2198,2199,2203,2207,2211,2215,2278,2313,2465],{"title":2193,"path":2195,"stem":2196},{"title":2200,"path":2201,"stem":2202},"Робота з Формами в React","\u002Fjavascript\u002Freact\u002Freact-forms","03.javascript\u002F04.react\u002F01.react-forms",{"title":2204,"path":2205,"stem":2206},"React Hook Form: Професійна Робота з Формами","\u002Fjavascript\u002Freact\u002Freact-hook-form","03.javascript\u002F04.react\u002F02.react-hook-form",{"title":2208,"path":2209,"stem":2210},"React Hook Form: Глибоке Розуміння Архітектури та Оптимізації","\u002Fjavascript\u002Freact\u002Freact-hook-form-new","03.javascript\u002F04.react\u002F02.react-hook-form-new",{"title":2212,"path":2213,"stem":2214},"Axios та React: Професійна Архітектура Запитів","\u002Fjavascript\u002Freact\u002Fdata-fetching-axios","03.javascript\u002F04.react\u002F03.data-fetching-axios",{"title":2216,"icon":132,"path":2217,"stem":2218,"children":2219},"Tanstack Query","\u002Fjavascript\u002Freact\u002Ftanstack-query","03.javascript\u002F04.react\u002F04.tanstack-query\u002Findex",[2220,2222,2226,2230,2234,2238,2242,2246,2250,2254,2258,2262,2266,2270,2274],{"title":2221,"path":2217,"stem":2218},"TanStack Query: Майстерність Керування Станом Сервера",{"title":2223,"path":2224,"stem":2225},"Парадигма Server State: Чому useEffect недостатньо","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-state-paradigm","03.javascript\u002F04.react\u002F04.tanstack-query\u002F01.server-state-paradigm",{"title":2227,"path":2228,"stem":2229},"Встановлення та Налаштування: Фундамент","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Finstallation-and-devtools","03.javascript\u002F04.react\u002F04.tanstack-query\u002F02.installation-and-devtools",{"title":2231,"path":2232,"stem":2233},"Основи Запитів та Магія Ключів","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fquery-basics-and-keys","03.javascript\u002F04.react\u002F04.tanstack-query\u002F03.query-basics-and-keys",{"title":2235,"path":2236,"stem":2237},"Синхронізація Даних: Життєвий Цикл Запиту","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fdata-synchronization","03.javascript\u002F04.react\u002F04.tanstack-query\u002F04.data-synchronization",{"title":2239,"path":2240,"stem":2241},"Мутації та Інвалідація: Зміна Даних","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fmutations-and-invalidation","03.javascript\u002F04.react\u002F04.tanstack-query\u002F05.mutations-and-invalidation",{"title":2243,"path":2244,"stem":2245},"Оптимістичні Оновлення: Швидше за Світло","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Foptimistic-updates","03.javascript\u002F04.react\u002F04.tanstack-query\u002F06.optimistic-updates",{"title":2247,"path":2248,"stem":2249},"Пагінація та Infinite Scroll","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fpagination-and-load-more","03.javascript\u002F04.react\u002F04.tanstack-query\u002F07.pagination-and-load-more",{"title":2251,"path":2252,"stem":2253},"Просунуті Патерни та Оптимізація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F04.tanstack-query\u002F08.advanced-patterns",{"title":2255,"path":2256,"stem":2257},"Архітектура та Best Practices","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Farchitecture-and-best-practices","03.javascript\u002F04.react\u002F04.tanstack-query\u002F09.architecture-and-best-practices",{"title":2259,"path":2260,"stem":2261},"Server-Side Rendering (SSR) та Гідратація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-side-rendering","03.javascript\u002F04.react\u002F04.tanstack-query\u002F10.server-side-rendering",{"title":2263,"path":2264,"stem":2265},"Стратегії Тестування","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Ftesting-strategies","03.javascript\u002F04.react\u002F04.tanstack-query\u002F11.testing-strategies",{"title":2267,"path":2268,"stem":2269},"Аутентифікація та Обробка Помилок","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fauthentication-and-errors","03.javascript\u002F04.react\u002F04.tanstack-query\u002F12.authentication-and-errors",{"title":2271,"path":2272,"stem":2273},"React Suspense та Майбутнє","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Freact-suspense","03.javascript\u002F04.react\u002F04.tanstack-query\u002F13.react-suspense",{"title":2275,"path":2276,"stem":2277},"Глибоке Занурення в Продуктивність","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fperformance-deep-dive","03.javascript\u002F04.react\u002F04.tanstack-query\u002F14.performance-deep-dive",{"title":2279,"icon":2194,"path":2280,"stem":2281,"children":2282},"React Router","\u002Fjavascript\u002Freact\u002Freact-router","03.javascript\u002F04.react\u002F05.react-router\u002Findex",[2283,2285,2289,2293,2297,2301,2305,2309],{"title":2284,"path":2280,"stem":2281},"React Router: Навігаційна система сучасного вебу",{"title":2286,"path":2287,"stem":2288},"Налаштування та Базовий Роутинг","\u002Fjavascript\u002Freact\u002Freact-router\u002Fsetup-and-basic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F01.setup-and-basic-routing",{"title":2290,"path":2291,"stem":2292},"Динамічна Навігація","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnavigation-and-links","03.javascript\u002F04.react\u002F05.react-router\u002F02.navigation-and-links",{"title":2294,"path":2295,"stem":2296},"Вкладені Маршрути та Макети","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnested-routes-and-layouts","03.javascript\u002F04.react\u002F05.react-router\u002F03.nested-routes-and-layouts",{"title":2298,"path":2299,"stem":2300},"Динамічні Маршрути та Параметри","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdynamic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F04.dynamic-routing",{"title":2302,"path":2303,"stem":2304},"Data APIs: Loaders та Actions","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdata-loading","03.javascript\u002F04.react\u002F05.react-router\u002F05.data-loading",{"title":2306,"path":2307,"stem":2308},"Просунуті Патерни","\u002Fjavascript\u002Freact\u002Freact-router\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F05.react-router\u002F06.advanced-patterns",{"title":2310,"path":2311,"stem":2312},"Legacy Routing: Компонентний підхід","\u002Fjavascript\u002Freact\u002Freact-router\u002Flegacy-routing","03.javascript\u002F04.react\u002F05.react-router\u002F07.legacy-routing",{"title":2314,"icon":132,"path":2315,"stem":2316,"children":2317},"Redux","\u002Fjavascript\u002Freact\u002Fredux","03.javascript\u002F04.react\u002F06.redux\u002Findex",[2318,2320,2336,2365,2374,2395,2411,2440],{"title":2319,"path":2315,"stem":2316},"Redux: Еволюція управління станом",{"title":14,"icon":15,"path":2321,"stem":2322,"children":2323,"page":59},"\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals",[2324,2328,2332],{"title":2325,"path":2326,"stem":2327},"Вступ до State Management","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fintro-state-management","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F01.intro-state-management",{"title":2329,"path":2330,"stem":2331},"Філософія Redux та Три Принципи","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fredux-philosophy","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F02.redux-philosophy",{"title":2333,"path":2334,"stem":2335},"Чисті функції та Іммутабельність","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fpure-functions-immutability","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F03.pure-functions-immutability",{"title":2337,"icon":132,"path":2338,"stem":2339,"children":2340,"page":59},"Classic Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux",[2341,2345,2349,2353,2357,2361],{"title":2342,"path":2343,"stem":2344},"Створення Store (Classic Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fstore-setup","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F01.store-setup",{"title":2346,"path":2347,"stem":2348},"Actions, Constants та Action Creators","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Factions-constants","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F02.actions-constants",{"title":2350,"path":2351,"stem":2352},"Логіка Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freducers","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F03.reducers",{"title":2354,"path":2355,"stem":2356},"Комбінування Reducers (Root Reducer)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fdata-flow","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F04.data-flow",{"title":2358,"path":2359,"stem":2360},"Підключення до React (React-Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freact-redux-connection","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F05.react-redux-connection",{"title":2362,"path":2363,"stem":2364},"Middleware та Асинхронність (Redux Thunk)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fmiddleware-thunk","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F06.middleware-thunk",{"title":2366,"icon":132,"path":2367,"stem":2368,"children":2369,"page":59},"Transition To Rtk","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk",[2370],{"title":2371,"path":2372,"stem":2373},"Проблеми класичного Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk\u002Fproblems-with-classic","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk\u002F01.problems-with-classic",{"title":2375,"icon":132,"path":2376,"stem":2377,"children":2378,"page":59},"Redux Toolkit","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit",[2379,2383,2387,2391],{"title":2380,"path":2381,"stem":2382},"Налаштування Store з configureStore","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fconfigure-store","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F01.configure-store",{"title":2384,"path":2385,"stem":2386},"createSlice: Революція в Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fcreate-slice","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F02.create-slice",{"title":2388,"path":2389,"stem":2390},"Асинхронність з createAsyncThunk","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fasync-thunks","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F03.async-thunks",{"title":2392,"path":2393,"stem":2394},"04. Entity Adapter: Керування нормалізованим станом","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fentity-adapter","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F04.entity-adapter",{"title":2396,"icon":92,"path":2397,"stem":2398,"children":2399,"page":59},"Advanced","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced",[2400,2404,2408],{"title":2401,"path":2402,"stem":2403},"Мемоізація та Селектори: Повний Гайд по Reselect","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Fselectors-reselect","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F01.selectors-reselect",{"title":2405,"path":2406,"stem":2407},"RTK Query: Архітектура Серверного Кешу","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Frtk-query-intro","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F02.rtk-query-intro",{"title":2255,"path":2409,"stem":2410},"\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Farchitecture-best-practices","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F03.architecture-best-practices",{"title":2412,"icon":132,"path":2413,"stem":2414,"children":2415,"page":59},"Project Kanban","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban",[2416,2420,2424,2428,2432,2436],{"title":2417,"path":2418,"stem":2419},"Проєкт: Kanban Board (Trello Clone)","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fproject-overview","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F01.project-overview",{"title":2421,"path":2422,"stem":2423},"Налаштування та Типізація","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fsetup-and-types","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F02.setup-and-types",{"title":2425,"path":2426,"stem":2427},"Board Slice: Серце Дошки","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fboard-slice","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F03.board-slice",{"title":2429,"path":2430,"stem":2431},"Логіка Drag & Drop","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fdrag-and-drop-logic","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F04.drag-and-drop-logic",{"title":2433,"path":2434,"stem":2435},"Інтеграція з RTK Query","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Frtk-query-integration","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F05.rtk-query-integration",{"title":2437,"path":2438,"stem":2439},"Optimistic Updates","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Foptimistic-updates","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F06.optimistic-updates",{"title":2441,"icon":132,"path":2442,"stem":2443,"children":2444,"page":59},"Testing","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting","03.javascript\u002F04.react\u002F06.redux\u002F07.testing",[2445,2449,2453,2457,2461],{"title":2446,"path":2447,"stem":2448},"Тестування Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Fintro-testing","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F01.intro-testing",{"title":2450,"path":2451,"stem":2452},"Тестування Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-reducers","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F02.testing-reducers",{"title":2454,"path":2455,"stem":2456},"Тестування Селекторів","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-selectors","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F03.testing-selectors",{"title":2458,"path":2459,"stem":2460},"Тестування Компонентів (Integration)","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-components","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F04.testing-components",{"title":2462,"path":2463,"stem":2464},"Тестування Async Thunks","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-thunks","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F05.testing-thunks",{"title":2466,"icon":132,"path":2467,"stem":2468,"children":2469},"Ui Libraries","\u002Fjavascript\u002Freact\u002Fui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002Findex",[2470,2472,2476,2480,2484,2488,2492],{"title":2471,"path":2467,"stem":2468},"UI Бібліотеки в React",{"title":2473,"path":2474,"stem":2475},"Вступ до UI Бібліотек: Навіщо Винаходити Велосипед Двічі?","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fintroduction-to-ui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002F01.introduction-to-ui-libraries",{"title":2477,"path":2478,"stem":2479},"Філософія shadcn\u002Fui: \"Not a Component Library\"","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-philosophy","03.javascript\u002F04.react\u002F07.ui-libraries\u002F02.shadcn-philosophy",{"title":2481,"path":2482,"stem":2483},"Установка та Налаштування shadcn\u002Fui","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-installation","03.javascript\u002F04.react\u002F07.ui-libraries\u002F03.shadcn-installation",{"title":2485,"path":2486,"stem":2487},"Базові Компоненти shadcn\u002Fui: Фундамент Інтерфейсу","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-basics","03.javascript\u002F04.react\u002F07.ui-libraries\u002F04.shadcn-components-basics",{"title":2489,"path":2490,"stem":2491},"Компоненти Форм: Побудова Інтерактивних Form","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-forms","03.javascript\u002F04.react\u002F07.ui-libraries\u002F05.shadcn-components-forms",{"title":2493,"path":2494,"stem":2495},"Складні Компоненти: Dialog, Dropdown, Table та Command","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-advanced","03.javascript\u002F04.react\u002F07.ui-libraries\u002F06.shadcn-components-advanced",{"title":2497,"icon":2498,"path":2499,"stem":2500,"children":2501,"page":59},"TypeScript","i-devicon-typescript","\u002Fjavascript\u002Ftypescript","03.javascript\u002F05.typescript",[2502,2506,2510,2514,2518,2522,2526,2530],{"title":2503,"path":2504,"stem":2505},"TypeScript: Броня для вашого коду","\u002Fjavascript\u002Ftypescript\u002Fintro-and-basic-types","03.javascript\u002F05.typescript\u002F01.intro-and-basic-types",{"title":2507,"path":2508,"stem":2509},"Майстерність Моделювання Даних: Інтерфейси та Просунуті Типи","\u002Fjavascript\u002Ftypescript\u002Finterfaces-and-advanced-types","03.javascript\u002F05.typescript\u002F02.interfaces-and-advanced-types",{"title":2511,"path":2512,"stem":2513},"Алхімія Типів: Generics та Utility Types","\u002Fjavascript\u002Ftypescript\u002Fgenerics-and-utilities","03.javascript\u002F05.typescript\u002F03.generics-and-utilities",{"title":2515,"path":2516,"stem":2517},"Архітектура та Шаблони: Класи в TypeScript","\u002Fjavascript\u002Ftypescript\u002Fclasses-and-oop","03.javascript\u002F05.typescript\u002F04.classes-and-oop",{"title":2519,"path":2520,"stem":2521},"Продакшн та Екосистема: Advanced Config & Workflow","\u002Fjavascript\u002Ftypescript\u002Fadvanced-patterns-and-config","03.javascript\u002F05.typescript\u002F05.advanced-patterns-and-config",{"title":2523,"path":2524,"stem":2525},"TypeScript у світі React","\u002Fjavascript\u002Ftypescript\u002Freact-basics","03.javascript\u002F05.typescript\u002F06.react-basics",{"title":2527,"path":2528,"stem":2529},"React + TypeScript: Продвинуті патерни","\u002Fjavascript\u002Ftypescript\u002Freact-advanced","03.javascript\u002F05.typescript\u002F07.react-advanced",{"title":2531,"path":2532,"stem":2533},"React + TypeScript: Екосистема та бібліотеки","\u002Fjavascript\u002Ftypescript\u002Freact-ecosystem","03.javascript\u002F05.typescript\u002F08.react-ecosystem",{"title":2535,"icon":2536,"path":2537,"stem":2538,"children":2539,"page":59},"Асинхронність","i-lucide-refresh-cw","\u002Fjavascript\u002Fasync-programming","03.javascript\u002F06.async-programming",[2540,2544,2548],{"title":2541,"path":2542,"stem":2543},"Event Loop: серце асинхронності в JavaScript","\u002Fjavascript\u002Fasync-programming\u002Fevent-loop-fundamentals","03.javascript\u002F06.async-programming\u002F01.event-loop-fundamentals",{"title":2545,"path":2546,"stem":2547},"Task Queue та Microtask Queue: пріоритети виконання","\u002Fjavascript\u002Fasync-programming\u002Ftask-queues","03.javascript\u002F06.async-programming\u002F02.task-queues",{"title":2549,"path":2550,"stem":2551},"Асинхронні патерни: від Callbacks до Async\u002FAwait","\u002Fjavascript\u002Fasync-programming\u002Fasync-patterns","03.javascript\u002F06.async-programming\u002F03.async-patterns",{"title":2553,"path":2554,"stem":2555},"Atomic Design","\u002Fjavascript\u002Fatomic-design","03.javascript\u002F2.atomic-design",{"title":2557,"icon":2558,"path":2559,"stem":2560,"children":2561,"page":59},"Java","i-devicon-java","\u002Fjava","04.java",[2562,2565,2568,2572,2576,2580,2584],{"title":162,"path":2563,"stem":2564},"\u002Fjava\u002Fdata-mapper-part1","04.java\u002F01.data-mapper-part1",{"title":166,"path":2566,"stem":2567},"\u002Fjava\u002Fdata-mapper-part2","04.java\u002F02.data-mapper-part2",{"title":2569,"path":2570,"stem":2571},"Service Layer: Організація бізнес-логіки","\u002Fjava\u002Fservice-layer","04.java\u002F03.service-layer",{"title":2573,"path":2574,"stem":2575},"Rich Domain Model та State Pattern","\u002Fjava\u002Frich-domain-model","04.java\u002F04.rich-domain-model",{"title":2577,"path":2578,"stem":2579},"Патерни для складної бізнес-логіки","\u002Fjava\u002Fbusiness-logic-patterns","04.java\u002F05.business-logic-patterns",{"title":2581,"path":2582,"stem":2583},"Обробка помилок та валідація","\u002Fjava\u002Ferror-handling-validation","04.java\u002F06.error-handling-validation",{"title":2585,"path":2586,"stem":2587,"children":2588,"page":59},"Проектування баз даних","\u002Fjava\u002Fpr2","04.java\u002Fpr2",[2589,2593,2597,2601,2605,2609,2613,2617,2621,2625,2629,2633,2637,2641,2645,2649,2653,2657,2661,2665,2669,2673,2677,2681,2685,2689,2693,2697,2701,2705,2709,2713,2717,2721,2725,2729,2733],{"title":2590,"path":2591,"stem":2592},"Концептуальне моделювання: Мистецтво розуміння предметної області","\u002Fjava\u002Fpr2\u002Fconceptual-modeling","04.java\u002Fpr2\u002F01.conceptual-modeling",{"title":2594,"path":2595,"stem":2596},"Логічне моделювання: Від бізнес-ідей до структур даних","\u002Fjava\u002Fpr2\u002Flogical-modeling","04.java\u002Fpr2\u002F02.logical-modeling",{"title":2598,"path":2599,"stem":2600},"Нормалізація: Гігієна даних та боротьба з аномаліями","\u002Fjava\u002Fpr2\u002Fnormalization","04.java\u002Fpr2\u002F03.normalization",{"title":2602,"path":2603,"stem":2604},"Фізична схема: Від абстракції до DDL","\u002Fjava\u002Fpr2\u002Fphysical-schema","04.java\u002Fpr2\u002F04.physical-schema",{"title":2606,"path":2607,"stem":2608},"Архітектурна класифікація таблиць","\u002Fjava\u002Fpr2\u002Ftable-classification","04.java\u002Fpr2\u002F05.table-classification",{"title":2610,"path":2611,"stem":2612},"Database Migrations: Версіонування схеми з Flyway","\u002Fjava\u002Fpr2\u002Fdatabase-migrations","04.java\u002Fpr2\u002F06.database-migrations",{"title":2614,"path":2615,"stem":2616},"А що, якби це була не реляційна БД?","\u002Fjava\u002Fpr2\u002Fbeyond-relational","04.java\u002Fpr2\u002F07.beyond-relational",{"title":2618,"path":2619,"stem":2620},"Object-Relational Impedance Mismatch: Два світи, що не хочуть дружити","\u002Fjava\u002Fpr2\u002Fimpedance-mismatch","04.java\u002Fpr2\u002F09.impedance-mismatch",{"title":2622,"path":2623,"stem":2624},"JDBC: Перший контакт із базою даних","\u002Fjava\u002Fpr2\u002Fjdbc-fundamentals","04.java\u002Fpr2\u002F10.jdbc-fundamentals",{"title":2626,"path":2627,"stem":2628},"Якість коду: Spotless, SpotBugs та SonarQube","\u002Fjava\u002Fpr2\u002F10a.code-quality","04.java\u002Fpr2\u002F10a.code-quality",{"title":2630,"path":2631,"stem":2632},"Connection Pool: Патерн Object Pool для JDBC-з'єднань","\u002Fjava\u002Fpr2\u002Fconnection-pool","04.java\u002Fpr2\u002F11.connection-pool",{"title":2634,"path":2635,"stem":2636},"Row Data Gateway: Об'єкт як обгортка рядка таблиці","\u002Fjava\u002Fpr2\u002Frow-data-gateway","04.java\u002Fpr2\u002F12.row-data-gateway",{"title":2638,"path":2639,"stem":2640},"Table Data Gateway: Фасад таблиці як архітектурний відступ","\u002Fjava\u002Fpr2\u002Ftable-data-gateway","04.java\u002Fpr2\u002F13.table-data-gateway",{"title":2642,"path":2643,"stem":2644},"Repository + Data Mapper: Правильна шарова архітектура з JDBC","\u002Fjava\u002Fpr2\u002Frepository-data-mapper","04.java\u002Fpr2\u002F14.repository-data-mapper",{"title":2646,"path":2647,"stem":2648},"Identity Map: Кешування сутностей у рамках сесії","\u002Fjava\u002Fpr2\u002Fidentity-map","04.java\u002Fpr2\u002F15.identity-map",{"title":2650,"path":2651,"stem":2652},"Unit of Work: Відстеження змін і координація JDBC-транзакцій","\u002Fjava\u002Fpr2\u002Funit-of-work","04.java\u002Fpr2\u002F16.unit-of-work",{"title":2654,"path":2655,"stem":2656},"Strategy: Замінювані SQL-стратегії для підтримки різних СУБД","\u002Fjava\u002Fpr2\u002Fstrategy-sql","04.java\u002Fpr2\u002F17.strategy-sql",{"title":2658,"path":2659,"stem":2660},"Proxy: Lazy Loading для One-To-Many колекцій","\u002Fjava\u002Fpr2\u002Fproxy-lazy-loading","04.java\u002Fpr2\u002F18.proxy-lazy-loading",{"title":2662,"path":2663,"stem":2664},"Generic Repository через Java Reflection: анотації та динамічний SQL","\u002Fjava\u002Fpr2\u002Fgeneric-repository-reflection","04.java\u002Fpr2\u002F19.generic-repository-reflection",{"title":2666,"path":2667,"stem":2668},"Specification Pattern: Композиція бізнес-правил для складних запитів","\u002Fjava\u002Fpr2\u002Fspecification-pattern","04.java\u002Fpr2\u002F20.specification-pattern",{"title":2670,"path":2671,"stem":2672},"Розширені можливості Specification Pattern: підзапити, агрегації та гібридний підхід","\u002Fjava\u002Fpr2\u002F20a.advanced-specifications","04.java\u002Fpr2\u002F20a.advanced-specifications",{"title":2674,"path":2675,"stem":2676},"Асинхронність у JDBC: Від блокуючих викликів до CompletableFuture","\u002Fjava\u002Fpr2\u002Fasynchronous-jdbc","04.java\u002Fpr2\u002F21.asynchronous-jdbc",{"title":2678,"path":2679,"stem":2680},"Інтеграційне тестування JDBC-репозиторіїв: Embedded H2 та патерн AAA","\u002Fjava\u002Fpr2\u002Fintegration-testing-h2","04.java\u002Fpr2\u002F22.integration-testing-h2",{"title":2682,"path":2683,"stem":2684},"Testcontainers: Тестування з реальною PostgreSQL у Docker-контейнерах","\u002Fjava\u002Fpr2\u002Fintegration-testing-testcontainers","04.java\u002Fpr2\u002F23.integration-testing-testcontainers",{"title":2686,"path":2687,"stem":2688},"Google Guice: Впровадження залежностей у JavaFX-проєкті","\u002Fjava\u002Fpr2\u002Fdependency-injection-guice","04.java\u002Fpr2\u002F24.dependency-injection-guice",{"title":2690,"path":2691,"stem":2692},"JavaFX: Основи побудови графічних інтерфейсів","\u002Fjava\u002Fpr2\u002Fjavafx-fundamentals","04.java\u002Fpr2\u002F25.javafx-fundamentals",{"title":2694,"path":2695,"stem":2696},"Properties та Bindings: Реактивність у JavaFX","\u002Fjava\u002Fpr2\u002Fjavafx-properties-bindings","04.java\u002Fpr2\u002F26.javafx-properties-bindings",{"title":2698,"path":2699,"stem":2700},"MVC vs MVP vs MVVM: Еволюція архітектурних патернів UI","\u002Fjava\u002Fpr2\u002Fui-architecture-patterns","04.java\u002Fpr2\u002F27.ui-architecture-patterns",{"title":2702,"path":2703,"stem":2704},"MVVM на практиці: Побудова ViewModel","\u002Fjava\u002Fpr2\u002Fmvvm-viewmodel-implementation","04.java\u002Fpr2\u002F28.mvvm-viewmodel-implementation",{"title":2706,"path":2707,"stem":2708},"View та Controller: Зв'язування з ViewModel через FXML","\u002Fjava\u002Fpr2\u002Fmvvm-view-controller","04.java\u002Fpr2\u002F29.mvvm-view-controller",{"title":2710,"path":2711,"stem":2712},"Інтеграція MVVM з Guice: Автоматична ін'єкція залежностей","\u002Fjava\u002Fpr2\u002Fmvvm-guice-integration","04.java\u002Fpr2\u002F30.mvvm-guice-integration",{"title":2714,"path":2715,"stem":2716},"Валідація та обробка помилок у MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-validation-error-handling","04.java\u002Fpr2\u002F31.mvvm-validation-error-handling",{"title":2718,"path":2719,"stem":2720},"Навігація та управління екранами у JavaFX MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-navigation-screen-management","04.java\u002Fpr2\u002F32.mvvm-navigation-screen-management",{"title":2722,"path":2723,"stem":2724},"Тестування JavaFX MVVM-додатків","\u002Fjava\u002Fpr2\u002Fmvvm-testing","04.java\u002Fpr2\u002F33.mvvm-testing",{"title":2726,"path":2727,"stem":2728},"Стилізація та теми у JavaFX: CSS та User Experience","\u002Fjava\u002Fpr2\u002Fjavafx-styling-themes","04.java\u002Fpr2\u002F34.javafx-styling-themes",{"title":2730,"path":2731,"stem":2732},"AtlantaFX: Сучасні теми для JavaFX додатків","\u002Fjava\u002Fpr2\u002Fatlantafx-modern-themes","04.java\u002Fpr2\u002F35.atlantafx-modern-themes",{"title":2734,"path":2735,"stem":2736},"Пакування та розповсюдження JavaFX-додатків","\u002Fjava\u002Fpr2\u002Fjar-packaging-distribution","04.java\u002Fpr2\u002F36.jar-packaging-distribution",{"title":2738,"icon":2739,"path":2740,"stem":2741,"children":2742,"page":59},"Python","i-devicon-python","\u002Fpython","05.python",[2743,2747,2750,2754,2758,2762,2766,2770,2774,2778,2782,2786,2790,2794,2798,2859],{"title":2744,"path":2745,"stem":2746},"Модулі, Пакети та Віртуальні Середовища","\u002Fpython\u002Fmodules-packages-venv","05.python\u002F00.modules-packages-venv",{"title":71,"path":2748,"stem":2749},"\u002Fpython\u002Fclasses-objects","05.python\u002F01.classes-objects",{"title":2751,"path":2752,"stem":2753},"Інкапсуляція, Керування Доступом та Властивості","\u002Fpython\u002Fencapsulation","05.python\u002F02.encapsulation",{"title":2755,"path":2756,"stem":2757},"Наслідування, MRO та суперсила super()","\u002Fpython\u002Finheritance-mro","05.python\u002F03.inheritance-mro",{"title":2759,"path":2760,"stem":2761},"Абстракція — ABC проти Статичних Протоколів (PEP 544)","\u002Fpython\u002Fabstraction-protocols","05.python\u002F04.abstraction-protocols",{"title":2763,"path":2764,"stem":2765},"Магічні методи (Dunder) та Емуляція протоколів","\u002Fpython\u002Fdunder-methods","05.python\u002F05.dunder-methods",{"title":2767,"path":2768,"stem":2769},"Декоратори та Керування життєвим циклом методів","\u002Fpython\u002Fdecorators-static-class","05.python\u002F06.decorators-static-class",{"title":2771,"path":2772,"stem":2773},"Дескриптори — Магія доступу до атрибутів","\u002Fpython\u002Fdescriptors","05.python\u002F07.descriptors",{"title":2775,"path":2776,"stem":2777},"Метакласи — Динамічне створення класів під капотом CPython","\u002Fpython\u002Fmetaclasses","05.python\u002F08.metaclasses",{"title":2779,"path":2780,"stem":2781},"Dataclasses, NamedTuple та сучасні контейнери Python","\u002Fpython\u002Fmodern-containers","05.python\u002F09.modern-containers",{"title":2783,"path":2784,"stem":2785},"GIL та модель конкурентності CPython — фундамент перед потоками і процесами","\u002Fpython\u002Fgil-concurrency-intro","05.python\u002F11.gil-concurrency-intro",{"title":2787,"path":2788,"stem":2789},"Threading — конкурентність для I\u002FO-bound задач","\u002Fpython\u002Fthreading","05.python\u002F12.threading",{"title":2791,"path":2792,"stem":2793},"Multiprocessing — справжній паралелізм для CPU-bound задач","\u002Fpython\u002Fmultiprocessing","05.python\u002F13.multiprocessing",{"title":2795,"path":2796,"stem":2797},"asyncio — кооперативна конкурентність та event loop","\u002Fpython\u002Fasyncio","05.python\u002F14.asyncio",{"title":2799,"icon":92,"path":2800,"stem":2801,"children":2802,"page":59},"FastAPI","\u002Fpython\u002Ffastapi","05.python\u002Ffastapi",[2803,2807,2811,2815,2819,2823,2827,2831,2835,2839,2843,2847,2851,2855],{"title":2804,"path":2805,"stem":2806},"Глибокий Typing та Pydantic v2 — від анотацій до валідації","\u002Fpython\u002Ffastapi\u002Ftyping-pydantic","05.python\u002Ffastapi\u002F15.typing-pydantic",{"title":2808,"path":2809,"stem":2810},"WSGI, ASGI та Python Web-екосистема","\u002Fpython\u002Ffastapi\u002Fwsgi-asgi-ecosystem","05.python\u002Ffastapi\u002F16.wsgi-asgi-ecosystem",{"title":2812,"path":2813,"stem":2814},"FastAPI: Перший додаток, Uvicorn та OpenAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-intro","05.python\u002Ffastapi\u002F17.fastapi-intro",{"title":2816,"path":2817,"stem":2818},"Маршрутизація, параметри запитів та APIRouter","\u002Fpython\u002Ffastapi\u002Ffastapi-routing-params","05.python\u002Ffastapi\u002F18.fastapi-routing-params",{"title":2820,"path":2821,"stem":2822},"Pydantic v2 у FastAPI — схеми, валідація та серіалізація","\u002Fpython\u002Ffastapi\u002Ffastapi-pydantic-schemas","05.python\u002Ffastapi\u002F19.fastapi-pydantic-schemas",{"title":2824,"path":2825,"stem":2826},"Dependency Injection — серце архітектури FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-dependency-injection","05.python\u002Ffastapi\u002F20.fastapi-dependency-injection",{"title":2828,"path":2829,"stem":2830},"Обробка помилок, Middleware та CORS у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-errors-middleware","05.python\u002Ffastapi\u002F21.fastapi-errors-middleware",{"title":2832,"path":2833,"stem":2834},"SQLAlchemy 2.0 — ORM, Core та Async Engine","\u002Fpython\u002Ffastapi\u002Fsqlalchemy-orm","05.python\u002Ffastapi\u002F22.sqlalchemy-orm",{"title":2836,"path":2837,"stem":2838},"Alembic — міграції бази даних","\u002Fpython\u002Ffastapi\u002Falembic-migrations","05.python\u002Ffastapi\u002F23.alembic-migrations",{"title":2840,"path":2841,"stem":2842},"Repository Pattern та Clean Architecture у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-repository-clean-arch","05.python\u002Ffastapi\u002F24.fastapi-repository-clean-arch",{"title":2844,"path":2845,"stem":2846},"Автентифікація та авторизація — JWT, OAuth2, RBAC","\u002Fpython\u002Ffastapi\u002Ffastapi-auth-security","05.python\u002Ffastapi\u002F25.fastapi-auth-security",{"title":2848,"path":2849,"stem":2850},"Тестування FastAPI — pytest, httpx, fixtures","\u002Fpython\u002Ffastapi\u002Ffastapi-testing","05.python\u002Ffastapi\u002F26.fastapi-testing",{"title":2852,"path":2853,"stem":2854},"Async на повну — Background Tasks, WebSockets, SSE та Celery","\u002Fpython\u002Ffastapi\u002Ffastapi-async-advanced","05.python\u002Ffastapi\u002F27.fastapi-async-advanced",{"title":2856,"path":2857,"stem":2858},"Deployment — Docker, CI\u002FCD, Monitoring","\u002Fpython\u002Ffastapi\u002Ffastapi-deployment","05.python\u002Ffastapi\u002F28.fastapi-deployment",{"title":2860,"path":2861,"stem":2862},"[object Object]","\u002Fpython\u002Foop-plan","05.python\u002Foop-plan",{"title":2864,"icon":2865,"path":2866,"stem":2867,"children":2868,"page":59},"Бази даних","i-lucide-database","\u002Fdatabases","06.databases",[2869,2899,2922,2959,2988,3006,3040,3052,3061],{"title":2870,"icon":2871,"path":2872,"stem":2873,"children":2874,"page":59},"Intro","i-lucide-play","\u002Fdatabases\u002Fintro","06.databases\u002F01.intro",[2875,2879,2883,2887,2891,2895],{"title":2876,"path":2877,"stem":2878},"Введення в теорію баз даних","\u002Fdatabases\u002Fintro\u002Fintroduction-to-databases","06.databases\u002F01.intro\u002F01.introduction-to-databases",{"title":2880,"path":2881,"stem":2882},"Реляційна модель даних","\u002Fdatabases\u002Fintro\u002Frelational-model-theory","06.databases\u002F01.intro\u002F02.relational-model-theory",{"title":2884,"path":2885,"stem":2886},"ER-моделювання","\u002Fdatabases\u002Fintro\u002Fer-modeling","06.databases\u002F01.intro\u002F03.er-modeling",{"title":2888,"path":2889,"stem":2890},"Логічне проектування БД","\u002Fdatabases\u002Fintro\u002Flogical-schema","06.databases\u002F01.intro\u002F04.logical-schema",{"title":2892,"path":2893,"stem":2894},"Класифікація таблиць","\u002Fdatabases\u002Fintro\u002Ftable-classification","06.databases\u002F01.intro\u002F05.table-classification",{"title":2896,"path":2897,"stem":2898},"PlantUML для баз даних","\u002Fdatabases\u002Fintro\u002Fplantuml-diagrams","06.databases\u002F01.intro\u002F06.plantuml-diagrams",{"title":2900,"icon":2865,"path":2901,"stem":2902,"children":2903,"page":59},"MS SQL Server Start","\u002Fdatabases\u002Fms-sql-server-start","06.databases\u002F02.ms-sql-server-start",[2904,2908,2914,2918],{"title":2905,"path":2906,"stem":2907},"Типи даних у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fdata-types","06.databases\u002F02.ms-sql-server-start\u002F01.data-types",{"title":2909,"path":2910,"stem":2911,"children":2912},"Індекси у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-indexes","06.databases\u002F02.ms-sql-server-start\u002F02.sql-indexes",[2913],{"title":2909,"path":2910,"stem":2911},{"title":2915,"path":2916,"stem":2917},"Системні бази даних MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsystem-databases","06.databases\u002F02.ms-sql-server-start\u002F03.system-databases",{"title":2919,"path":2920,"stem":2921},"Огляд мови SQL та запитів","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-queries-overview","06.databases\u002F02.ms-sql-server-start\u002F04.sql-queries-overview",{"title":2923,"icon":2865,"path":2924,"stem":2925,"children":2926,"page":59},"SQL","\u002Fdatabases\u002Fsql","06.databases\u002F03.sql",[2927,2931,2935,2939,2943,2947,2951,2955],{"title":2928,"path":2929,"stem":2930},"Налаштування демонстраційної бази даних","\u002Fdatabases\u002Fsql\u002Fsample-database-setup","06.databases\u002F03.sql\u002F00.sample-database-setup",{"title":2932,"path":2933,"stem":2934},"DDL - Створення таблиць (CREATE TABLE)","\u002Fdatabases\u002Fsql\u002Fddl-create-table","06.databases\u002F03.sql\u002F01.ddl-create-table",{"title":2936,"path":2937,"stem":2938},"DDL - Зміна та видалення таблиць (ALTER, DROP)","\u002Fdatabases\u002Fsql\u002Fddl-alter-drop-table","06.databases\u002F03.sql\u002F02.ddl-alter-drop-table",{"title":2940,"path":2941,"stem":2942},"SELECT запити - Основи","\u002Fdatabases\u002Fsql\u002Fselect-queries-fundamentals","06.databases\u002F03.sql\u002F03.select-queries-fundamentals",{"title":2944,"path":2945,"stem":2946},"SELECT запити - Розширені можливості","\u002Fdatabases\u002Fsql\u002Fselect-queries-advanced","06.databases\u002F03.sql\u002F04.select-queries-advanced",{"title":2948,"path":2949,"stem":2950},"INSERT запити - Додавання даних","\u002Fdatabases\u002Fsql\u002Finsert-queries","06.databases\u002F03.sql\u002F05.insert-queries",{"title":2952,"path":2953,"stem":2954},"UPDATE та DELETE запити","\u002Fdatabases\u002Fsql\u002Fupdate-delete-queries","06.databases\u002F03.sql\u002F06.update-delete-queries",{"title":2956,"path":2957,"stem":2958},"Транзакції в SQL","\u002Fdatabases\u002Fsql\u002Ftransactions","06.databases\u002F03.sql\u002F07.transactions",{"title":2960,"icon":2865,"path":2961,"stem":2962,"children":2963,"page":59},"Multi Table Databases","\u002Fdatabases\u002Fmulti-table-databases","06.databases\u002F04.multi-table-databases",[2964,2968,2972,2976,2980,2984],{"title":2965,"path":2966,"stem":2967},"Зв'язки та нормалізація БД","\u002Fdatabases\u002Fmulti-table-databases\u002Frelationships-and-normalization","06.databases\u002F04.multi-table-databases\u002F00.relationships-and-normalization",{"title":2969,"path":2970,"stem":2971},"INNER JOIN - З'єднання таблиць","\u002Fdatabases\u002Fmulti-table-databases\u002Finner-join","06.databases\u002F04.multi-table-databases\u002F01.inner-join",{"title":2973,"path":2974,"stem":2975},"OUTER JOINs - LEFT, RIGHT, FULL","\u002Fdatabases\u002Fmulti-table-databases\u002Fouter-joins","06.databases\u002F04.multi-table-databases\u002F02.outer-joins",{"title":2977,"path":2978,"stem":2979},"CROSS та SELF JOINs","\u002Fdatabases\u002Fmulti-table-databases\u002Fcross-self-joins","06.databases\u002F04.multi-table-databases\u002F03.cross-self-joins",{"title":2981,"path":2982,"stem":2983},"Підзапити (Subqueries)","\u002Fdatabases\u002Fmulti-table-databases\u002Fsubqueries","06.databases\u002F04.multi-table-databases\u002F04.subqueries",{"title":2985,"path":2986,"stem":2987},"Агрегації з JOIN","\u002Fdatabases\u002Fmulti-table-databases\u002Faggregations-with-joins","06.databases\u002F04.multi-table-databases\u002F05.aggregations-with-joins",{"title":2989,"icon":2990,"path":2991,"stem":2992,"children":2993,"page":59},"Aggregate Functions","i-lucide-calculator","\u002Fdatabases\u002Faggregate-functions","06.databases\u002F05.aggregate-functions",[2994,2998,3002],{"title":2995,"path":2996,"stem":2997},"Функції агрегування в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fintroduction-aggregate-functions","06.databases\u002F05.aggregate-functions\u002F01.introduction-aggregate-functions",{"title":2999,"path":3000,"stem":3001},"Групування даних в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fgrouping-data","06.databases\u002F05.aggregate-functions\u002F02.grouping-data",{"title":3003,"path":3004,"stem":3005},"Підзапити з агрегатними функціями","\u002Fdatabases\u002Faggregate-functions\u002Fsubqueries-aggregates","06.databases\u002F05.aggregate-functions\u002F03.subqueries-aggregates",{"title":3007,"icon":3008,"path":3009,"stem":3010,"children":3011,"page":59},"Тригери та зберігаємі процедури","i-lucide-database-zap","\u002Fdatabases\u002Ftriggers-stored-procedures","06.databases\u002F07.triggers-stored-procedures",[3012,3016,3020,3024,3028,3032,3036],{"title":3013,"path":3014,"stem":3015},"DML-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fdml-triggers","06.databases\u002F07.triggers-stored-procedures\u002F01.dml-triggers",{"title":3017,"path":3018,"stem":3019},"DDL-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fddl-triggers","06.databases\u002F07.triggers-stored-procedures\u002F02.ddl-triggers",{"title":3021,"path":3022,"stem":3023},"Transact-SQL розширення","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransact-sql-extensions","06.databases\u002F07.triggers-stored-procedures\u002F03.transact-sql-extensions",{"title":3025,"path":3026,"stem":3027},"Транзакції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransactions","06.databases\u002F07.triggers-stored-procedures\u002F04.transactions",{"title":3029,"path":3030,"stem":3031},"Зберігаємі процедури","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fstored-procedures","06.databases\u002F07.triggers-stored-procedures\u002F05.stored-procedures",{"title":3033,"path":3034,"stem":3035},"Користувацькі функції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fuser-defined-functions","06.databases\u002F07.triggers-stored-procedures\u002F06.user-defined-functions",{"title":3037,"path":3038,"stem":3039},"Безпека баз даних","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fsecurity","06.databases\u002F07.triggers-stored-procedures\u002F08.security",{"title":3037,"icon":793,"path":3041,"stem":3042,"children":3043,"page":59},"\u002Fdatabases\u002Fsecurity","06.databases\u002F08.security",[3044,3048],{"title":3045,"path":3046,"stem":3047},"Вступ до безпеки баз даних","\u002Fdatabases\u002Fsecurity\u002Fintroduction","06.databases\u002F08.security\u002F01.introduction",{"title":3049,"path":3050,"stem":3051},"Системні представлення та метадані","\u002Fdatabases\u002Fsecurity\u002Fsystem-views","06.databases\u002F08.security\u002F02.system-views",{"title":3053,"icon":3054,"path":3055,"stem":3056,"children":3057,"page":59},"Резервне копіювання та відновлення","i-lucide-database-backup","\u002Fdatabases\u002Fbackup-recovery","06.databases\u002F09.backup-recovery",[3058],{"title":3053,"path":3059,"stem":3060},"\u002Fdatabases\u002Fbackup-recovery\u002Fbackup-restore","06.databases\u002F09.backup-recovery\u002F01.backup-restore",{"title":3062,"icon":3063,"path":3064,"stem":3065,"children":3066,"page":59},"Повнотекстовий пошук","i-lucide-search","\u002Fdatabases\u002Ffull-text-search","06.databases\u002F10.full-text-search",[3067],{"title":3062,"path":3068,"stem":3069},"\u002Fdatabases\u002Ffull-text-search\u002Ffull-text-search","06.databases\u002F10.full-text-search\u002F01.full-text-search",{"title":3071,"icon":3072,"path":3073,"stem":3074,"children":3075,"page":59},"Tools","i-lucide-wrench","\u002Ftools","07.tools",[3076,3152],{"title":3077,"icon":3078,"path":3079,"stem":3080,"children":3081},"Docker","i-simple-icons-docker","\u002Ftools\u002Fdocker","07.tools\u002F01.docker\u002Findex",[3082,3084,3088,3092,3096,3100,3104,3108,3112,3116,3120,3124,3128,3132,3136,3140,3144,3148],{"title":3083,"path":3079,"stem":3080},"Docker: від нуля до production",{"title":3085,"path":3086,"stem":3087},"Контейнеризація — від проблеми до рішення","\u002Ftools\u002Fdocker\u002Fcontainerization-concept","07.tools\u002F01.docker\u002F01.containerization-concept",{"title":3089,"path":3090,"stem":3091},"Docker — що це і навіщо?","\u002Ftools\u002Fdocker\u002Fdocker-what-and-why","07.tools\u002F01.docker\u002F02.docker-what-and-why",{"title":3093,"path":3094,"stem":3095},"Архітектура Docker Engine","\u002Ftools\u002Fdocker\u002Fdocker-architecture","07.tools\u002F01.docker\u002F03.docker-architecture",{"title":3097,"path":3098,"stem":3099},"Встановлення Docker","\u002Ftools\u002Fdocker\u002Finstallation","07.tools\u002F01.docker\u002F04.installation",{"title":3101,"path":3102,"stem":3103},"Перший контейнер — docker run","\u002Ftools\u002Fdocker\u002Ffirst-container","07.tools\u002F01.docker\u002F05.first-container",{"title":3105,"path":3106,"stem":3107},"Життєвий цикл контейнера","\u002Ftools\u002Fdocker\u002Fcontainer-lifecycle","07.tools\u002F01.docker\u002F06.container-lifecycle",{"title":3109,"path":3110,"stem":3111},"Docker Images — фундаментальні концепції","\u002Ftools\u002Fdocker\u002Fdocker-images-fundamentals","07.tools\u002F01.docker\u002F07.docker-images-fundamentals",{"title":3113,"path":3114,"stem":3115},"Dockerfile — основи","\u002Ftools\u002Fdocker\u002Fdockerfile-basics","07.tools\u002F01.docker\u002F08.dockerfile-basics",{"title":3117,"path":3118,"stem":3119},"Dockerfile — просунуті техніки","\u002Ftools\u002Fdocker\u002Fdockerfile-advanced","07.tools\u002F01.docker\u002F09.dockerfile-advanced",{"title":3121,"path":3122,"stem":3123},"Build Context та кешування шарів","\u002Ftools\u002Fdocker\u002Fbuild-context-and-cache","07.tools\u002F01.docker\u002F10.build-context-and-cache",{"title":3125,"path":3126,"stem":3127},"Реєстри Docker-образів","\u002Ftools\u002Fdocker\u002Fimage-registries","07.tools\u002F01.docker\u002F11.image-registries",{"title":3129,"path":3130,"stem":3131},"Контейнеризація .NET додатків","\u002Ftools\u002Fdocker\u002Fdotnet-containerization","07.tools\u002F01.docker\u002F12.dotnet-containerization",{"title":3133,"path":3134,"stem":3135},"Томи та збереження даних","\u002Ftools\u002Fdocker\u002Fvolumes-and-data","07.tools\u002F01.docker\u002F13.volumes-and-data",{"title":3137,"path":3138,"stem":3139},"Основи мережі в Docker","\u002Ftools\u002Fdocker\u002Fnetworking-basics","07.tools\u002F01.docker\u002F14.networking-basics",{"title":3141,"path":3142,"stem":3143},"Змінні оточення та конфігурація","\u002Ftools\u002Fdocker\u002Fenvironment-and-configuration","07.tools\u002F01.docker\u002F15.environment-and-configuration",{"title":3145,"path":3146,"stem":3147},"Docker Compose — оркестрація контейнерів","\u002Ftools\u002Fdocker\u002Fdocker-compose-basics","07.tools\u002F01.docker\u002F16.docker-compose-basics",{"title":3149,"path":3150,"stem":3151},"Docker Compose — Multi-Service застосунки","\u002Ftools\u002Fdocker\u002Fcompose-multi-service","07.tools\u002F01.docker\u002F17.compose-multi-service",{"title":3153,"icon":3154,"path":3155,"stem":3156,"children":3157},"Kubernetes","simple-icons:kubernetes","\u002Ftools\u002Fkubernetes","07.tools\u002F02.kubernetes\u002Findex",[3158,3160,3164,3168,3172,3176,3180,3184,3188],{"title":3159,"path":3155,"stem":3156},"Kubernetes: від розробки до production",{"title":3161,"path":3162,"stem":3163},"Kubernetes — коли Docker Compose більше не вистачає","\u002Ftools\u002Fkubernetes\u002Fwhy-kubernetes","07.tools\u002F02.kubernetes\u002F01.why-kubernetes",{"title":3165,"path":3166,"stem":3167},"Архітектура Kubernetes — анатомія кластера","\u002Ftools\u002Fkubernetes\u002Fkubernetes-architecture","07.tools\u002F02.kubernetes\u002F02.kubernetes-architecture",{"title":3169,"path":3170,"stem":3171},"Локальне середовище — minikube, kind та k3s","\u002Ftools\u002Fkubernetes\u002Flocal-environment","07.tools\u002F02.kubernetes\u002F03.local-environment",{"title":3173,"path":3174,"stem":3175},"Pod — атомарна одиниця Kubernetes","\u002Ftools\u002Fkubernetes\u002Fpods-and-containers","07.tools\u002F02.kubernetes\u002F04.pods-and-containers",{"title":3177,"path":3178,"stem":3179},"Патерни використання Pod","\u002Ftools\u002Fkubernetes\u002Fpod-patterns","07.tools\u002F02.kubernetes\u002F05.pod-patterns",{"title":3181,"path":3182,"stem":3183},"Deployment — декларативне управління Pod","\u002Ftools\u002Fkubernetes\u002Fdeployment-basics","07.tools\u002F02.kubernetes\u002F06.deployment-basics",{"title":3185,"path":3186,"stem":3187},"Rolling Updates та управління життєвим циклом Deployment","\u002Ftools\u002Fkubernetes\u002Fdeployment-rolling-updates","07.tools\u002F02.kubernetes\u002F07.deployment-rolling-updates",{"title":3189,"path":3190,"stem":3191},"Service — мережева абстракція для Pod","\u002Ftools\u002Fkubernetes\u002Fservices-networking","07.tools\u002F02.kubernetes\u002F08.services-networking",{"title":3193,"icon":3194,"path":3195,"stem":3196,"children":3197,"page":59},"Software Engineering","i-lucide-code-2","\u002Fsoftware-engineering","09.software-engineering",[3198,3202,3206,3210,3214,3218,3222,3226,3230,3234,3238],{"title":3199,"path":3200,"stem":3201},"1. Аналіз предметної області. Експертні знання та складність","\u002Fsoftware-engineering\u002Fintro-subdomains","09.software-engineering\u002F01.intro-subdomains",{"title":3203,"path":3204,"stem":3205},"2. Обмежені контексти. Інтеграція обмежених контекстів","\u002Fsoftware-engineering\u002Fintegrating-limited-contexts","09.software-engineering\u002F02.integrating-limited-contexts",{"title":3207,"path":3208,"stem":3209},"3. Реалізація простої бізнес-логіки","\u002Fsoftware-engineering\u002Fsimple","09.software-engineering\u002F03.simple",{"title":3211,"path":3212,"stem":3213},"4. Опрацювання складної бізнес-логіки","\u002Fsoftware-engineering\u002Fcomplex-business-logic","09.software-engineering\u002F04.complex-business-logic",{"title":3215,"path":3216,"stem":3217},"5. Моделювання фактора часу. Подієво-орієнтована архітектура.","\u002Fsoftware-engineering\u002Fmodelling-the-time-factor","09.software-engineering\u002F05.modelling-the-time-factor",{"title":3219,"path":3220,"stem":3221},"6. Архітектурні патерни","\u002Fsoftware-engineering\u002Farchitectural-patterns","09.software-engineering\u002F06.architectural-patterns",{"title":3223,"path":3224,"stem":3225},"Паттерни взаємодії","\u002Fsoftware-engineering\u002Fpatterns-of-interaction","09.software-engineering\u002F07.patterns-of-interaction",{"title":3227,"path":3228,"stem":3229},"Евристика проєктування","\u002Fsoftware-engineering\u002Fdesign-heuristics","09.software-engineering\u002F08.design-heuristics",{"title":3231,"path":3232,"stem":3233},"Еволюція проєктних рішень","\u002Fsoftware-engineering\u002Fevolution-of-design-solutions","09.software-engineering\u002F09.evolution-of-design-solutions",{"title":3235,"path":3236,"stem":3237},"EventStorming","\u002Fsoftware-engineering\u002Feventstorming","09.software-engineering\u002F10.eventstorming",{"title":3239,"path":3240,"stem":3241},"DDD на практиці","\u002Fsoftware-engineering\u002Fddd-in-practice","09.software-engineering\u002F11.ddd-in-practice",{"title":3243,"icon":943,"path":3244,"stem":3245,"children":3246,"page":59},"DDD","\u002Fddd","10.ddd",[3247,3251,3255,3259,3263,3267,3271,3275,3279,3283,3287,3291,3295],{"title":3248,"path":3249,"stem":3250},"Аналіз предметної області","\u002Fddd\u002Fdomain-analysis","10.ddd\u002F01.domain-analysis",{"title":3252,"path":3253,"stem":3254},"Експертні знання про предметну область","\u002Fddd\u002Fdomain-expert-knowledge","10.ddd\u002F02.domain-expert-knowledge",{"title":3256,"path":3257,"stem":3258},"Як осмислити складність предметної області","\u002Fddd\u002Fmanaging-domain-complexity","10.ddd\u002F03.managing-domain-complexity",{"title":3260,"path":3261,"stem":3262},"Інтеграція обмежених контекстів","\u002Fddd\u002Fbounded-context-integration","10.ddd\u002F04.bounded-context-integration",{"title":3264,"path":3265,"stem":3266},"Реалізація простої бізнес-логіки","\u002Fddd\u002Fsimple-business-logic","10.ddd\u002F05.simple-business-logic",{"title":3268,"path":3269,"stem":3270},"Обробка складної бізнес-логіки","\u002Fddd\u002Fcomplex-business-logic","10.ddd\u002F06.complex-business-logic",{"title":3272,"path":3273,"stem":3274},"Моделювання фактора часу","\u002Fddd\u002Ftime-modeling","10.ddd\u002F07.time-modeling",{"title":3276,"path":3277,"stem":3278},"Глава 8. Архітектурні Патерни","\u002Fddd\u002Farchitectural-patterns","10.ddd\u002F08.architectural-patterns",{"title":3280,"path":3281,"stem":3282},"Глава 9. Патерни Взаємодії","\u002Fddd\u002Finteraction-patterns","10.ddd\u002F09.interaction-patterns",{"title":3284,"path":3285,"stem":3286},"Глава 10. Проектні Евристики","\u002Fddd\u002Fdesign-heuristics","10.ddd\u002F10.design-heuristics",{"title":3288,"path":3289,"stem":3290},"Глава 11. Еволюція Проектних Рішень","\u002Fddd\u002Fevolution-of-design-decisions","10.ddd\u002F11.evolution-of-design-decisions",{"title":3292,"path":3293,"stem":3294},"Глава 12. EventStorming","\u002Fddd\u002Fevent-storming","10.ddd\u002F12.event-storming",{"title":3296,"path":3297,"stem":3298},"Глава 13. DDD на Практиці","\u002Fddd\u002Fddd-in-practice","10.ddd\u002F13.ddd-in-practice",{"title":3300,"icon":3301,"path":3302,"stem":3303,"children":3304,"page":59},"Media Streaming","i-lucide-video","\u002Fmedia-streaming","11.media-streaming",[3305,3309,3313,3317,3321,3325,3329],{"title":3306,"path":3307,"stem":3308},"01. Магія Стрімінгу: Що відбувається, коли ви натискаєте \"Play\"","\u002Fmedia-streaming\u002Fintroduction","11.media-streaming\u002F01.introduction",{"title":3310,"path":3311,"stem":3312},"02. Анатомія Медіа: Кодеки, Контейнери та Стиснення","\u002Fmedia-streaming\u002Faudio-video-anatomy","11.media-streaming\u002F02.audio-video-anatomy",{"title":3314,"path":3315,"stem":3316},"03. The Gym: FFmpeg Deep Dive","\u002Fmedia-streaming\u002Fffmpeg-gym","11.media-streaming\u002F03.ffmpeg-gym",{"title":3318,"path":3319,"stem":3320},"04. HLS Protocol: HTTP Live Streaming у Деталях","\u002Fmedia-streaming\u002Fhls-protocol","11.media-streaming\u002F04.hls-protocol",{"title":3322,"path":3323,"stem":3324},"05. DASH Protocol: Відкритий Стандарт","\u002Fmedia-streaming\u002Fdash-protocol","11.media-streaming\u002F05.dash-protocol",{"title":3326,"path":3327,"stem":3328},"06. Масштабування: CDN та Adaptive Bitrate","\u002Fmedia-streaming\u002Fcdn-and-adaptive-bitrate","11.media-streaming\u002F06.cdn-and-adaptive-bitrate",{"title":3330,"path":3331,"stem":3332},"07. Війна із Затримкою (Latency)","\u002Fmedia-streaming\u002Frealtime-latency","11.media-streaming\u002F07.realtime-latency",{"title":3334,"icon":3335,"path":3336,"stem":3337,"children":3338,"page":59},"HTML & CSS","i-devicon-html5","\u002Fhtml-css","12.html-css",[3339,3343,3347,3351,3355,3359,3363,3367,3371,3375,3379,3383,3387,3391,3395,3399,3403,3407,3411,3415,3419,3423,3427,3431,3435,3439,3443,3447,3451,3455],{"title":3340,"path":3341,"stem":3342},"Вступ до HTML. Структура документа","\u002Fhtml-css\u002Fintro-html-structure","12.html-css\u002F01.intro-html-structure",{"title":3344,"path":3345,"stem":3346},"Форматування тексту в HTML","\u002Fhtml-css\u002Fhtml-text-formatting","12.html-css\u002F02.html-text-formatting",{"title":3348,"path":3349,"stem":3350},"Посилання та зображення в HTML","\u002Fhtml-css\u002Fhtml-links-images","12.html-css\u002F03.html-links-images",{"title":3352,"path":3353,"stem":3354},"Списки та таблиці в HTML","\u002Fhtml-css\u002Fhtml-lists-tables","12.html-css\u002F04.html-lists-tables",{"title":3356,"path":3357,"stem":3358},"Форми в HTML","\u002Fhtml-css\u002Fhtml-forms","12.html-css\u002F05.html-forms",{"title":3360,"path":3361,"stem":3362},"Семантичні елементи HTML5","\u002Fhtml-css\u002Fhtml-semantic-elements","12.html-css\u002F06.html-semantic-elements",{"title":3364,"path":3365,"stem":3366},"Мультимедіа та розширені елементи HTML","\u002Fhtml-css\u002Fhtml-multimedia-advanced","12.html-css\u002F07.html-multimedia-advanced",{"title":3368,"path":3369,"stem":3370},"Мікророзмітка та SEO в HTML","\u002Fhtml-css\u002Fhtml-microdata-seo","12.html-css\u002F08.html-microdata-seo",{"title":3372,"path":3373,"stem":3374},"Вступ до CSS. Селектори та специфічність","\u002Fhtml-css\u002Fcss-intro-selectors","12.html-css\u002F09.css-intro-selectors",{"title":3376,"path":3377,"stem":3378},"Блокова модель CSS. Відступи. Box Sizing","\u002Fhtml-css\u002Fcss-box-model","12.html-css\u002F10.css-box-model",{"title":3380,"path":3381,"stem":3382},"Розміри у CSS: повний довідник одиниць і ключових слів","\u002Fhtml-css\u002F10a.css-sizing","12.html-css\u002F10a.css-sizing",{"title":3384,"path":3385,"stem":3386},"Типографіка в CSS. Шрифти та текст","\u002Fhtml-css\u002Fcss-typography","12.html-css\u002F11.css-typography",{"title":3388,"path":3389,"stem":3390},"Кольори та фони в CSS","\u002Fhtml-css\u002Fcss-colors-backgrounds","12.html-css\u002F12.css-colors-backgrounds",{"title":3392,"path":3393,"stem":3394},"Тіні та фільтри в CSS","\u002Fhtml-css\u002F12b.css-shadows-filters","12.html-css\u002F12b.css-shadows-filters",{"title":3396,"path":3397,"stem":3398},"CSS Flexbox: Фундамент гнучких макетів","\u002Fhtml-css\u002Fcss-flexbox-fundamentals","12.html-css\u002F13.css-flexbox-fundamentals",{"title":3400,"path":3401,"stem":3402},"CSS Flexbox: Вирівнювання та Позиціонування","\u002Fhtml-css\u002Fcss-flexbox-alignment-sizing-and-patterns","12.html-css\u002F14.css-flexbox-alignment-sizing-and-patterns",{"title":3404,"path":3405,"stem":3406},"CSS Grid. Двовимірний макет. Частина 1","\u002Fhtml-css\u002Fcss-layout-grid","12.html-css\u002F15.css-layout-grid",{"title":3408,"path":3409,"stem":3410},"CSS Grid. Двовимірний макет. Частина 2","\u002Fhtml-css\u002Fcss-layout-grid-advanced","12.html-css\u002F16.css-layout-grid-advanced",{"title":3412,"path":3413,"stem":3414},"Позиціонування в CSS. Z-index. Stacking Context","\u002Fhtml-css\u002Fcss-positioning","12.html-css\u002F17.css-positioning",{"title":3416,"path":3417,"stem":3418},"CSS Анімації та Переходи","\u002Fhtml-css\u002Fcss-animations-transitions","12.html-css\u002F18.css-animations-transitions",{"title":3420,"path":3421,"stem":3422},"Адаптивний дизайн. Media Queries. Частина 1","\u002Fhtml-css\u002Fcss-responsive-media-queries","12.html-css\u002F19.css-responsive-media-queries",{"title":3424,"path":3425,"stem":3426},"Адаптивний дизайн. Частина 2: clamp(), Container Queries, @layer","\u002Fhtml-css\u002Fcss-responsive-advanced","12.html-css\u002F20.css-responsive-advanced",{"title":3428,"path":3429,"stem":3430},"CSS Custom Properties. Методології. Сучасний CSS","\u002Fhtml-css\u002Fcss-variables-methodologies","12.html-css\u002F21.css-variables-methodologies",{"title":3432,"path":3433,"stem":3434},"Сучасний CSS 2023–2025: Нові можливості","\u002Fhtml-css\u002Fcss-modern-features","12.html-css\u002F22.css-modern-features",{"title":3436,"path":3437,"stem":3438},"CSS Nesting, @layer, @scope та @property: нативний препроцесор","\u002Fhtml-css\u002F22a.css-nesting-modern-syntax","12.html-css\u002F22a.css-nesting-modern-syntax",{"title":3440,"path":3441,"stem":3442},"CSS для форм та інтерактивних станів","\u002Fhtml-css\u002Fcss-forms-interactive-states","12.html-css\u002F23.css-forms-interactive-states",{"title":3444,"path":3445,"stem":3446},"Доступність у CSS (CSS Accessibility)","\u002Fhtml-css\u002Fcss-accessibility","12.html-css\u002F24.css-accessibility",{"title":3448,"path":3449,"stem":3450},"CSS-функції та сучасні sizing primitives","\u002Fhtml-css\u002Fcss-functions-sizing","12.html-css\u002F25.css-functions-sizing",{"title":3452,"path":3453,"stem":3454},"Rendering Pipeline і CSS Performance","\u002Fhtml-css\u002Fcss-rendering-performance","12.html-css\u002F26.css-rendering-performance",{"title":3456,"path":3457,"stem":3458},"CSS Best Practices: типові ситуації та правильні рішення","\u002Fhtml-css\u002Fcss-best-practices","12.html-css\u002F27.css-best-practices",{"title":3460,"path":3461,"stem":3462,"children":3463,"page":59},"AWS","\u002Faws","13.aws",[3464,3468,3472,3476,3480,3484,3488,3492,3496,3500,3504,3508,3512,3516,3520,3524,3528,3532],{"title":3465,"path":3466,"stem":3467},"Реєстрація AWS акаунту та студентські програми","\u002Faws\u002Faccount-registration","13.aws\u002F00.account-registration",{"title":3469,"path":3470,"stem":3471},"Вступ до хмарних обчислень та AWS","\u002Faws\u002Fintroduction-to-cloud","13.aws\u002F01.introduction-to-cloud",{"title":3473,"path":3474,"stem":3475},"AWS IAM — Identity and Access Management","\u002Faws\u002Fiam","13.aws\u002F02.iam",{"title":3477,"path":3478,"stem":3479},"AWS IAM CLI — Довідник команд","\u002Faws\u002F02a.iam-doc","13.aws\u002F02a.iam-doc",{"title":3481,"path":3482,"stem":3483},"Docker та контейнеризація в AWS — ECR, ECS та Fargate","\u002Faws\u002Fdocker-ecs","13.aws\u002F03.docker-ecs",{"title":3485,"path":3486,"stem":3487},"AWS ECR \u002F ECS CLI — Довідник команд","\u002Faws\u002F03a.docker-ecs-doc","13.aws\u002F03a.docker-ecs-doc",{"title":3489,"path":3490,"stem":3491},"Amazon EC2 — Elastic Compute Cloud","\u002Faws\u002Fec2","13.aws\u002F04.ec2",{"title":3493,"path":3494,"stem":3495},"AWS EC2 CLI — Довідник команд","\u002Faws\u002F04a.ec2-doc","13.aws\u002F04a.ec2-doc",{"title":3497,"path":3498,"stem":3499},"Elastic Load Balancing та Auto Scaling","\u002Faws\u002Falb-asg","13.aws\u002F05.alb-asg",{"title":3501,"path":3502,"stem":3503},"Amazon S3 — Simple Storage Service","\u002Faws\u002Fs3","13.aws\u002F06.s3",{"title":3505,"path":3506,"stem":3507},"Amazon CloudFront — Content Delivery Network","\u002Faws\u002Fcloudfront","13.aws\u002F07.cloudfront",{"title":3509,"path":3510,"stem":3511},"Amazon RDS — Relational Database Service","\u002Faws\u002Frds","13.aws\u002F08.rds",{"title":3513,"path":3514,"stem":3515},"Amazon DynamoDB — NoSQL Database","\u002Faws\u002Fdynamodb","13.aws\u002F09.dynamodb",{"title":3517,"path":3518,"stem":3519},"AWS Lambda та Serverless Compute","\u002Faws\u002Flambda","13.aws\u002F10.lambda",{"title":3521,"path":3522,"stem":3523},"Amazon Bedrock - Foundation Models, RAG та Agents","\u002Faws\u002Fbedrock","13.aws\u002F22.bedrock",{"title":3525,"path":3526,"stem":3527},"Amazon Rekognition - Комп'ютерний зір","\u002Faws\u002Frekognition","13.aws\u002F23.rekognition",{"title":3529,"path":3530,"stem":3531},"Amazon Textract - Інтелектуальний аналіз документів","\u002Faws\u002Ftextract","13.aws\u002F24.textract",{"title":3533,"path":3534,"stem":3535},"Amazon Polly, Transcribe, Comprehend та Translate","\u002Faws\u002Faudio-nlp-services","13.aws\u002F25.audio-nlp-services",{"title":3537,"path":3538,"stem":3539,"children":3540,"page":59},"Ai Development","\u002Fai-development","14.ai-development",[3541],{"title":3542,"path":3543,"stem":3544,"children":3545,"page":59},"Foundations","\u002Fai-development\u002Ffoundations","14.ai-development\u002F00.foundations",[3546],{"title":3547,"path":3548,"stem":3549},"Модуль 0.1. Що таке Large Language Model (LLM)","\u002Fai-development\u002Ffoundations\u002Fwhat-is-llm","14.ai-development\u002F00.foundations\u002F01.what-is-llm",{"title":3551,"path":3552,"stem":3553,"children":3554,"page":59},"React Native","\u002Freact-native","15.react-native",[3555,3576],{"title":3556,"path":3557,"stem":3558,"children":3559,"page":59},"Version1","\u002Freact-native\u002Fversion1","15.react-native\u002Fversion1",[3560,3564,3568,3572],{"title":3561,"path":3562,"stem":3563},"Що таке React Native","\u002Freact-native\u002Fversion1\u002Fwhat-is-react-native","15.react-native\u002Fversion1\u002F01.what-is-react-native",{"title":3565,"path":3566,"stem":3567},"Як влаштований React Native «під капотом»","\u002Freact-native\u002Fversion1\u002Freact-native-architecture","15.react-native\u002Fversion1\u002F02.react-native-architecture",{"title":3569,"path":3570,"stem":3571},"Від React до React Native: ключові відмінності","\u002Freact-native\u002Fversion1\u002Freact-native-vs-react","15.react-native\u002Fversion1\u002F03.react-native-vs-react",{"title":3573,"path":3574,"stem":3575},"View та Text — фундаментальні будівельні блоки","\u002Freact-native\u002Fversion1\u002Fview-and-text","15.react-native\u002Fversion1\u002F04.view-and-text",{"title":3577,"path":3578,"stem":3579,"children":3580,"page":59},"Version2","\u002Freact-native\u002Fversion2","15.react-native\u002Fversion2",[3581,3585,3589,3593,3597,3601,3605,3609,3613,3617,3621,3625,3629,3633,3637,3641,3645,3649,3653,3657,3661,3665,3669,3673,3677,3681,3685],{"title":3582,"path":3583,"stem":3584},"React Native — навіщо він потрібен","\u002Freact-native\u002Fversion2\u002Fwhy-react-native","15.react-native\u002Fversion2\u002F01.why-react-native",{"title":3586,"path":3587,"stem":3588},"Налаштування середовища розробки","\u002Freact-native\u002Fversion2\u002Fenvironment-setup","15.react-native\u002Fversion2\u002F02.environment-setup",{"title":3590,"path":3591,"stem":3592},"Expo і класичний React Native — два шляхи одного фреймворку","\u002Freact-native\u002Fversion2\u002Fexpo-vs-cli-landscape","15.react-native\u002Fversion2\u002F03.expo-vs-cli-landscape",{"title":3594,"path":3595,"stem":3596},"Середовище Expo — перший запуск","\u002Freact-native\u002Fversion2\u002Fexpo-setup-and-tooling","15.react-native\u002Fversion2\u002F04.expo-setup-and-tooling",{"title":3598,"path":3599,"stem":3600},"Структура проєкту та перші UI-примітиви","\u002Freact-native\u002Fversion2\u002Fproject-structure-and-conventions","15.react-native\u002Fversion2\u002F05.project-structure-and-conventions",{"title":3602,"path":3603,"stem":3604},"Базові компоненти React Native","\u002Freact-native\u002Fversion2\u002Fcore-components","15.react-native\u002Fversion2\u002F06.core-components",{"title":3606,"path":3607,"stem":3608},"Flexbox і layout у React Native","\u002Freact-native\u002Fversion2\u002Fflexbox-and-layout","15.react-native\u002Fversion2\u002F07.flexbox-and-layout",{"title":3610,"path":3611,"stem":3612},"StyleSheet і теми (light \u002F dark)","\u002Freact-native\u002Fversion2\u002Fstylesheet-and-theming","15.react-native\u002Fversion2\u002F08.stylesheet-and-theming",{"title":3614,"path":3615,"stem":3616},"Списки та віртуалізація","\u002Freact-native\u002Fversion2\u002Flists-and-virtualization","15.react-native\u002Fversion2\u002F09.lists-and-virtualization",{"title":3618,"path":3619,"stem":3620},"Форми, ввід і валідація","\u002Freact-native\u002Fversion2\u002Fforms-input-validation","15.react-native\u002Fversion2\u002F10.forms-input-validation",{"title":3622,"path":3623,"stem":3624},"Основи Expo Router","\u002Freact-native\u002Fversion2\u002Fexpo-router-basics","15.react-native\u002Fversion2\u002F11.expo-router-basics",{"title":3626,"path":3627,"stem":3628},"Вкладені навігатори та модалки","\u002Freact-native\u002Fversion2\u002Fnested-navigators-and-modals","15.react-native\u002Fversion2\u002F12.nested-navigators-and-modals",{"title":3630,"path":3631,"stem":3632},"Deep linking і параметри маршрутів","\u002Freact-native\u002Fversion2\u002Fdeep-linking-and-params","15.react-native\u002Fversion2\u002F13.deep-linking-and-params",{"title":3634,"path":3635,"stem":3636},"Робота з мережею та життєвий цикл застосунку","\u002Freact-native\u002Fversion2\u002Fnetworking-and-app-lifecycle","15.react-native\u002Fversion2\u002F14.networking-and-app-lifecycle",{"title":3638,"path":3639,"stem":3640},"Redux Toolkit на мобільних платформах","\u002Freact-native\u002Fversion2\u002Fredux-toolkit-on-mobile","15.react-native\u002Fversion2\u002F15.redux-toolkit-on-mobile",{"title":3642,"path":3643,"stem":3644},"RTK Query на мобільних платформах","\u002Freact-native\u002Fversion2\u002Frtk-query-mobile","15.react-native\u002Fversion2\u002F16.rtk-query-mobile",{"title":3646,"path":3647,"stem":3648},"Автентифікація та Безпечне Зберігання","\u002Freact-native\u002Fversion2\u002Fauth-secure-storage","15.react-native\u002Fversion2\u002F18.auth-secure-storage",{"title":3650,"path":3651,"stem":3652},"Локальне сховище — AsyncStorage, MMKV, SQLite","\u002Freact-native\u002Fversion2\u002Flocal-storage-mmkv-sqlite","15.react-native\u002Fversion2\u002F19.local-storage-mmkv-sqlite",{"title":3654,"path":3655,"stem":3656},"Офлайн-First і синхронізація","\u002Freact-native\u002Fversion2\u002Foffline-first-sync","15.react-native\u002Fversion2\u002F20.offline-first-sync",{"title":3658,"path":3659,"stem":3660},"Камера, медіа та файлова система","\u002Freact-native\u002Fversion2\u002Fcamera-media-filesystem","15.react-native\u002Fversion2\u002F21.camera-media-filesystem",{"title":3662,"path":3663,"stem":3664},"Карти та геолокація","\u002Freact-native\u002Fversion2\u002Fmaps-and-location","15.react-native\u002Fversion2\u002F22.maps-and-location",{"title":3666,"path":3667,"stem":3668},"Жести та дотики","\u002Freact-native\u002Fversion2\u002Fgestures-and-touch","15.react-native\u002Fversion2\u002F23.gestures-and-touch",{"title":3670,"path":3671,"stem":3672},"Анімації з Reanimated","\u002Freact-native\u002Fversion2\u002Freanimated-animations","15.react-native\u002Fversion2\u002F24.reanimated-animations",{"title":3674,"path":3675,"stem":3676},"Push і локальні сповіщення","\u002Freact-native\u002Fversion2\u002Fpush-and-local-notifications","15.react-native\u002Fversion2\u002F25.push-and-local-notifications",{"title":3678,"path":3679,"stem":3680},"Інтернаціоналізація та доступність","\u002Freact-native\u002Fversion2\u002Faccessibility-and-i18n","15.react-native\u002Fversion2\u002F26.accessibility-and-i18n",{"title":3682,"path":3683,"stem":3684},"EAS Build та профілі збірки","\u002Freact-native\u002Fversion2\u002Feas-build-and-profiles","15.react-native\u002Fversion2\u002F29.eas-build-and-profiles",{"title":3686,"path":3687,"stem":3688},"Публікація в App Store та Google Play","\u002Freact-native\u002Fversion2\u002Fapp-store-play-release","15.react-native\u002Fversion2\u002F30.app-store-play-release",{"title":3690,"path":3691,"stem":3692,"children":3693,"page":59},"Ai Python","\u002Fai-python","16.ai-python",[3694,3703,3712,3721,3750,3776,3801,3834,3851,3864,3873,3886,3895,3916,3929,3950],{"title":3695,"path":3696,"stem":3697,"children":3698,"page":59},"Intro To Ai","\u002Fai-python\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai",[3699],{"title":3700,"path":3701,"stem":3702},"Вступ до штучного інтелекту та машинного навчання","\u002Fai-python\u002Fintro-to-ai\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai\u002F01.intro-to-ai",{"title":3704,"path":3705,"stem":3706,"children":3707,"page":59},"Jupyter Notebook","\u002Fai-python\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook",[3708],{"title":3709,"path":3710,"stem":3711},"Знайомство з Jupyter Notebook та JupyterLab","\u002Fai-python\u002Fjupyter-notebook\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook\u002F02.jupyter-notebook",{"title":3713,"path":3714,"stem":3715,"children":3716,"page":59},"Numpy Pandas","\u002Fai-python\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas",[3717],{"title":3718,"path":3719,"stem":3720},"Робота з даними з використанням NumPy і pandas","\u002Fai-python\u002Fnumpy-pandas\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas\u002F03.numpy-pandas",{"title":3722,"path":3723,"stem":3724,"children":3725,"page":59},"Statistics Basics","\u002Fai-python\u002Fstatistics-basics","16.ai-python\u002F04.statistics-basics",[3726,3730,3734,3738,3742,3746],{"title":3727,"path":3728,"stem":3729},"Випадкові величини та їх типи","\u002Fai-python\u002Fstatistics-basics\u002Frandom-variables","16.ai-python\u002F04.statistics-basics\u002F01.random-variables",{"title":3731,"path":3732,"stem":3733},"Міри центральної тенденції","\u002Fai-python\u002Fstatistics-basics\u002Fcentral-tendency","16.ai-python\u002F04.statistics-basics\u002F02.central-tendency",{"title":3735,"path":3736,"stem":3737},"Міри варіації (розсіювання)","\u002Fai-python\u002Fstatistics-basics\u002Fvariability","16.ai-python\u002F04.statistics-basics\u002F03.variability",{"title":3739,"path":3740,"stem":3741},"Розподіли випадкових величин","\u002Fai-python\u002Fstatistics-basics\u002Fdistributions","16.ai-python\u002F04.statistics-basics\u002F04.distributions",{"title":3743,"path":3744,"stem":3745},"Кореляція та взаємозв'язки","\u002Fai-python\u002Fstatistics-basics\u002Fcorrelation","16.ai-python\u002F04.statistics-basics\u002F05.correlation",{"title":3747,"path":3748,"stem":3749},"Викиди та аномалії","\u002Fai-python\u002Fstatistics-basics\u002Foutliers","16.ai-python\u002F04.statistics-basics\u002F06.outliers",{"title":3751,"path":3752,"stem":3753,"children":3754},"Візуалізація даних за допомогою matplotlib","\u002Fai-python\u002Fdata-visualization","16.ai-python\u002F05.data-visualization\u002Findex",[3755,3756,3760,3764,3768,3772],{"title":3751,"path":3752,"stem":3753},{"title":3757,"path":3758,"stem":3759},"Основи matplotlib — Figure, Axes та перший графік","\u002Fai-python\u002Fdata-visualization\u002Fmatplotlib-basics","16.ai-python\u002F05.data-visualization\u002F01.matplotlib-basics",{"title":3761,"path":3762,"stem":3763},"Візуалізація розподілів — гістограми та box plots","\u002Fai-python\u002Fdata-visualization\u002Fdistributions","16.ai-python\u002F05.data-visualization\u002F02.distributions",{"title":3765,"path":3766,"stem":3767},"Візуалізація залежностей — scatter plots та кореляція","\u002Fai-python\u002Fdata-visualization\u002Frelationships","16.ai-python\u002F05.data-visualization\u002F03.relationships",{"title":3769,"path":3770,"stem":3771},"Візуалізація категоріальних даних — bar charts та pie charts","\u002Fai-python\u002Fdata-visualization\u002Fcategorical","16.ai-python\u002F05.data-visualization\u002F04.categorical",{"title":3773,"path":3774,"stem":3775},"Композиції та стилізація — subplots та багатопанельні дашборди","\u002Fai-python\u002Fdata-visualization\u002Fsubplots-styling","16.ai-python\u002F05.data-visualization\u002F05.subplots-styling",{"title":3777,"path":3778,"stem":3779,"children":3780,"page":59},"Linear Regression","\u002Fai-python\u002Flinear-regression","16.ai-python\u002F06.linear-regression",[3781,3785,3789,3793,3797],{"title":3782,"path":3783,"stem":3784},"Регресійна задача та лінійна регресія з однією змінною","\u002Fai-python\u002Flinear-regression\u002Fregression-task","16.ai-python\u002F06.linear-regression\u002F01.regression-task",{"title":3786,"path":3787,"stem":3788},"Метрики якості регресії — як оцінити модель","\u002Fai-python\u002Flinear-regression\u002Fquality-metrics","16.ai-python\u002F06.linear-regression\u002F02.quality-metrics",{"title":3790,"path":3791,"stem":3792},"Градієнтний спуск — як модель навчається","\u002Fai-python\u002Flinear-regression\u002Fgradient-descent","16.ai-python\u002F06.linear-regression\u002F03.gradient-descent",{"title":3794,"path":3795,"stem":3796},"Множинна лінійна регресія — модель з багатьма ознаками","\u002Fai-python\u002Flinear-regression\u002Fmultiple-regression","16.ai-python\u002F06.linear-regression\u002F04.multiple-regression",{"title":3798,"path":3799,"stem":3800},"Практичні завдання та резюме модуля","\u002Fai-python\u002Flinear-regression\u002Fpractice","16.ai-python\u002F06.linear-regression\u002F05.practice",{"title":3802,"path":3803,"stem":3804,"children":3805,"page":59},"Practical Regression","\u002Fai-python\u002Fpractical-regression","16.ai-python\u002F07.practical-regression",[3806,3810,3814,3818,3822,3826,3830],{"title":3807,"path":3808,"stem":3809},"Знайомство з scikit-learn","\u002Fai-python\u002Fpractical-regression\u002Fintro-scikit-learn","16.ai-python\u002F07.practical-regression\u002F01.intro-scikit-learn",{"title":3811,"path":3812,"stem":3813},"Exploratory Data Analysis датасету Housing Prices","\u002Fai-python\u002Fpractical-regression\u002Fhousing-dataset-eda","16.ai-python\u002F07.practical-regression\u002F02.housing-dataset-eda",{"title":3815,"path":3816,"stem":3817},"Попередня обробка даних (Data Preprocessing)","\u002Fai-python\u002Fpractical-regression\u002Fdata-preprocessing","16.ai-python\u002F07.practical-regression\u002F03.data-preprocessing",{"title":3819,"path":3820,"stem":3821},"Train\u002FTest Split та перша повноцінна модель","\u002Fai-python\u002Fpractical-regression\u002Ftrain-test-split","16.ai-python\u002F07.practical-regression\u002F04.train-test-split",{"title":3823,"path":3824,"stem":3825},"Перенавчання та недонавчання","\u002Fai-python\u002Fpractical-regression\u002Foverfitting-underfitting","16.ai-python\u002F07.practical-regression\u002F05.overfitting-underfitting",{"title":3827,"path":3828,"stem":3829},"Крос-валідація (Cross-Validation)","\u002Fai-python\u002Fpractical-regression\u002Fcross-validation","16.ai-python\u002F07.practical-regression\u002F06.cross-validation",{"title":3831,"path":3832,"stem":3833},"Гіперпараметри та їх оптимізація","\u002Fai-python\u002Fpractical-regression\u002Fhyperparameter-tuning","16.ai-python\u002F07.practical-regression\u002F07.hyperparameter-tuning",{"title":3835,"path":3836,"stem":3837,"children":3838,"page":59},"Polynomial Regression","\u002Fai-python\u002Fpolynomial-regression","16.ai-python\u002F08.polynomial-regression",[3839,3843,3847],{"title":3840,"path":3841,"stem":3842},"Нелінійні залежності та поліноміальна регресія","\u002Fai-python\u002Fpolynomial-regression\u002Fnonlinear-patterns","16.ai-python\u002F08.polynomial-regression\u002F01.nonlinear-patterns",{"title":3844,"path":3845,"stem":3846},"Регуляризація в регресії — Ridge та Lasso","\u002Fai-python\u002Fpolynomial-regression\u002Fregularization-methods","16.ai-python\u002F08.polynomial-regression\u002F02.regularization-methods",{"title":3848,"path":3849,"stem":3850},"Практика — поліноміальна регресія та регуляризація на Housing Prices","\u002Fai-python\u002Fpolynomial-regression\u002Fhousing-prices-practice","16.ai-python\u002F08.polynomial-regression\u002F03.housing-prices-practice",{"title":3852,"path":3853,"stem":3854,"children":3855,"page":59},"Decision Trees Random Forest","\u002Fai-python\u002Fdecision-trees-random-forest","16.ai-python\u002F09.decision-trees-random-forest",[3856,3860],{"title":3857,"path":3858,"stem":3859},"Дерева рішень — моделі з прозорою та зрозумілою логікою","\u002Fai-python\u002Fdecision-trees-random-forest\u002Fdecision-trees","16.ai-python\u002F09.decision-trees-random-forest\u002F01.decision-trees",{"title":3861,"path":3862,"stem":3863},"Random Forest — ансамблі дерев рішень","\u002Fai-python\u002Fdecision-trees-random-forest\u002Frandom-forest","16.ai-python\u002F09.decision-trees-random-forest\u002F02.random-forest",{"title":3865,"path":3866,"stem":3867,"children":3868,"page":59},"Gradient Boosting","\u002Fai-python\u002Fgradient-boosting","16.ai-python\u002F10.gradient-boosting",[3869],{"title":3870,"path":3871,"stem":3872},"Градієнтний бустинг та XGBoost — послідовне виправлення помилок","\u002Fai-python\u002Fgradient-boosting\u002Fgradient-boosting-xgboost","16.ai-python\u002F10.gradient-boosting\u002F01.gradient-boosting-xgboost",{"title":3874,"path":3875,"stem":3876,"children":3877,"page":59},"Logistic Regression Classification","\u002Fai-python\u002Flogistic-regression-classification","16.ai-python\u002F11.logistic-regression-classification",[3878,3882],{"title":3879,"path":3880,"stem":3881},"Основи класифікації та логістична регресія","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-basics","16.ai-python\u002F11.logistic-regression-classification\u002F01.classification-basics",{"title":3883,"path":3884,"stem":3885},"Метрики якості класифікації","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-metrics","16.ai-python\u002F11.logistic-regression-classification\u002F02.classification-metrics",{"title":3887,"path":3888,"stem":3889,"children":3890,"page":59},"Neural Networks Basics","\u002Fai-python\u002Fneural-networks-basics","16.ai-python\u002F12.neural-networks-basics",[3891],{"title":3892,"path":3893,"stem":3894},"Вступ до нейронних мереж — від персептрона до багатошарових мереж","\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp","16.ai-python\u002F12.neural-networks-basics\u002F01.perceptron-to-mlp",{"title":3896,"path":3897,"stem":3898,"children":3899,"page":59},"Pytorch Intro","\u002Fai-python\u002Fpytorch-intro","16.ai-python\u002F13.pytorch-intro",[3900,3904,3908,3912],{"title":3901,"path":3902,"stem":3903},"Тензори та автоматичне диференціювання в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Ftensors-and-autograd","16.ai-python\u002F13.pytorch-intro\u002F01.tensors-and-autograd",{"title":3905,"path":3906,"stem":3907},"Побудова та тренування нейронних мереж у PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fbuilding-and-training","16.ai-python\u002F13.pytorch-intro\u002F02.building-and-training",{"title":3909,"path":3910,"stem":3911},"Робота з даними та регуляризація в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fdata-and-regularization","16.ai-python\u002F13.pytorch-intro\u002F03.data-and-regularization",{"title":3913,"path":3914,"stem":3915},"Просунуті теми PyTorch — GPU, оптимізація та deployment","\u002Fai-python\u002Fpytorch-intro\u002Fadvanced-topics","16.ai-python\u002F13.pytorch-intro\u002F04.advanced-topics",{"title":3917,"path":3918,"stem":3919,"children":3920,"page":59},"Activation Functions Heart Disease","\u002Fai-python\u002Factivation-functions-heart-disease","16.ai-python\u002F14.activation-functions-heart-disease",[3921,3925],{"title":3922,"path":3923,"stem":3924},"Функції активації та побудова нейронної мережі для передбачення вад серця","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fheart-disease-prediction","16.ai-python\u002F14.activation-functions-heart-disease\u002F01.heart-disease-prediction",{"title":3926,"path":3927,"stem":3928},"Бонус — Повний приклад Student Performance Prediction","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fstudent-performance-bonus","16.ai-python\u002F14.activation-functions-heart-disease\u002F02.student-performance-bonus",{"title":3930,"path":3931,"stem":3932,"children":3933,"page":59},"Cnn Image Classification","\u002Fai-python\u002Fcnn-image-classification","16.ai-python\u002F15.cnn-image-classification",[3934,3938,3942,3946],{"title":3935,"path":3936,"stem":3937},"Основи згорткових нейронних мереж — чому не MLP?","\u002Fai-python\u002Fcnn-image-classification\u002Fcnn-fundamentals","16.ai-python\u002F15.cnn-image-classification\u002F01.cnn-fundamentals",{"title":3939,"path":3940,"stem":3941},"Практична імплементація CNN для класифікації MNIST","\u002Fai-python\u002Fcnn-image-classification\u002Fmnist-classification","16.ai-python\u002F15.cnn-image-classification\u002F02.mnist-classification",{"title":3943,"path":3944,"stem":3945},"Глибші CNN та аугментація даних для CIFAR-10","\u002Fai-python\u002Fcnn-image-classification\u002Fcifar10-and-data-augmentation","16.ai-python\u002F15.cnn-image-classification\u002F03.cifar10-and-data-augmentation",{"title":3947,"path":3948,"stem":3949},"Transfer Learning та візуалізація внутрішніх представлень CNN","\u002Fai-python\u002Fcnn-image-classification\u002Ftransfer-learning-and-visualization","16.ai-python\u002F15.cnn-image-classification\u002F04.transfer-learning-and-visualization",{"title":3951,"path":3952,"stem":3953,"children":3954,"page":59},"Batching Normalization Deep Networks","\u002Fai-python\u002Fbatching-normalization-deep-networks","16.ai-python\u002F16.batching-normalization-deep-networks",[3955,3959,3963,3967,3971,3975,3979],{"title":3956,"path":3957,"stem":3958},"Mini-batch Gradient Descent та ефективна обробка даних","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fmini-batch-gradient-descent","16.ai-python\u002F16.batching-normalization-deep-networks\u002F01.mini-batch-gradient-descent",{"title":3960,"path":3961,"stem":3962},"Ініціалізація ваг — фундамент стабільного навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fweight-initialization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F02.weight-initialization",{"title":3964,"path":3965,"stem":3966},"Batch Normalization — прорив у глибокому навчанні","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fbatch-normalization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F03.batch-normalization",{"title":3968,"path":3969,"stem":3970},"Dropout та комбіновані стратегії регуляризації","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdropout-and-regularization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F04.dropout-and-regularization",{"title":3972,"path":3973,"stem":3974},"Проєктування глибоких мереж — від теорії до практики","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdeep-networks-architectures","16.ai-python\u002F16.batching-normalization-deep-networks\u002F05.deep-networks-architectures",{"title":3976,"path":3977,"stem":3978},"Планування learning rate — коли та як зменшувати крок навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Flearning-rate-scheduling","16.ai-python\u002F16.batching-normalization-deep-networks\u002F06.learning-rate-scheduling",{"title":3980,"path":3981,"stem":3982},"Підсумковий проєкт — побудова сучасного класифікатора зображень","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Ffinal-project-deep-classifier","16.ai-python\u002F16.batching-normalization-deep-networks\u002F07.final-project-deep-classifier",{"title":3984,"icon":658,"path":3985,"stem":3986,"children":3987,"page":59},"Клієнт-серверна архітектура","\u002Fclient-server-architecture","17.client-server-architecture",[3988,3992,3996,4000,4004,4008,4012,4016,4020,4024,4028,4032,4036,4040,4044,4048,4052,4056],{"title":3989,"path":3990,"stem":3991},"Архітектура клієнт-серверних систем та основи Go","\u002Fclient-server-architecture\u002Fclient-server-architecture-and-go","17.client-server-architecture\u002F01.client-server-architecture-and-go",{"title":3993,"path":3994,"stem":3995},"Система типів та модель пам’яті мови Go","\u002Fclient-server-architecture\u002Ftype-system-and-memory-model","17.client-server-architecture\u002F02.type-system-and-memory-model",{"title":3997,"path":3998,"stem":3999},"Інтерфейси та модель конкурентності мови Go","\u002Fclient-server-architecture\u002Finterfaces-and-concurrency-model","17.client-server-architecture\u002F03.interfaces-and-concurrency-model",{"title":4001,"path":4002,"stem":4003},"Сокетне програмування та протокол TCP у Go","\u002Fclient-server-architecture\u002Ftcp-socket-programming","17.client-server-architecture\u002F04.tcp-socket-programming",{"title":4005,"path":4006,"stem":4007},"Протокол UDP та датаграмна передача даних","\u002Fclient-server-architecture\u002Fudp-datagram-transmission","17.client-server-architecture\u002F05.udp-datagram-transmission",{"title":4009,"path":4010,"stem":4011},"Криптографічний захист каналів зв","\u002Fclient-server-architecture\u002Ftls-cryptographic-channel-protection","17.client-server-architecture\u002F06.tls-cryptographic-channel-protection",{"title":4013,"path":4014,"stem":4015},"Прикладні мережеві протоколи DNS та SMTP","\u002Fclient-server-architecture\u002Fdns-smtp-application-protocols","17.client-server-architecture\u002F07.dns-smtp-application-protocols",{"title":4017,"path":4018,"stem":4019},"Протокол HTTP та стандартний вебсервер Go","\u002Fclient-server-architecture\u002Fhttp-protocol-and-web-server","17.client-server-architecture\u002F08.http-protocol-and-web-server",{"title":4021,"path":4022,"stem":4023},"Проєктування REST API та маршрутизація засобами Chi","\u002Fclient-server-architecture\u002Frest-api-design-and-chi-routing","17.client-server-architecture\u002F09.rest-api-design-and-chi-routing",{"title":4025,"path":4026,"stem":4027},"Лекція 10. Шарувата архітектура та конвеєри обробки запитів","\u002Fclient-server-architecture\u002Flayered-architecture-and-middleware-pipelines","17.client-server-architecture\u002F10.layered-architecture-and-middleware-pipelines",{"title":4029,"path":4030,"stem":4031},"Лекція 11. Архітектура та маршрутизація фреймворку Gin","\u002Fclient-server-architecture\u002Fgin-framework-architecture-and-routing","17.client-server-architecture\u002F11.gin-framework-architecture-and-routing",{"title":4033,"path":4034,"stem":4035},"Лекція 12. Валідація даних, безпека та документування у Gin","\u002Fclient-server-architecture\u002Fdata-validation-security-and-documentation-in-gin","17.client-server-architecture\u002F12.data-validation-security-and-documentation-in-gin",{"title":4037,"path":4038,"stem":4039},"Лекція 13. Взаємодія з реляційними СУБД та технології ORM","\u002Fclient-server-architecture\u002Frelational-databases-and-orm","17.client-server-architecture\u002F13.relational-databases-and-orm",{"title":4041,"path":4042,"stem":4043},"Потокова передача даних та протокол WebSocket","\u002Fclient-server-architecture\u002Fstreaming-data-and-websockets","17.client-server-architecture\u002F14.streaming-data-and-websockets",{"title":4045,"path":4046,"stem":4047},"Міжсервісна взаємодія на основі протоколу gRPC","\u002Fclient-server-architecture\u002Fgrpc-inter-service-communication","17.client-server-architecture\u002F15.grpc-inter-service-communication",{"title":4049,"path":4050,"stem":4051},"Асинхронний обмін повідомленнями та протоколи черг","\u002Fclient-server-architecture\u002Fasynchronous-message-exchange-and-queue-protocols","17.client-server-architecture\u002F16.asynchronous-message-exchange-and-queue-protocols",{"title":4053,"path":4054,"stem":4055},"Протоколи потокового медіа та технологія WebRTC","\u002Fclient-server-architecture\u002Fstreaming-media-protocols-and-webrtc","17.client-server-architecture\u002F17.streaming-media-protocols-and-webrtc",{"title":4057,"path":4058,"stem":4059},"Моніторинг, безпека та контейнеризація застосунків","\u002Fclient-server-architecture\u002Fmonitoring-security-and-containerization","17.client-server-architecture\u002F18.monitoring-security-and-containerization",{"title":4061,"icon":2118,"path":4062,"stem":4063,"children":4064,"page":59},"Розробка WEB-застосувань","\u002Fweb-development","18.web-development",[4065,4110,4148,4177,4206,4263,4313,4407,4473,4555,4588,4616,4658,4704,4747],{"title":4066,"icon":658,"path":4067,"stem":4068,"children":4069,"page":59},"Архітектура комп'ютерних мереж та мережеві протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols","18.web-development\u002F01.network-architecture-and-protocols",[4070,4074,4078,4082,4086,4090,4094,4098,4102,4106],{"title":4071,"path":4072,"stem":4073},"Еволюція веброзробки та модель клієнт-сервер","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fweb-evolution-client-server","18.web-development\u002F01.network-architecture-and-protocols\u002F01.web-evolution-client-server",{"title":4075,"path":4076,"stem":4077},"Еталонна модель OSI","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fosi-model","18.web-development\u002F01.network-architecture-and-protocols\u002F02.osi-model",{"title":4079,"path":4080,"stem":4081},"Стек протоколів TCP\u002FIP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-ip-stack","18.web-development\u002F01.network-architecture-and-protocols\u002F03.tcp-ip-stack",{"title":4083,"path":4084,"stem":4085},"IP-адресація, порти та сокети","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fip-addressing-ports-sockets","18.web-development\u002F01.network-architecture-and-protocols\u002F04.ip-addressing-ports-sockets",{"title":4087,"path":4088,"stem":4089},"Протоколи TCP та UDP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-udp-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F05.tcp-udp-protocols",{"title":4091,"path":4092,"stem":4093},"Система доменних імен DNS","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fdns-system","18.web-development\u002F01.network-architecture-and-protocols\u002F06.dns-system",{"title":4095,"path":4096,"stem":4097},"Протокол SMTP та поштові протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fsmtp-email-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F07.smtp-email-protocols",{"title":4099,"path":4100,"stem":4101},"Протокол WebSocket","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fwebsocket-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F08.websocket-protocol",{"title":4103,"path":4104,"stem":4105},"Протокол SSH","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fssh-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F09.ssh-protocol",{"title":4107,"path":4108,"stem":4109},"Огляд сучасних серверних технологій","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fmodern-backend-technologies","18.web-development\u002F01.network-architecture-and-protocols\u002F10.modern-backend-technologies",{"title":4111,"icon":4112,"path":4113,"stem":4114,"children":4115,"page":59},"Протокол HTTP та захищена передача даних HTTPS","i-lucide-lock","\u002Fweb-development\u002Fhttp-and-https","18.web-development\u002F02.http-and-https",[4116,4120,4124,4128,4132,4136,4140,4144],{"title":4117,"path":4118,"stem":4119},"Вступ до протоколу HTTP та еволюція веб-технологій","\u002Fweb-development\u002Fhttp-and-https\u002Fintroduction-and-evolution","18.web-development\u002F02.http-and-https\u002F01.introduction-and-evolution",{"title":4121,"path":4122,"stem":4123},"Анатомія HTTP-запиту","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-request-structure","18.web-development\u002F02.http-and-https\u002F02.http-request-structure",{"title":4125,"path":4126,"stem":4127},"Анатомія HTTP-відповіді","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-response-structure","18.web-development\u002F02.http-and-https\u002F03.http-response-structure",{"title":4129,"path":4130,"stem":4131},"Методи HTTP та їхня семантика","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-methods","18.web-development\u002F02.http-and-https\u002F04.http-methods",{"title":4133,"path":4134,"stem":4135},"Коди статусу HTTP та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-status-codes","18.web-development\u002F02.http-and-https\u002F05.http-status-codes",{"title":4137,"path":4138,"stem":4139},"HTTP-заголовки та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-headers","18.web-development\u002F02.http-and-https\u002F06.http-headers",{"title":4141,"path":4142,"stem":4143},"CORS та механізми безпеки HTTP","\u002Fweb-development\u002Fhttp-and-https\u002Fcors-and-security","18.web-development\u002F02.http-and-https\u002F07.cors-and-security",{"title":4145,"path":4146,"stem":4147},"HTTPS та криптографічні основи TLS","\u002Fweb-development\u002Fhttp-and-https\u002Fhttps-and-tls","18.web-development\u002F02.http-and-https\u002F08.https-and-tls",{"title":4149,"icon":2498,"path":4150,"stem":4151,"children":4152,"page":59},"Система типів мови TypeScript","\u002Fweb-development\u002Ftypescript-type-system","18.web-development\u002F03.typescript-type-system",[4153,4157,4161,4165,4169,4173],{"title":4154,"path":4155,"stem":4156},"Знайомство з TypeScript Compiler","\u002Fweb-development\u002Ftypescript-type-system\u002Fintroduction-compiler-config","18.web-development\u002F03.typescript-type-system\u002F01.introduction-compiler-config",{"title":4158,"path":4159,"stem":4160},"Примітивні типи даних: string, number, boolean","\u002Fweb-development\u002Ftypescript-type-system\u002Fprimitive-special-types","18.web-development\u002F03.typescript-type-system\u002F02.primitive-special-types",{"title":4162,"path":4163,"stem":4164},"Масиви, кортежі та об","\u002Fweb-development\u002Ftypescript-type-system\u002Farrays-tuples-objects","18.web-development\u002F03.typescript-type-system\u002F03.arrays-tuples-objects",{"title":4166,"path":4167,"stem":4168},"Псевдоніми типів, Union типи, Intersection типи та літеральні типи","\u002Fweb-development\u002Ftypescript-type-system\u002Funion-intersection-literals","18.web-development\u002F03.typescript-type-system\u002F04.union-intersection-literals",{"title":4170,"path":4171,"stem":4172},"Type Narrowing (звуження типів)","\u002Fweb-development\u002Ftypescript-type-system\u002Ftype-narrowing","18.web-development\u002F03.typescript-type-system\u002F05.type-narrowing",{"title":4174,"path":4175,"stem":4176},"Типізація функцій","\u002Fweb-development\u002Ftypescript-type-system\u002Ffunctions-typing","18.web-development\u002F03.typescript-type-system\u002F06.functions-typing",{"title":4178,"icon":2498,"path":4179,"stem":4180,"children":4181,"page":59},"Розширені засоби мови TypeScript","\u002Fweb-development\u002Ftypescript-advanced","18.web-development\u002F04.typescript-advanced",[4182,4186,4190,4194,4198,4202],{"title":4183,"path":4184,"stem":4185},"Interfaces та Classes","\u002Fweb-development\u002Ftypescript-advanced\u002Finterfaces-classes","18.web-development\u002F04.typescript-advanced\u002F01.interfaces-classes",{"title":4187,"path":4188,"stem":4189},"Основи Generic типів","\u002Fweb-development\u002Ftypescript-advanced\u002Fgenerics-fundamentals","18.web-development\u002F04.typescript-advanced\u002F02.generics-fundamentals",{"title":4191,"path":4192,"stem":4193},"Enums та Decorators","\u002Fweb-development\u002Ftypescript-advanced\u002Fenums-decorators","18.web-development\u002F04.typescript-advanced\u002F03.enums-decorators",{"title":4195,"path":4196,"stem":4197},"Utility Types","\u002Fweb-development\u002Ftypescript-advanced\u002Futility-types","18.web-development\u002F04.typescript-advanced\u002F04.utility-types",{"title":4199,"path":4200,"stem":4201},"Mapped та Conditional Types","\u002Fweb-development\u002Ftypescript-advanced\u002Fmapped-conditional-types","18.web-development\u002F04.typescript-advanced\u002F05.mapped-conditional-types",{"title":4203,"path":4204,"stem":4205},"Модулі та Strict Mode","\u002Fweb-development\u002Ftypescript-advanced\u002Fmodules-strict-mode","18.web-development\u002F04.typescript-advanced\u002F06.modules-strict-mode",{"title":4207,"icon":4208,"path":4209,"stem":4210,"children":4211,"page":59},"Платформа Node.js як середовище виконання","i-devicon-nodejs","\u002Fweb-development\u002Fnodejs-platform","18.web-development\u002F05.nodejs-platform",[4212,4216,4220,4224,4228,4232,4236,4240,4244,4248,4252,4255,4259],{"title":4213,"path":4214,"stem":4215},"Що таке Node.js та його архітектура","\u002Fweb-development\u002Fnodejs-platform\u002Fwhat-is-nodejs","18.web-development\u002F05.nodejs-platform\u002F01.what-is-nodejs",{"title":4217,"path":4218,"stem":4219},"Event Loop — серце Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fevent-loop","18.web-development\u002F05.nodejs-platform\u002F02.event-loop",{"title":4221,"path":4222,"stem":4223},"Модульні системи: CommonJS vs ES Modules","\u002Fweb-development\u002Fnodejs-platform\u002Fmodule-systems","18.web-development\u002F05.nodejs-platform\u002F03.module-systems",{"title":4225,"path":4226,"stem":4227},"npm та package.json","\u002Fweb-development\u002Fnodejs-platform\u002Fnpm-package-json","18.web-development\u002F05.nodejs-platform\u002F04.npm-package-json",{"title":4229,"path":4230,"stem":4231},"Глобальні об\\","\u002Fweb-development\u002Fnodejs-platform\u002Fglobal-objects","18.web-development\u002F05.nodejs-platform\u002F05.global-objects",{"title":4233,"path":4234,"stem":4235},"Вбудований модуль fs (File System)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-fs","18.web-development\u002F05.nodejs-platform\u002F06.built-in-modules-fs",{"title":4237,"path":4238,"stem":4239},"Вбудований модуль path","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-path","18.web-development\u002F05.nodejs-platform\u002F07.built-in-modules-path",{"title":4241,"path":4242,"stem":4243},"Вбудований модуль http","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-http","18.web-development\u002F05.nodejs-platform\u002F08.built-in-modules-http",{"title":4245,"path":4246,"stem":4247},"Streams — потоки даних у Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fstreams","18.web-development\u002F05.nodejs-platform\u002F09.streams",{"title":4249,"path":4250,"stem":4251},"Вбудований модуль util (Utilities)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-util","18.web-development\u002F05.nodejs-platform\u002F10.built-in-modules-util",{"title":3141,"path":4253,"stem":4254},"\u002Fweb-development\u002Fnodejs-platform\u002Fenvironment-variables","18.web-development\u002F05.nodejs-platform\u002F11.environment-variables",{"title":4256,"path":4257,"stem":4258},"Інструменти налагодження та розробки","\u002Fweb-development\u002Fnodejs-platform\u002Fdebugging-tools","18.web-development\u002F05.nodejs-platform\u002F12.debugging-tools",{"title":4260,"path":4261,"stem":4262},"Продуктивність та Best Practices","\u002Fweb-development\u002Fnodejs-platform\u002Fperformance-best-practices","18.web-development\u002F05.nodejs-platform\u002F13.performance-best-practices",{"title":4264,"icon":4265,"path":4266,"stem":4267,"children":4268,"page":59},"Асинхронне програмування у Node.js","i-lucide-clock","\u002Fweb-development\u002Fasync-programming-nodejs","18.web-development\u002F06.async-programming-nodejs",[4269,4273,4277,4281,4285,4289,4293,4297,4301,4305,4309],{"title":4270,"path":4271,"stem":4272},"Синхронний vs асинхронний код","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fsync-vs-async","18.web-development\u002F06.async-programming-nodejs\u002F01.sync-vs-async",{"title":4274,"path":4275,"stem":4276},"Callbacks — перша парадигма асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fcallbacks","18.web-development\u002F06.async-programming-nodejs\u002F02.callbacks",{"title":4278,"path":4279,"stem":4280},"Promises — стандарт асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromises","18.web-development\u002F06.async-programming-nodejs\u002F03.promises",{"title":4282,"path":4283,"stem":4284},"Promise комбінатори","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromise-combinators","18.web-development\u002F06.async-programming-nodejs\u002F04.promise-combinators",{"title":4286,"path":4287,"stem":4288},"Async\u002FAwait — синтаксичний цукор над Promises","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fasync-await","18.web-development\u002F06.async-programming-nodejs\u002F05.async-await",{"title":4290,"path":4291,"stem":4292},"Паралельне vs послідовне виконання","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fparallel-vs-sequential","18.web-development\u002F06.async-programming-nodejs\u002F06.parallel-vs-sequential",{"title":4294,"path":4295,"stem":4296},"EventEmitter — подієва модель Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fevent-emitter","18.web-development\u002F06.async-programming-nodejs\u002F07.event-emitter",{"title":4298,"path":4299,"stem":4300},"Worker Threads — багатопотоковість у Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fworker-threads","18.web-development\u002F06.async-programming-nodejs\u002F08.worker-threads",{"title":4302,"path":4303,"stem":4304},"Child Processes — запуск зовнішніх процесів","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fchild-processes","18.web-development\u002F06.async-programming-nodejs\u002F09.child-processes",{"title":4306,"path":4307,"stem":4308},"Обробка помилок у асинхронному коді","\u002Fweb-development\u002Fasync-programming-nodejs\u002Ferror-handling","18.web-development\u002F06.async-programming-nodejs\u002F10.error-handling",{"title":4310,"path":4311,"stem":4312},"Порівняння Node.js фреймворків","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fnodejs-frameworks","18.web-development\u002F06.async-programming-nodejs\u002F11.nodejs-frameworks",{"title":4314,"icon":4315,"path":4316,"stem":4317,"children":4318,"page":59},"Тема 7. Фреймворк NestJS. Контролери та маршрутизація","i-lucide-route","\u002Fweb-development\u002Fnestjs-controllers-routing","18.web-development\u002F07.nestjs-controllers-routing",[4319,4323,4327,4331,4335,4339,4343,4347,4351,4355,4359,4363,4367,4371,4375,4379,4383,4387,4391,4395,4399,4403],{"title":4320,"path":4321,"stem":4322},"Філософія та архітектура NestJS","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-philosophy","18.web-development\u002F07.nestjs-controllers-routing\u002F01.nestjs-philosophy",{"title":4324,"path":4325,"stem":4326},"Три стовпи архітектури: модулі, контролери, провайдери","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fthree-pillars","18.web-development\u002F07.nestjs-controllers-routing\u002F02.three-pillars",{"title":4328,"path":4329,"stem":4330},"Інверсія керування (IoC) та ін","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fioc-and-di","18.web-development\u002F07.nestjs-controllers-routing\u002F03.ioc-and-di",{"title":4332,"path":4333,"stem":4334},"Встановлення NestJS CLI та створення проєкту","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-setup","18.web-development\u002F07.nestjs-controllers-routing\u002F04.nestjs-cli-setup",{"title":4336,"path":4337,"stem":4338},"Структура проєкту NestJS та конвенції","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fproject-structure","18.web-development\u002F07.nestjs-controllers-routing\u002F05.project-structure",{"title":4340,"path":4341,"stem":4342},"Контролери: основи маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontrollers-basics","18.web-development\u002F07.nestjs-controllers-routing\u002F06.controllers-basics",{"title":4344,"path":4345,"stem":4346},"Декоратори маршрутизації HTTP-методів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F07.route-decorators",{"title":4348,"path":4349,"stem":4350},"Параметри маршруту та декоратор @Param","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F08.route-parameters",{"title":4352,"path":4353,"stem":4354},"Query-параметри та декоратор @Query","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fquery-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F09.query-parameters",{"title":4356,"path":4357,"stem":4358},"Тіло запиту та декоратор @Body","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-body","18.web-development\u002F07.nestjs-controllers-routing\u002F10.request-body",{"title":4360,"path":4361,"stem":4362},"Робота з заголовками запиту та відповіді","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fheaders-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F11.headers-decorators",{"title":4364,"path":4365,"stem":4366},"Data Transfer Objects (DTO): визначення та призначення","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fdto-introduction","18.web-development\u002F07.nestjs-controllers-routing\u002F12.dto-introduction",{"title":4368,"path":4369,"stem":4370},"Об'єкти Request та Response","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-response-objects","18.web-development\u002F07.nestjs-controllers-routing\u002F13.request-response-objects",{"title":4372,"path":4373,"stem":4374},"HTTP-статус коди та декоратор @HttpCode","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fhttp-status-codes","18.web-development\u002F07.nestjs-controllers-routing\u002F14.http-status-codes",{"title":4376,"path":4377,"stem":4378},"Перенаправлення (Redirects) та декоратор @Redirect","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fredirects","18.web-development\u002F07.nestjs-controllers-routing\u002F15.redirects",{"title":4380,"path":4381,"stem":4382},"Асинхронні обробники та Observables","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fasync-handlers","18.web-development\u002F07.nestjs-controllers-routing\u002F16.async-handlers",{"title":4384,"path":4385,"stem":4386},"Маршрутизація за піддоменами та версіонування API","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fsub-domain-routing","18.web-development\u002F07.nestjs-controllers-routing\u002F17.sub-domain-routing",{"title":4388,"path":4389,"stem":4390},"Області видимості контролерів (Scopes)","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontroller-scopes","18.web-development\u002F07.nestjs-controllers-routing\u002F18.controller-scopes",{"title":4392,"path":4393,"stem":4394},"Основні команди NestJS CLI","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-commands","18.web-development\u002F07.nestjs-controllers-routing\u002F19.nestjs-cli-commands",{"title":4396,"path":4397,"stem":4398},"Практичний приклад: створення CRUD-контролера","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcrud-example","18.web-development\u002F07.nestjs-controllers-routing\u002F20.crud-example",{"title":4400,"path":4401,"stem":4402},"Тестування контролерів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Ftesting-controllers","18.web-development\u002F07.nestjs-controllers-routing\u002F21.testing-controllers",{"title":4404,"path":4405,"stem":4406},"Best Practices для контролерів та маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fbest-practices","18.web-development\u002F07.nestjs-controllers-routing\u002F22.best-practices",{"title":4408,"icon":4409,"path":4410,"stem":4411,"children":4412,"page":59},"Тема 8. Провайдери, сервіси та модульна система NestJS","i-lucide-package","\u002Fweb-development\u002Fnestjs-providers-modules","18.web-development\u002F08.nestjs-providers-modules",[4413,4417,4421,4425,4429,4433,4437,4441,4445,4449,4453,4457,4461,4465,4469],{"title":4414,"path":4415,"stem":4416},"Концепція провайдерів у NestJS","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fproviders-concept","18.web-development\u002F08.nestjs-providers-modules\u002F01.providers-concept",{"title":4418,"path":4419,"stem":4420},"Сервіси: інкапсуляція бізнес-логіки","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fservices-business-logic","18.web-development\u002F08.nestjs-providers-modules\u002F02.services-business-logic",{"title":4422,"path":4423,"stem":4424},"Практика ін","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdependency-injection-practice","18.web-development\u002F08.nestjs-providers-modules\u002F03.dependency-injection-practice",{"title":4426,"path":4427,"stem":4428},"Custom Providers: useValue, useClass, useFactory, useExisting","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcustom-providers","18.web-development\u002F08.nestjs-providers-modules\u002F04.custom-providers",{"title":4430,"path":4431,"stem":4432},"Injection Tokens: рядкові та символьні токени","\u002Fweb-development\u002Fnestjs-providers-modules\u002Finjection-tokens","18.web-development\u002F08.nestjs-providers-modules\u002F05.injection-tokens",{"title":4434,"path":4435,"stem":4436},"Опціональні провайдери та декоратор @Optional","\u002Fweb-development\u002Fnestjs-providers-modules\u002Foptional-providers","18.web-development\u002F08.nestjs-providers-modules\u002F07.optional-providers",{"title":4438,"path":4439,"stem":4440},"Структура модулів: imports, controllers, providers, exports","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodules-structure","18.web-development\u002F08.nestjs-providers-modules\u002F08.modules-structure",{"title":4442,"path":4443,"stem":4444},"Feature Modules: ізоляція функціональності","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ffeature-modules","18.web-development\u002F08.nestjs-providers-modules\u002F09.feature-modules",{"title":4446,"path":4447,"stem":4448},"Shared Modules: перевикористання провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fshared-modules","18.web-development\u002F08.nestjs-providers-modules\u002F10.shared-modules",{"title":4450,"path":4451,"stem":4452},"Global Modules та декоратор @Global","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fglobal-modules","18.web-development\u002F08.nestjs-providers-modules\u002F11.global-modules",{"title":4454,"path":4455,"stem":4456},"Dynamic Modules: конфігурація під час виконання","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdynamic-modules","18.web-development\u002F08.nestjs-providers-modules\u002F12.dynamic-modules",{"title":4458,"path":4459,"stem":4460},"Циклічні залежності та forwardRef","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcircular-dependencies","18.web-development\u002F08.nestjs-providers-modules\u002F13.circular-dependencies",{"title":4462,"path":4463,"stem":4464},"Lifecycle Hooks: хуки життєвого циклу","\u002Fweb-development\u002Fnestjs-providers-modules\u002Flifecycle-hooks","18.web-development\u002F08.nestjs-providers-modules\u002F14.lifecycle-hooks",{"title":4466,"path":4467,"stem":4468},"ModuleRef: динамічний доступ до провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodule-reference","18.web-development\u002F08.nestjs-providers-modules\u002F15.module-reference",{"title":4470,"path":4471,"stem":4472},"Тестування сервісів та провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ftesting-services","18.web-development\u002F08.nestjs-providers-modules\u002F16.testing-services",{"title":4474,"icon":4475,"path":4476,"stem":4477,"children":4478,"page":59},"Тема 9. Валідація даних та конвеєр обробки запитів у NestJS","i-lucide-filter","\u002Fweb-development\u002Fnestjs-validation-pipeline","18.web-development\u002F09.nestjs-validation-pipeline",[4479,4483,4487,4491,4495,4499,4503,4507,4511,4515,4519,4523,4527,4531,4535,4539,4543,4547,4551],{"title":4480,"path":4481,"stem":4482},"Request Pipeline: конвеєр обробки запитів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Frequest-pipeline","18.web-development\u002F09.nestjs-validation-pipeline\u002F01.request-pipeline",{"title":4484,"path":4485,"stem":4486},"Pipes: концепція трансформації та валідації","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipes-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F02.pipes-concept",{"title":4488,"path":4489,"stem":4490},"Вбудовані pipes: ParseIntPipe, ParseBoolPipe, ParseUUIDPipe","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fbuilt-in-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F03.built-in-pipes",{"title":4492,"path":4493,"stem":4494},"ValidationPipe: автоматична валідація DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fvalidation-pipe","18.web-development\u002F09.nestjs-validation-pipeline\u002F04.validation-pipe",{"title":4496,"path":4497,"stem":4498},"Декоратори class-validator для DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fclass-validator-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F05.class-validator-decorators",{"title":4500,"path":4501,"stem":4502},"Створення кастомних валідаторів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-validators","18.web-development\u002F09.nestjs-validation-pipeline\u002F06.custom-validators",{"title":4504,"path":4505,"stem":4506},"Створення власних Pipes","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F07.custom-pipes",{"title":4508,"path":4509,"stem":4510},"Основи Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-basics","18.web-development\u002F09.nestjs-validation-pipeline\u002F08.middleware-basics",{"title":4512,"path":4513,"stem":4514},"Практичні приклади Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F09.middleware-examples",{"title":4516,"path":4517,"stem":4518},"Guards: захисні перехоплювачі доступу","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fguards-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F10.guards-concept",{"title":4520,"path":4521,"stem":4522},"Створення кастомних Guards","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-guards","18.web-development\u002F09.nestjs-validation-pipeline\u002F11.custom-guards",{"title":4524,"path":4525,"stem":4526},"Interceptors: перехоплення та трансформація відповідей","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptors-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F12.interceptors-concept",{"title":4528,"path":4529,"stem":4530},"Практичні приклади Interceptors","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptor-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F13.interceptor-examples",{"title":4532,"path":4533,"stem":4534},"Exception Filters: обробка виключень","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F14.exception-filters",{"title":4536,"path":4537,"stem":4538},"Custom Exception Filters: спеціалізовані фільтри","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-exception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F15.custom-exception-filters",{"title":4540,"path":4541,"stem":4542},"Execution Context: контекст виконання","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexecution-context","18.web-development\u002F09.nestjs-validation-pipeline\u002F16.execution-context",{"title":4544,"path":4545,"stem":4546},"Custom Decorators: власні декоратори","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F17.custom-decorators",{"title":4548,"path":4549,"stem":4550},"Global Components: глобальні компоненти","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fglobal-components","18.web-development\u002F09.nestjs-validation-pipeline\u002F18.global-components",{"title":4552,"path":4553,"stem":4554},"Pipeline Best Practices: найкращі практики","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipeline-best-practices","18.web-development\u002F09.nestjs-validation-pipeline\u002F19.pipeline-best-practices",{"title":4556,"icon":2865,"path":4557,"stem":4558,"children":4559,"page":59},"Інтеграція реляційних баз даних засобами TypeORM","\u002Fweb-development\u002Ftypeorm-integration","18.web-development\u002F10.typeorm-integration",[4560,4564,4568,4572,4576,4580,4584],{"title":4561,"path":4562,"stem":4563},"Робота з базами даних у Node.js через нативні драйвери","\u002Fweb-development\u002Ftypeorm-integration\u002F01-nodejs-database-drivers","18.web-development\u002F10.typeorm-integration\u002F01-nodejs-database-drivers",{"title":4565,"path":4566,"stem":4567},"ORM та знайомство з TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F02-orm-and-typeorm-intro","18.web-development\u002F10.typeorm-integration\u002F02-orm-and-typeorm-intro",{"title":4569,"path":4570,"stem":4571},"Налаштування TypeORM у NestJS проєкті","\u002Fweb-development\u002Ftypeorm-integration\u002F03-typeorm-setup-nestjs","18.web-development\u002F10.typeorm-integration\u002F03-typeorm-setup-nestjs",{"title":4573,"path":4574,"stem":4575},"Entity класи та декоратори TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F04-entities-and-decorators","18.web-development\u002F10.typeorm-integration\u002F04-entities-and-decorators",{"title":4577,"path":4578,"stem":4579},"Repository Pattern та CRUD операції","\u002Fweb-development\u002Ftypeorm-integration\u002F05-repository-pattern-crud","18.web-development\u002F10.typeorm-integration\u002F05-repository-pattern-crud",{"title":4581,"path":4582,"stem":4583},"Пагінація та фільтрація даних","\u002Fweb-development\u002Ftypeorm-integration\u002F06-pagination-filtering","18.web-development\u002F10.typeorm-integration\u002F06-pagination-filtering",{"title":4585,"path":4586,"stem":4587},"QueryBuilder для складних запитів","\u002Fweb-development\u002Ftypeorm-integration\u002F07-query-builder","18.web-development\u002F10.typeorm-integration\u002F07-query-builder",{"title":4589,"icon":4590,"path":4591,"stem":4592,"children":4593,"page":59},"Зв'язки між сутностями, міграції та оптимізація запитів","i-lucide-git-branch","\u002Fweb-development\u002Fentity-relations-migrations","18.web-development\u002F11.entity-relations-migrations",[4594,4598,4602,4606,4610],{"title":4595,"path":4596,"stem":4597},"Зв'язки One-to-Many та Many-to-One","\u002Fweb-development\u002Fentity-relations-migrations\u002F01-one-to-many-many-to-one","18.web-development\u002F11.entity-relations-migrations\u002F01-one-to-many-many-to-one",{"title":4599,"path":4600,"stem":4601},"Зв'язки One-to-One та Many-to-Many","\u002Fweb-development\u002Fentity-relations-migrations\u002F02-one-to-one-many-to-many","18.web-development\u002F11.entity-relations-migrations\u002F02-one-to-one-many-to-many",{"title":4603,"path":4604,"stem":4605},"Керування міграціями бази даних","\u002Fweb-development\u002Fentity-relations-migrations\u002F03-migrations-management","18.web-development\u002F11.entity-relations-migrations\u002F03-migrations-management",{"title":4607,"path":4608,"stem":4609},"Транзакції у TypeORM","\u002Fweb-development\u002Fentity-relations-migrations\u002F04-transactions","18.web-development\u002F11.entity-relations-migrations\u002F04-transactions",{"title":4611,"path":4612,"stem":4613,"children":4614},"Індекси та оптимізація запитів","\u002Fweb-development\u002Fentity-relations-migrations\u002F05-indexes-optimization","18.web-development\u002F11.entity-relations-migrations\u002F05-indexes-optimization",[4615],{"title":4611,"path":4612,"stem":4613},{"title":4617,"icon":4618,"path":4619,"stem":4620,"children":4621,"page":59},"Механізми автентифікації у вебзастосунках","i-lucide-key","\u002Fweb-development\u002Fauthentication","18.web-development\u002F12.authentication",[4622,4626,4630,4634,4638,4642,4646,4650,4654],{"title":4623,"path":4624,"stem":4625},"Автентифікація vs Авторизація","\u002Fweb-development\u002Fauthentication\u002F01-authentication-vs-authorization","18.web-development\u002F12.authentication\u002F01-authentication-vs-authorization",{"title":4627,"path":4628,"stem":4629},"Стратегії автентифікації","\u002Fweb-development\u002Fauthentication\u002F02-authentication-strategies","18.web-development\u002F12.authentication\u002F02-authentication-strategies",{"title":4631,"path":4632,"stem":4633},"Автентифікація на основі сесій","\u002Fweb-development\u002Fauthentication\u002F03-session-based-authentication","18.web-development\u002F12.authentication\u002F03-session-based-authentication",{"title":4635,"path":4636,"stem":4637},"Структура JSON Web Token (JWT)","\u002Fweb-development\u002Fauthentication\u002F04-jwt-structure","18.web-development\u002F12.authentication\u002F04-jwt-structure",{"title":4639,"path":4640,"stem":4641},"Інтеграція JWT у NestJS","\u002Fweb-development\u002Fauthentication\u002F05-nestjs-jwt-integration","18.web-development\u002F12.authentication\u002F05-nestjs-jwt-integration",{"title":4643,"path":4644,"stem":4645},"Passport.js стратегії у NestJS","\u002Fweb-development\u002Fauthentication\u002F06-passport-strategies","18.web-development\u002F12.authentication\u002F06-passport-strategies",{"title":4647,"path":4648,"stem":4649},"Безпечне зберігання паролів: хешування та криптографічний захист","\u002Fweb-development\u002Fauthentication\u002F07-password-hashing","18.web-development\u002F12.authentication\u002F07-password-hashing",{"title":4651,"path":4652,"stem":4653},"Refresh Token та безпечне оновлення доступу","\u002Fweb-development\u002Fauthentication\u002F08-refresh-tokens","18.web-development\u002F12.authentication\u002F08-refresh-tokens",{"title":4655,"path":4656,"stem":4657},"OAuth 2.0 та OpenID Connect: делегована автентифікація","\u002Fweb-development\u002Fauthentication\u002F09-oauth2-openid","18.web-development\u002F12.authentication\u002F09-oauth2-openid",{"title":4659,"icon":4660,"path":4661,"stem":4662,"children":4663,"page":59},"Авторизація та безпека серверних застосунків","i-lucide-shield","\u002Fweb-development\u002Fauthorization-security","18.web-development\u002F13.authorization-security",[4664,4668,4672,4676,4680,4684,4688,4692,4696,4700],{"title":4665,"path":4666,"stem":4667},"Моделі авторизації","\u002Fweb-development\u002Fauthorization-security\u002F01-authorization-models","18.web-development\u002F13.authorization-security\u002F01-authorization-models",{"title":4669,"path":4670,"stem":4671},"Реалізація RBAC у NestJS","\u002Fweb-development\u002Fauthorization-security\u002F02-rbac-implementation","18.web-development\u002F13.authorization-security\u002F02-rbac-implementation",{"title":4673,"path":4674,"stem":4675},"Permission-Based Access Control","\u002Fweb-development\u002Fauthorization-security\u002F03-permission-based-access","18.web-development\u002F13.authorization-security\u002F03-permission-based-access",{"title":4677,"path":4678,"stem":4679},"ABAC та бібліотека CASL","\u002Fweb-development\u002Fauthorization-security\u002F04-abac-casl","18.web-development\u002F13.authorization-security\u002F04-abac-casl",{"title":4681,"path":4682,"stem":4683},"Кастомні декоратори та метадані","\u002Fweb-development\u002Fauthorization-security\u002F05-custom-decorators-metadata","18.web-development\u002F13.authorization-security\u002F05-custom-decorators-metadata",{"title":4685,"path":4686,"stem":4687},"Конфігурація CORS","\u002Fweb-development\u002Fauthorization-security\u002F06-cors-configuration","18.web-development\u002F13.authorization-security\u002F06-cors-configuration",{"title":4689,"path":4690,"stem":4691},"Захист через HTTP Security Headers (Helmet)","\u002Fweb-development\u002Fauthorization-security\u002F07-helmet-security-headers","18.web-development\u002F13.authorization-security\u002F07-helmet-security-headers",{"title":4693,"path":4694,"stem":4695},"Rate Limiting та Throttling","\u002Fweb-development\u002Fauthorization-security\u002F08-rate-limiting-throttling","18.web-development\u002F13.authorization-security\u002F08-rate-limiting-throttling",{"title":4697,"path":4698,"stem":4699},"Захист від поширених атак","\u002Fweb-development\u002Fauthorization-security\u002F09-common-attacks-protection","18.web-development\u002F13.authorization-security\u002F09-common-attacks-protection",{"title":4701,"path":4702,"stem":4703},"HTTPS у продакшені","\u002Fweb-development\u002Fauthorization-security\u002F10-https-production","18.web-development\u002F13.authorization-security\u002F10-https-production",{"title":4705,"icon":871,"path":4706,"stem":4707,"children":4708,"page":59},"Комунікація у реальному часі, нотифікації та фонові задачі","\u002Fweb-development\u002Frealtime-notifications-jobs","18.web-development\u002F14.realtime-notifications-jobs",[4709,4713,4717,4721,4725,4729,4732,4735,4739,4743],{"title":4710,"path":4711,"stem":4712},"Методи комунікації у реальному часі","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F01-realtime-communication-methods","18.web-development\u002F14.realtime-notifications-jobs\u002F01-realtime-communication-methods",{"title":4714,"path":4715,"stem":4716},"WebSocket Gateway у NestJS","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F02-websocket-gateway","18.web-development\u002F14.realtime-notifications-jobs\u002F02-websocket-gateway",{"title":4718,"path":4719,"stem":4720},"Lifecycle та Rooms у WebSocket","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F03-websocket-lifecycle-rooms","18.web-development\u002F14.realtime-notifications-jobs\u002F03-websocket-lifecycle-rooms",{"title":4722,"path":4723,"stem":4724},"Server-Sent Events (SSE)","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F04-server-sent-events","18.web-development\u002F14.realtime-notifications-jobs\u002F04-server-sent-events",{"title":4726,"path":4727,"stem":4728},"Архітектура системи нотифікацій","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F05-notification-system","18.web-development\u002F14.realtime-notifications-jobs\u002F05-notification-system",{"title":904,"path":4730,"stem":4731},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F06-email-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F06-email-notifications",{"title":900,"path":4733,"stem":4734},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F07-web-push-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F07-web-push-notifications",{"title":4736,"path":4737,"stem":4738},"Фонові задачі та черги","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F08-background-jobs-queues","18.web-development\u002F14.realtime-notifications-jobs\u002F08-background-jobs-queues",{"title":4740,"path":4741,"stem":4742},"Планувальники та Cron jobs","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F09-schedulers-cron","18.web-development\u002F14.realtime-notifications-jobs\u002F09-schedulers-cron",{"title":4744,"path":4745,"stem":4746},"Практичні сценарії застосування","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F10-practical-scenarios","18.web-development\u002F14.realtime-notifications-jobs\u002F10-practical-scenarios",{"title":4748,"icon":4749,"path":4750,"stem":4751,"children":4752,"page":59},"Тестування, документування та розгортання застосунків","i-lucide-rocket","\u002Fweb-development\u002Ftesting-documentation-deployment","18.web-development\u002F15.testing-documentation-deployment",[4753,4757,4761,4765,4769,4773,4777,4781,4785,4789],{"title":4754,"path":4755,"stem":4756},"Піраміда тестування та стратегія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F01-testing-pyramid-strategy","18.web-development\u002F15.testing-documentation-deployment\u002F01-testing-pyramid-strategy",{"title":4758,"path":4759,"stem":4760},"Основи Jest у NestJS","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F02-jest-nestjs-basics","18.web-development\u002F15.testing-documentation-deployment\u002F02-jest-nestjs-basics",{"title":4762,"path":4763,"stem":4764},"Unit-тестування сервісів","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F03-unit-testing-services","18.web-development\u002F15.testing-documentation-deployment\u002F03-unit-testing-services",{"title":4766,"path":4767,"stem":4768},"E2E тестування та покриття коду","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F04-e2e-testing-coverage","18.web-development\u002F15.testing-documentation-deployment\u002F04-e2e-testing-coverage",{"title":4770,"path":4771,"stem":4772},"Swagger, OpenAPI, Scalar та Arazzo","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F05-swagger-openapi","18.web-development\u002F15.testing-documentation-deployment\u002F05-swagger-openapi",{"title":4774,"path":4775,"stem":4776},"Керування конфігурацією","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F06-configuration-management","18.web-development\u002F15.testing-documentation-deployment\u002F06-configuration-management",{"title":4778,"path":4779,"stem":4780},"Docker та контейнеризація","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F07-docker-containerization","18.web-development\u002F15.testing-documentation-deployment\u002F07-docker-containerization",{"title":4782,"path":4783,"stem":4784},"CI\u002FCD Pipelines","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F08-cicd-pipelines","18.web-development\u002F15.testing-documentation-deployment\u002F08-cicd-pipelines",{"title":4786,"path":4787,"stem":4788},"Логування та моніторинг","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F09-logging-monitoring","18.web-development\u002F15.testing-documentation-deployment\u002F09-logging-monitoring",{"title":4790,"path":4791,"stem":4792},"Серіалізація та компресія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F10-serialization-compression","18.web-development\u002F15.testing-documentation-deployment\u002F10-serialization-compression",{"title":4794,"icon":4795,"path":4796,"stem":4797,"children":4798,"page":59},"AI Core: мислення AI","i-lucide-brain","\u002Fai-core","19.ai-core",[4799,4840,4889,4927],{"title":4800,"icon":4749,"path":4801,"stem":4802,"children":4803,"page":59},"Вхід у професію AI Native Developer","\u002Fai-core\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer",[4804,4808,4812,4816,4820,4824,4828,4832,4836],{"title":4805,"path":4806,"stem":4807},"Вступ до професії розробника цифрових продуктів","\u002Fai-core\u002Fai-native-developer\u002Fdigital-products","19.ai-core\u002F01.ai-native-developer\u002F01.digital-products",{"title":4809,"path":4810,"stem":4811},"Професія розробника програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fsoftware-developer","19.ai-core\u002F01.ai-native-developer\u002F02.software-developer",{"title":4813,"path":4814,"stem":4815},"Професія AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer\u002F03.ai-native-developer",{"title":4817,"path":4818,"stem":4819},"Вплив AI на розробку програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fai-impact-on-development","19.ai-core\u002F01.ai-native-developer\u002F04.ai-impact-on-development",{"title":4821,"path":4822,"stem":4823},"Життєвий цикл цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fproduct-lifecycle","19.ai-core\u002F01.ai-native-developer\u002F05.product-lifecycle",{"title":4825,"path":4826,"stem":4827},"Застосування AI на етапах створення цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fai-in-product-creation","19.ai-core\u002F01.ai-native-developer\u002F06.ai-in-product-creation",{"title":4829,"path":4830,"stem":4831},"Розподіл завдань між людиною та AI","\u002Fai-core\u002Fai-native-developer\u002Fhuman-vs-ai-tasks","19.ai-core\u002F01.ai-native-developer\u002F07.human-vs-ai-tasks",{"title":4833,"path":4834,"stem":4835},"Компетенції AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcompetencies","19.ai-core\u002F01.ai-native-developer\u002F08.competencies",{"title":4837,"path":4838,"stem":4839},"Карта професійного розвитку AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcareer-roadmap","19.ai-core\u002F01.ai-native-developer\u002F09.career-roadmap",{"title":4841,"icon":255,"path":4842,"stem":4843,"children":4844,"page":59},"Штучний інтелект і машинне навчання","\u002Fai-core\u002Fai-and-machine-learning","19.ai-core\u002F02.ai-and-machine-learning",[4845,4849,4853,4857,4861,4865,4869,4873,4877,4881,4885],{"title":4846,"path":4847,"stem":4848},"Штучний інтелект","\u002Fai-core\u002Fai-and-machine-learning\u002Fwhat-is-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F01.what-is-ai",{"title":4850,"path":4851,"stem":4852},"Відмінність AI від інших програмних систем","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-vs-automation","19.ai-core\u002F02.ai-and-machine-learning\u002F02.ai-vs-automation",{"title":4854,"path":4855,"stem":4856},"Завдання штучного інтелекту","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-tasks","19.ai-core\u002F02.ai-and-machine-learning\u002F03.ai-tasks",{"title":4858,"path":4859,"stem":4860},"Machine Learning","\u002Fai-core\u002Fai-and-machine-learning\u002Fmachine-learning","19.ai-core\u002F02.ai-and-machine-learning\u002F04.machine-learning",{"title":4862,"path":4863,"stem":4864},"Machine Learning Workflow","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-workflow","19.ai-core\u002F02.ai-and-machine-learning\u002F05.ml-workflow",{"title":4866,"path":4867,"stem":4868},"Типи машинного навчання","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-types","19.ai-core\u002F02.ai-and-machine-learning\u002F06.ml-types",{"title":4870,"path":4871,"stem":4872},"Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fgenerative-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F07.generative-ai",{"title":4874,"path":4875,"stem":4876},"Типи контенту, створюваного AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-content-types","19.ai-core\u002F02.ai-and-machine-learning\u002F08.ai-content-types",{"title":4878,"path":4879,"stem":4880},"Великі мовні моделі","\u002Fai-core\u002Fai-and-machine-learning\u002Flarge-language-models","19.ai-core\u002F02.ai-and-machine-learning\u002F09.large-language-models",{"title":4882,"path":4883,"stem":4884},"Можливості та обмеження Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fcapabilities-and-limitations","19.ai-core\u002F02.ai-and-machine-learning\u002F10.capabilities-and-limitations",{"title":4886,"path":4887,"stem":4888},"Сучасні AI-асистенти","\u002Fai-core\u002Fai-and-machine-learning\u002Fmodern-ai-assistants","19.ai-core\u002F02.ai-and-machine-learning\u002F11.modern-ai-assistants",{"title":4890,"icon":4891,"path":4892,"stem":4893,"children":4894,"page":59},"Постановка завдань для AI: принципи створення промптів","i-lucide-message-square-text","\u002Fai-core\u002Fprompt-engineering","19.ai-core\u002F03.prompt-engineering",[4895,4899,4903,4907,4911,4915,4919,4923],{"title":4896,"path":4897,"stem":4898},"Промпт як інструмент","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-as-tool","19.ai-core\u002F03.prompt-engineering\u002F01.prompt-as-tool",{"title":4900,"path":4901,"stem":4902},"Принципи створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-principles","19.ai-core\u002F03.prompt-engineering\u002F02.prompt-principles",{"title":4904,"path":4905,"stem":4906},"Структура промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-structure","19.ai-core\u002F03.prompt-engineering\u002F03.prompt-structure",{"title":4908,"path":4909,"stem":4910},"Види промптів за типом задачі","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-types","19.ai-core\u002F03.prompt-engineering\u002F04.prompt-types",{"title":4912,"path":4913,"stem":4914},"Прийоми посилення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-enhancement","19.ai-core\u002F03.prompt-engineering\u002F05.prompt-enhancement",{"title":4916,"path":4917,"stem":4918},"Розбір і покращення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-analysis","19.ai-core\u002F03.prompt-engineering\u002F06.prompt-analysis",{"title":4920,"path":4921,"stem":4922},"Типові помилки під час створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fcommon-mistakes","19.ai-core\u002F03.prompt-engineering\u002F07.common-mistakes",{"title":4924,"path":4925,"stem":4926},"Практикум: особиста бібліотека промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-library","19.ai-core\u002F03.prompt-engineering\u002F08.prompt-library",{"title":4928,"icon":793,"path":4929,"stem":4930,"children":4931,"page":59},"Перевірка результатів, безпека та AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow","19.ai-core\u002F04.verification-security-workflow",[4932,4936,4940,4944,4948,4952,4956,4960,4964],{"title":4933,"path":4934,"stem":4935},"Межі можливостей AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-limitations","19.ai-core\u002F04.verification-security-workflow\u002F01.ai-limitations",{"title":4937,"path":4938,"stem":4939},"Галюцинації AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-hallucinations","19.ai-core\u002F04.verification-security-workflow\u002F02.ai-hallucinations",{"title":4941,"path":4942,"stem":4943},"Критичне мислення під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fcritical-thinking","19.ai-core\u002F04.verification-security-workflow\u002F03.critical-thinking",{"title":4945,"path":4946,"stem":4947},"Перевірка результатів роботи AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresult-verification","19.ai-core\u002F04.verification-security-workflow\u002F04.result-verification",{"title":4949,"path":4950,"stem":4951},"Захист даних під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fdata-protection","19.ai-core\u002F04.verification-security-workflow\u002F05.data-protection",{"title":4953,"path":4954,"stem":4955},"Авторське право та навчальна доброчесність","\u002Fai-core\u002Fverification-security-workflow\u002Fcopyright-integrity","19.ai-core\u002F04.verification-security-workflow\u002F06.copyright-integrity",{"title":4957,"path":4958,"stem":4959},"Відповідальне використання AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresponsible-use","19.ai-core\u002F04.verification-security-workflow\u002F07.responsible-use",{"title":4961,"path":4962,"stem":4963},"AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow\u002Fai-native-workflow","19.ai-core\u002F04.verification-security-workflow\u002F08.ai-native-workflow",{"title":4965,"path":4966,"stem":4967},"Застосування AI Native Workflow під час створення цифрового продукту","\u002Fai-core\u002Fverification-security-workflow\u002Fworkflow-in-practice","19.ai-core\u002F04.verification-security-workflow\u002F09.workflow-in-practice",{"title":4969,"icon":4970,"path":4971,"stem":4972,"children":4973,"page":59},"AI Developer: Vibe Coding Sprint","i-lucide-code-xml","\u002Fai-developer","20.ai-developer",[4974,5000,5022,5043],{"title":4975,"icon":4976,"path":4977,"stem":4978,"children":4979,"page":59},"Проєктування і чорнова версія","i-lucide-pencil-ruler","\u002Fai-developer\u002Fdraft-creation","20.ai-developer\u002F01.draft-creation",[4980,4984,4988,4992,4996],{"title":4981,"path":4982,"stem":4983},"Парадигма Vibe Coding Workflow","\u002Fai-developer\u002Fdraft-creation\u002Fvibe-coding-workflow","20.ai-developer\u002F01.draft-creation\u002F01.vibe-coding-workflow",{"title":4985,"path":4986,"stem":4987},"AI-середовище швидкої розробки","\u002Fai-developer\u002Fdraft-creation\u002Fai-ide-environment","20.ai-developer\u002F01.draft-creation\u002F02.ai-ide-environment",{"title":4989,"path":4990,"stem":4991},"Користувацьке завдання та межі першої версії","\u002Fai-developer\u002Fdraft-creation\u002Fproduct-scope-and-mvp","20.ai-developer\u002F01.draft-creation\u002F03.product-scope-and-mvp",{"title":4993,"path":4994,"stem":4995},"Архітектура інтерфейсу та стани застосунку","\u002Fai-developer\u002Fdraft-creation\u002Fapplication-architecture-and-states","20.ai-developer\u002F01.draft-creation\u002F04.application-architecture-and-states",{"title":4997,"path":4998,"stem":4999},"Генерація та фіксація чорнової версії","\u002Fai-developer\u002Fdraft-creation\u002Fgenerating-draft-version","20.ai-developer\u002F01.draft-creation\u002F05.generating-draft-version",{"title":5001,"icon":5002,"path":5003,"stem":5004,"children":5005,"page":59},"Перша робоча версія","i-lucide-play-circle","\u002Fai-developer\u002Ffirst-working-version","20.ai-developer\u002F02.first-working-version",[5006,5010,5014,5018],{"title":5007,"path":5008,"stem":5009},"Уточнення контексту проєкту для AI","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-project-context","20.ai-developer\u002F02.first-working-version\u002F01.refining-project-context",{"title":5011,"path":5012,"stem":5013},"Стратегія завдань для AI-розробки","\u002Fai-developer\u002Ffirst-working-version\u002Fai-prompting-strategy","20.ai-developer\u002F02.first-working-version\u002F02.ai-prompting-strategy",{"title":5015,"path":5016,"stem":5017},"Доопрацювання до першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-to-working-version","20.ai-developer\u002F02.first-working-version\u002F03.refining-to-working-version",{"title":5019,"path":5020,"stem":5021},"Перевірка першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Ftesting-first-working-version","20.ai-developer\u002F02.first-working-version\u002F04.testing-first-working-version",{"title":5023,"icon":3072,"path":5024,"stem":5025,"children":5026,"page":59},"Ітерації, дебагінг та відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery","20.ai-developer\u002F03.iteration-debugging-recovery",[5027,5031,5035,5039],{"title":5028,"path":5029,"stem":5030},"Управління точковими змінами продукту","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fchange-management","20.ai-developer\u002F03.iteration-debugging-recovery\u002F01.change-management",{"title":5032,"path":5033,"stem":5034},"Надійність інтерфейсу та обробка помилок","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fscenario-reliability-and-errors","20.ai-developer\u002F03.iteration-debugging-recovery\u002F02.scenario-reliability-and-errors",{"title":5036,"path":5037,"stem":5038},"Керування контекстом і збереження версій","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fproject-context-and-versions","20.ai-developer\u002F03.iteration-debugging-recovery\u002F03.project-context-and-versions",{"title":5040,"path":5041,"stem":5042},"Збої AI-розробки, ліміти та аварійне відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fai-breakdowns-and-recovery","20.ai-developer\u002F03.iteration-debugging-recovery\u002F04.ai-breakdowns-and-recovery",{"title":5044,"icon":5045,"path":5046,"stem":5047,"children":5048,"page":59},"Перевірка та завершення продукту","i-lucide-check-check","\u002Fai-developer\u002Fverification-and-completion","20.ai-developer\u002F04.verification-and-completion",[5049,5053,5057],{"title":5050,"path":5051,"stem":5052},"Комплексний аудит та підсумкове тестування","\u002Fai-developer\u002Fverification-and-completion\u002Ffinal-product-testing","20.ai-developer\u002F04.verification-and-completion\u002F01.final-product-testing",{"title":5054,"path":5055,"stem":5056},"Підготовка підсумкової версії коду","\u002Fai-developer\u002Fverification-and-completion\u002Fpreparing-release-version","20.ai-developer\u002F04.verification-and-completion\u002F02.preparing-release-version",{"title":5058,"path":5059,"stem":5060},"Демонстрація, публікація та критерії оцінювання","\u002Fai-developer\u002Fverification-and-completion\u002Fproduct-showcase-and-publishing","20.ai-developer\u002F04.verification-and-completion\u002F03.product-showcase-and-publishing",{"title":5062,"path":5063,"stem":5064,"children":5065,"page":59},"Tailwind","\u002Ftailwind","21.tailwind",[5066,5070,5074,5078,5082,5086,5090,5094,5098,5102,5106,5110],{"title":5067,"path":5068,"stem":5069},"Що таке Tailwind CSS і навіщо він потрібен","\u002Ftailwind\u002Ftailwind-intro-philosophy","21.tailwind\u002F01.tailwind-intro-philosophy",{"title":5071,"path":5072,"stem":5073},"Встановлення та налаштування Tailwind CSS v4","\u002Ftailwind\u002Ftailwind-installation-setup","21.tailwind\u002F02.tailwind-installation-setup",{"title":5075,"path":5076,"stem":5077},"Utility-класи: основи та система Tailwind","\u002Ftailwind\u002Ftailwind-utility-classes-core","21.tailwind\u002F03.tailwind-utility-classes-core",{"title":5079,"path":5080,"stem":5081},"Layout: Flexbox та Grid через Tailwind","\u002Ftailwind\u002Ftailwind-flexbox-grid","21.tailwind\u002F04.tailwind-flexbox-grid",{"title":5083,"path":5084,"stem":5085},"Кастомізація теми через @theme у Tailwind v4","\u002Ftailwind\u002Ftailwind-theme-customization","21.tailwind\u002F05.tailwind-theme-customization",{"title":5087,"path":5088,"stem":5089},"Варіанти: hover, focus, responsive, dark mode та нові v4","\u002Ftailwind\u002Ftailwind-variants-states","21.tailwind\u002F06.tailwind-variants-states",{"title":5091,"path":5092,"stem":5093},"Типографіка та система кольорів у Tailwind v4","\u002Ftailwind\u002Ftailwind-typography-colors","21.tailwind\u002F07.tailwind-typography-colors",{"title":5095,"path":5096,"stem":5097},"Компоненти та повторюваність: @apply, @utility та патерни","\u002Ftailwind\u002Ftailwind-components-patterns","21.tailwind\u002F08.tailwind-components-patterns",{"title":5099,"path":5100,"stem":5101},"Темна тема та система дизайн-токенів у Tailwind v4","\u002Ftailwind\u002Ftailwind-dark-mode-theming","21.tailwind\u002F09.tailwind-dark-mode-theming",{"title":5103,"path":5104,"stem":5105},"Довільні значення та контейнерні запити у Tailwind v4","\u002Ftailwind\u002Ftailwind-arbitrary-container-queries","21.tailwind\u002F10.tailwind-arbitrary-container-queries",{"title":5107,"path":5108,"stem":5109},"Анімації, трансформації та 3D у Tailwind v4","\u002Ftailwind\u002Ftailwind-animations-transforms","21.tailwind\u002F11.tailwind-animations-transforms",{"title":5111,"path":5112,"stem":5113},"Tailwind CLI, PostCSS та інтеграція з фреймворками","\u002Ftailwind\u002Ftailwind-cli-tooling","21.tailwind\u002F12.tailwind-cli-tooling",{"title":5115,"path":5116,"stem":5117,"children":5118,"page":59},"React Typescript","\u002Freact-typescript","22.react-typescript",[5119,5144,5148,5152,5156,5160,5164,5168,5172],{"title":5120,"path":5121,"stem":5122,"children":5123,"page":59},"From Html To Project","\u002Freact-typescript\u002Ffrom-html-to-project","22.react-typescript\u002F01.from-html-to-project",[5124,5128,5132,5136,5140],{"title":5125,"path":5126,"stem":5127},"Від одного HTML-файлу до повноцінного проєкту","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fevolution","22.react-typescript\u002F01.from-html-to-project\u002F01.evolution",{"title":5129,"path":5130,"stem":5131},"Що таке React","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fwhat-is-react","22.react-typescript\u002F01.from-html-to-project\u002F02.what-is-react",{"title":5133,"path":5134,"stem":5135},"JSX та TSX — синтаксичний цукор, а не магія","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-tsx-syntax","22.react-typescript\u002F01.from-html-to-project\u002F03.jsx-tsx-syntax",{"title":5137,"path":5138,"stem":5139},"Компоненти — будівельні блоки інтерфейсу","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fcomponents","22.react-typescript\u002F01.from-html-to-project\u002F04.components",{"title":5141,"path":5142,"stem":5143},"JSX — розмітка всередині TypeScript","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-expressions","22.react-typescript\u002F01.from-html-to-project\u002F05.jsx-expressions",{"title":5145,"path":5146,"stem":5147},"Хук useReducer: структуроване управління складним станом","\u002Freact-typescript\u002Fuse-reducer","22.react-typescript\u002F23.use-reducer",{"title":5149,"path":5150,"stem":5151},"Context API: передавання даних без «пропс-дрілінгу»","\u002Freact-typescript\u002Fcontext-api","22.react-typescript\u002F24.context-api",{"title":5153,"path":5154,"stem":5155},"Синхронізація з ефектами: хук useEffect та функції очищення","\u002Freact-typescript\u002Fuse-effect","22.react-typescript\u002F27.use-effect",{"title":5157,"path":5158,"stem":5159},"Можливо, вам не потрібен ефект: антипатерни та альтернативи","\u002Freact-typescript\u002Fyou-might-not-need-effect","22.react-typescript\u002F28.you-might-not-need-effect",{"title":5161,"path":5162,"stem":5163},"Життєвий цикл реактивних ефектів: мислення процесами синхронізації","\u002Freact-typescript\u002Flifecycle-of-reactive-effects","22.react-typescript\u002F29.lifecycle-of-reactive-effects",{"title":5165,"path":5166,"stem":5167},"Розділення подій та ефектів: реактивна проти нереактивної логіки","\u002Freact-typescript\u002Fseparating-events-from-effects","22.react-typescript\u002F30.separating-events-from-effects",{"title":5169,"path":5170,"stem":5171},"Видалення зайвих залежностей ефектів та оптимізація синхронізації","\u002Freact-typescript\u002Fremoving-effect-dependencies","22.react-typescript\u002F31.removing-effect-dependencies",{"title":5173,"path":5174,"stem":5175},"Кастомні хуки: повторне використання та композиція реактивної логіки","\u002Freact-typescript\u002Fcustom-hooks","22.react-typescript\u002F32.custom-hooks",{"title":5177,"path":5178,"stem":5179},"Тестування компонентів діаграм та пісочниць","\u002Ftest-components","98.test-components",{"id":5181,"title":3892,"body":5182,"description":15511,"extension":15512,"links":15513,"meta":15514,"navigation":5205,"path":3893,"seo":15515,"stem":3894,"__hash__":15516},"docs\u002F16.ai-python\u002F12.neural-networks-basics\u002F01.perceptron-to-mlp.md",{"type":5183,"value":5184,"toc":15456},"minimark",[5185,5190,5194,5202,5229,5240,5308,5311,5315,5321,5328,5350,5355,5358,5498,5500,5504,5519,5787,5789,5793,5800,5805,5862,5872,5881,5884,6338,6349,6356,6498,6500,6504,6514,6519,6566,6574,6582,6584,6588,6599,7127,7155,7296,7298,7302,7313,7320,7347,7360,7367,7386,7388,7392,7402,7409,7462,7466,7472,7493,7495,7499,7502,7525,7713,7717,7720,8424,8431,8553,8591,8593,8597,8604,8608,8615,8618,8621,8624,8627,8637,8640,8649,8670,8672,8676,8679,8683,8688,8691,8699,8704,8715,9835,9997,10002,10025,10035,10037,10041,10045,10048,10055,10060,10071,10076,10081,10090,10100,10102,10106,10110,10113,10120,10125,10153,10158,10165,10173,10192,10199,10201,10205,10209,10212,10222,10227,10246,10251,10253,10257,10266,10269,10273,10292,10300,10694,10696,10700,10854,10884,10886,10890,10893,10899,10903,10914,10917,10920,10923,10962,10964,10968,10971,11000,11007,11434,11436,11440,12193,12236,12238,12242,12255,12264,12268,12328,12330,12334,12337,12340,12354,12357,12362,12384,12391,12547,12549,12553,12559,12661,12663,12667,12670,12752,12759,12803,12821,12823,12827,12830,12835,12860,12865,13821,13851,13853,13857,13860,13864,13869,13872,13882,13887,13906,13908,13912,13922,13926,13929,13933,13941,13945,13953,13955,13959,13967,13971,13974,13980,13984,13995,14007,14009,14013,14019,14025,14030,14033,14036,14046,14050,14059,14066,14090,14094,14105,14107,14111,14117,14121,14139,14143,14146,14149,14152,14155,14158,14161,14166,14192,14196,14213,14221,14223,14227,14359,14366,14401,14432,14434,14438,14565,15098,15171,15173,15177,15235,15237,15241,15396,15398,15402,15409,15426,15452],[5186,5187,5189],"h2",{"id":5188},"від-одного-нейрона-до-мереж-чому-лінійності-недостатньо","Від одного нейрона до мереж — чому лінійності недостатньо",[5191,5192,5193],"p",{},"Уявіть, що ви програміст у 1950-х роках і отримуєте завдання: навчити комп'ютер розпізнавати рукописні цифри. У вас немає готових бібліотек, лише базові математичні операції. З чого почати?",[5191,5195,5196,5197,5201],{},"Інтуїція підказує: кожен піксель зображення — це число (яскравість). Якщо помножити кожен піксель на свою «вагу важливості» та просумувати, отримаємо «оцінку схожості» на певну цифру. Саме так народилася ідея ",[5198,5199,5200],"strong",{},"персептрона"," — першої нейронної мережі.",[5203,5204,5213,5214,5213,5219,5213,5223],"video",{"controls":5205,"autoPlay":5205,"loop":5205,"muted":5205,"playsInline":5205,"poster":5206,"className":5207},true,"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fpixel_weights_similarity_poster.png",[5208,5209,5210,5211,5212],"diagram-img","rounded-xl","shadow-lg","w-full","my-6","\n  ",[5215,5216],"source",{"src":5217,"type":5218},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fpixel_weights_similarity.mp4","video\u002Fmp4",[5215,5220],{"src":5221,"type":5222},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fpixel_weights_similarity.webm","video\u002Fwebm",[5224,5225],"img",{"src":5226,"alt":5227,"className":5228},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fpixel_weights_similarity.gif","Анімація інтуїції персептрона: множення пікселів на ваги та розрахунок схожості на цифру",[5208],[5191,5230,5231,5232,5235,5236,5239],{},"Але швидко з'ясувалося: одного персептрона недостатньо. Він може розв'язати лише найпростіші задачі — ті, де класи можна розділити ",[5198,5233,5234],{},"прямою лінією",". Більшість реальних задач — складніші. Потрібна ",[5198,5237,5238],{},"мережа персептронів",", де виходи одних стають входами для інших. Так з'явилися багатошарові нейронні мережі.",[5241,5242,5243,5267],"card-group",{},[5244,5245,5248],"card",{"icon":5246,"title":5247},"i-lucide-target","🎯 Мета статті",[5249,5250,5251,5255,5258,5261,5264],"ul",{},[5252,5253,5254],"li",{},"Зрозуміти структуру та обмеження одношарового персептрона",[5252,5256,5257],{},"Опанувати концепцію багатошарового персептрона (MLP) та роль прихованих шарів",[5252,5259,5260],{},"Вивчити функції активації та їхню критичну роль у створенні нелінійності",[5252,5262,5263],{},"Розібрати алгоритми прямого поширення (forward propagation) та зворотного поширення помилки (backpropagation)",[5252,5265,5266],{},"Познайомитися з оптимізаторами SGD, Momentum та Adam",[5244,5268,5270],{"icon":4618,"title":5269},"🔑 Ключові терміни",[5249,5271,5272,5278,5284,5290,5296,5302],{},[5252,5273,5274,5277],{},[5198,5275,5276],{},"Персептрон (Perceptron):"," найпростіша нейронна мережа з одним шаром ваг",[5252,5279,5280,5283],{},[5198,5281,5282],{},"MLP (Multi-Layer Perceptron):"," багатошарова нейронна мережа з прихованими шарами",[5252,5285,5286,5289],{},[5198,5287,5288],{},"Функція активації (Activation Function):"," нелінійна функція, що перетворює зважену суму нейрона",[5252,5291,5292,5295],{},[5198,5293,5294],{},"Прямий прохід (Forward Propagation):"," обчислення виходу мережі від входу до виходу",[5252,5297,5298,5301],{},[5198,5299,5300],{},"Зворотний прохід (Backpropagation):"," обчислення градієнтів втрат по всіх вагах мережі",[5252,5303,5304,5307],{},[5198,5305,5306],{},"Оптимізатор (Optimizer):"," алгоритм оновлення ваг на основі градієнтів",[5309,5310],"hr",{},[5186,5312,5314],{"id":5313},"архітектура-персептрона-перший-штучний-нейрон","Архітектура персептрона — перший штучний нейрон",[5191,5316,5317,5320],{},[5198,5318,5319],{},"Персептрон"," — це математична модель біологічного нейрона, запропонована Френком Розенблаттом у 1957 році. Його структура надзвичайно проста, але концептуально революційна для свого часу.",[5191,5322,5323],{},[5224,5324],{"alt":5325,"className":5326,"src":5327},"Порівняння структури біологічного нейрона та математичного персептрона Розенблатта",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F01.png",[5329,5330,5332,5335,5338,5341,5344,5347],"plant-uml",{"alt":5331},"Порівняння біологічного нейрона та математичного персептрона",[5191,5333,5334],{},"@startuml\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, sans-serif\nskinparam roundcorner 8\nskinparam shadowing false\nskinparam handwritten false",[5191,5336,5337],{},"!define BIO_COLOR EFF6FF\n!define MATH_COLOR F0FDF4",[5191,5339,5340],{},"rectangle \"Біологічний нейрон\" as bio #BIO_COLOR {\ncard \"Дендрити (Dendrites)\\nПрийом вхідних електрохімічних імпульсів\" as d\ncard \"Тіло клітини \u002F Сома (Soma)\\nСумація та інтеграція потенціалів\" as s\ncard \"Аксон (Axon) & Синапс (Synapse)\\nГенерація спайку при перевищенні порогу\" as a\nd -right-> s\ns -right-> a\n}",[5191,5342,5343],{},"rectangle \"Математичний персептрон Розенблатта\" as math #MATH_COLOR {\ncard \"Входи x₁, x₂, ..., xₙ\\nЧислові ознаки з вагами wᵢ\" as x\ncard \"Суматор Σ (Linear Sum)\\nz = Σ wᵢ·xᵢ + b\" as sum\ncard \"Функція активації σ(z)\\nПороговий перехід: ŷ = 1 якщо z ≥ 0, інакше 0\" as act\nx -right-> sum\nsum -right-> act\n}",[5191,5345,5346],{},"d .down.> x : аналог\ns .down.> sum : аналог\na .down.> act : аналог",[5191,5348,5349],{},"@enduml",[5351,5352,5354],"h3",{"id":5353},"структура-персептрона","Структура персептрона",[5191,5356,5357],{},"Персептрон складається з чотирьох компонентів:",[5359,5360,5361,5365,5374,5400,5404,5418,5428,5432,5435,5438,5441,5444,5448,5463,5466,5473,5483,5486,5489],"steps",{},[5351,5362,5364],{"id":5363},"крок-1-вхідний-шар-input-layer","Крок 1. Вхідний шар (Input Layer)",[5191,5366,5367,5368,5373],{},"Кожна ознака об'єкта — це окремий вхід ",[5369,5370],"math-formula",{"tex":5371,":inline":5372},"x_i","true",". Наприклад, для класифікації квіта Ірис:",[5249,5375,5376,5382,5388,5394],{},[5252,5377,5378,5381],{},[5369,5379],{"tex":5380,":inline":5372},"x_1"," = довжина пелюстки",[5252,5383,5384,5387],{},[5369,5385],{"tex":5386,":inline":5372},"x_2"," = ширина пелюстки",[5252,5389,5390,5393],{},[5369,5391],{"tex":5392,":inline":5372},"x_3"," = довжина чашолистка",[5252,5395,5396,5399],{},[5369,5397],{"tex":5398,":inline":5372},"x_4"," = ширина чашолистка",[5351,5401,5403],{"id":5402},"крок-2-ваги-weights-та-зсув-bias","Крок 2. Ваги (Weights) та зсув (Bias)",[5191,5405,5406,5407,5409,5410,5413,5414,5417],{},"Кожен вхід ",[5369,5408],{"tex":5371,":inline":5372}," має свою вагу ",[5369,5411],{"tex":5412,":inline":5372},"w_i",", яка визначає, наскільки ця ознака важлива для передбачення. Додатково є зсув ",[5369,5415],{"tex":5416,":inline":5372},"b"," (bias), що дозволяє зміщувати порогову межу.",[5191,5419,5420,5423,5424,5427],{},[5198,5421,5422],{},"Інтуїція:"," Якщо довжина пелюстки дуже важлива для розпізнавання виду, то ",[5369,5425],{"tex":5426,":inline":5372},"w_1"," буде великою вагою. Якщо ознака неінформативна — вага буде близькою до нуля.",[5351,5429,5431],{"id":5430},"крок-3-зважена-сума-weighted-sum","Крок 3. Зважена сума (Weighted Sum)",[5191,5433,5434],{},"Обчислюється лінійна комбінація входів та ваг:",[5369,5436],{"tex":5437},"z = w*1 x_1 + w_2 x_2 + \\ldots + w_n x_n + b = \\sum*{i=1}^{n} w_i x_i + b",[5191,5439,5440],{},"Або у векторній формі:",[5369,5442],{"tex":5443},"z = \\mathbf{w}^T \\mathbf{x} + b",[5351,5445,5447],{"id":5446},"крок-4-функція-активації-activation-function","Крок 4. Функція активації (Activation Function)",[5191,5449,5450,5451,5454,5455,5458,5459,5462],{},"Зважена сума ",[5369,5452],{"tex":5453,":inline":5372},"z"," перетворюється функцією активації ",[5369,5456],{"tex":5457,":inline":5372},"\\sigma(z)",". Для класичного персептрона це ",[5198,5460,5461],{},"функція кроку (step function)",":",[5369,5464,5465],{},"\\hat{y} = \\sigma(z) = \\begin{cases}\n1, & \\text{якщо } z \\geq 0 \\\n0, & \\text{якщо } z \u003C 0\n\\end{cases}",[5191,5467,5468,5469,5472],{},"Результат ",[5369,5470],{"tex":5471,":inline":5372},"\\hat{y}"," — це передбачення класу: 1 або 0.",[5191,5474,5475,5476,5479,5480,5462],{},"Об'єднуючи зважену суму та функцію активації, отримуємо ",[5198,5477,5478],{},"повну математичну формулу функції персептрона"," ",[5369,5481],{"tex":5482,":inline":5372},"\\hat{y} = f(\\mathbf{x})",[5369,5484,5485],{},"\\hat{y} = f(\\mathbf{x}) = \\sigma(\\mathbf{w}^T \\mathbf{x} + b) = \\begin{cases}\n1, & \\text{якщо } \\mathbf{w}^T \\mathbf{x} + b \\geq 0 \\\n0, & \\text{якщо } \\mathbf{w}^T \\mathbf{x} + b \u003C 0\n\\end{cases}",[5191,5487,5488],{},"Або у розгорнутій формі через суму всіх вхідних ознак:",[5369,5490,5491,5492,5497],{},"\\hat{y} = f(\\mathbf{x}) = \\sigma\\left(\\sum*^{n} w_i x_i + b\\right) = \\begin{cases}\n1, & \\text{якщо } \\sum*^{n} w",[5493,5494,5496],"em",{"i":5495},"1","i x_i + b \\geq 0 \\\n0, & \\text{якщо } \\sum","^{n} w_i x_i + b \u003C 0\n\\end{cases}",[5309,5499],{},[5351,5501,5503],{"id":5502},"візуалізація-персептрона","Візуалізація персептрона",[5203,5505,5213,5508,5213,5511,5213,5514],{"controls":5205,"autoPlay":5205,"loop":5205,"muted":5205,"playsInline":5205,"poster":5506,"className":5507},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fperceptron_computation_poster.png",[5208,5209,5210,5211,5212],[5215,5509],{"src":5510,"type":5218},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fperceptron_computation.mp4",[5215,5512],{"src":5513,"type":5222},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fperceptron_computation.webm",[5224,5515],{"src":5516,"alt":5517,"className":5518},"\u002Fvideos\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002Fperceptron_computation.gif","Анімація анатомії персептрона та прямого поширення сигналу",[5208],[5329,5520,5522],{"alt":5521},"Архітектура персептрона",[5523,5524,5529],"pre",{"className":5525,"code":5526,"language":5527,"meta":5528,"style":5528},"language-plantuml shiki shiki-themes light-plus dark-plus dark-plus","@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define INPUT_COLOR DBEAFE\n!define NEURON_COLOR FEF3C7\n!define OUTPUT_COLOR DCFCE7\n\nrectangle \"Вхідні ознаки\" as input {\n  (x₁) #INPUT_COLOR\n  (x₂) #INPUT_COLOR\n  (x₃) #INPUT_COLOR\n  (x₄) #INPUT_COLOR\n}\n\nrectangle \"Нейрон (Персептрон)\" as neuron #NEURON_COLOR {\n  card \"z = Σ wᵢxᵢ + b\" as sum\n  card \"σ(z)\" as activation\n  sum -down-> activation : активація\n}\n\nrectangle \"Вихід\" as output {\n  (ŷ) #OUTPUT_COLOR\n}\n\n(x₁) -right-> sum : w₁\n(x₂) -right-> sum : w₂\n(x₃) -right-> sum : w₃\n(x₄) -right-> sum : w₄\n\nactivation -right-> (ŷ) : клас 0 або 1\n\nnote right of sum\n  Зважена сума:\n  **z = w₁·x₁ + w₂·x₂ + w₃·x₃ + w₄·x₄ + b**\nend note\n\nnote right of activation\n  Функція кроку:\n  **σ(z) = 1 якщо z ≥ 0, інакше 0**\nend note\n\n@enduml\n","plantuml","",[5530,5531,5532,5540,5546,5552,5558,5564,5570,5576,5582,5587,5593,5599,5605,5611,5617,5623,5628,5634,5640,5646,5652,5657,5662,5668,5674,5679,5684,5690,5696,5702,5708,5713,5719,5724,5730,5736,5742,5748,5753,5759,5765,5771,5776,5781],"code",{"__ignoreMap":5528},[5533,5534,5537],"span",{"class":5535,"line":5536},"line",1,[5533,5538,5539],{},"@startuml\n",[5533,5541,5543],{"class":5535,"line":5542},2,[5533,5544,5545],{},"skinparam style plain\n",[5533,5547,5549],{"class":5535,"line":5548},3,[5533,5550,5551],{},"skinparam backgroundColor #FFFFFF\n",[5533,5553,5555],{"class":5535,"line":5554},4,[5533,5556,5557],{},"skinparam defaultFontName \"SF Pro Display, Arial\"\n",[5533,5559,5561],{"class":5535,"line":5560},5,[5533,5562,5563],{"emptyLinePlaceholder":5205},"\n",[5533,5565,5567],{"class":5535,"line":5566},6,[5533,5568,5569],{},"!define INPUT_COLOR DBEAFE\n",[5533,5571,5573],{"class":5535,"line":5572},7,[5533,5574,5575],{},"!define NEURON_COLOR FEF3C7\n",[5533,5577,5579],{"class":5535,"line":5578},8,[5533,5580,5581],{},"!define OUTPUT_COLOR DCFCE7\n",[5533,5583,5585],{"class":5535,"line":5584},9,[5533,5586,5563],{"emptyLinePlaceholder":5205},[5533,5588,5590],{"class":5535,"line":5589},10,[5533,5591,5592],{},"rectangle \"Вхідні ознаки\" as input {\n",[5533,5594,5596],{"class":5535,"line":5595},11,[5533,5597,5598],{},"  (x₁) #INPUT_COLOR\n",[5533,5600,5602],{"class":5535,"line":5601},12,[5533,5603,5604],{},"  (x₂) #INPUT_COLOR\n",[5533,5606,5608],{"class":5535,"line":5607},13,[5533,5609,5610],{},"  (x₃) #INPUT_COLOR\n",[5533,5612,5614],{"class":5535,"line":5613},14,[5533,5615,5616],{},"  (x₄) #INPUT_COLOR\n",[5533,5618,5620],{"class":5535,"line":5619},15,[5533,5621,5622],{},"}\n",[5533,5624,5626],{"class":5535,"line":5625},16,[5533,5627,5563],{"emptyLinePlaceholder":5205},[5533,5629,5631],{"class":5535,"line":5630},17,[5533,5632,5633],{},"rectangle \"Нейрон (Персептрон)\" as neuron #NEURON_COLOR {\n",[5533,5635,5637],{"class":5535,"line":5636},18,[5533,5638,5639],{},"  card \"z = Σ wᵢxᵢ + b\" as sum\n",[5533,5641,5643],{"class":5535,"line":5642},19,[5533,5644,5645],{},"  card \"σ(z)\" as activation\n",[5533,5647,5649],{"class":5535,"line":5648},20,[5533,5650,5651],{},"  sum -down-> activation : активація\n",[5533,5653,5655],{"class":5535,"line":5654},21,[5533,5656,5622],{},[5533,5658,5660],{"class":5535,"line":5659},22,[5533,5661,5563],{"emptyLinePlaceholder":5205},[5533,5663,5665],{"class":5535,"line":5664},23,[5533,5666,5667],{},"rectangle \"Вихід\" as output {\n",[5533,5669,5671],{"class":5535,"line":5670},24,[5533,5672,5673],{},"  (ŷ) #OUTPUT_COLOR\n",[5533,5675,5677],{"class":5535,"line":5676},25,[5533,5678,5622],{},[5533,5680,5682],{"class":5535,"line":5681},26,[5533,5683,5563],{"emptyLinePlaceholder":5205},[5533,5685,5687],{"class":5535,"line":5686},27,[5533,5688,5689],{},"(x₁) -right-> sum : w₁\n",[5533,5691,5693],{"class":5535,"line":5692},28,[5533,5694,5695],{},"(x₂) -right-> sum : w₂\n",[5533,5697,5699],{"class":5535,"line":5698},29,[5533,5700,5701],{},"(x₃) -right-> sum : w₃\n",[5533,5703,5705],{"class":5535,"line":5704},30,[5533,5706,5707],{},"(x₄) -right-> sum : w₄\n",[5533,5709,5711],{"class":5535,"line":5710},31,[5533,5712,5563],{"emptyLinePlaceholder":5205},[5533,5714,5716],{"class":5535,"line":5715},32,[5533,5717,5718],{},"activation -right-> (ŷ) : клас 0 або 1\n",[5533,5720,5722],{"class":5535,"line":5721},33,[5533,5723,5563],{"emptyLinePlaceholder":5205},[5533,5725,5727],{"class":5535,"line":5726},34,[5533,5728,5729],{},"note right of sum\n",[5533,5731,5733],{"class":5535,"line":5732},35,[5533,5734,5735],{},"  Зважена сума:\n",[5533,5737,5739],{"class":5535,"line":5738},36,[5533,5740,5741],{},"  **z = w₁·x₁ + w₂·x₂ + w₃·x₃ + w₄·x₄ + b**\n",[5533,5743,5745],{"class":5535,"line":5744},37,[5533,5746,5747],{},"end note\n",[5533,5749,5751],{"class":5535,"line":5750},38,[5533,5752,5563],{"emptyLinePlaceholder":5205},[5533,5754,5756],{"class":5535,"line":5755},39,[5533,5757,5758],{},"note right of activation\n",[5533,5760,5762],{"class":5535,"line":5761},40,[5533,5763,5764],{},"  Функція кроку:\n",[5533,5766,5768],{"class":5535,"line":5767},41,[5533,5769,5770],{},"  **σ(z) = 1 якщо z ≥ 0, інакше 0**\n",[5533,5772,5774],{"class":5535,"line":5773},42,[5533,5775,5747],{},[5533,5777,5779],{"class":5535,"line":5778},43,[5533,5780,5563],{"emptyLinePlaceholder":5205},[5533,5782,5784],{"class":5535,"line":5783},44,[5533,5785,5786],{},"@enduml\n",[5309,5788],{},[5351,5790,5792],{"id":5791},"приклад-персептрон-для-логічного-або-or","Приклад: персептрон для логічного АБО (OR)",[5191,5794,5795,5796,5799],{},"Розглянемо найпростішу задачу: навчити персептрон логічній операції ",[5198,5797,5798],{},"OR",".",[5191,5801,5802],{},[5198,5803,5804],{},"Таблиця істинності OR:",[5806,5807,5808,5825],"table",{},[5809,5810,5811],"thead",{},[5812,5813,5814,5819,5822],"tr",{},[5815,5816,5818],"th",{"align":5817},"center","x₁",[5815,5820,5821],{"align":5817},"x₂",[5815,5823,5824],{"align":5817},"y (OR)",[5826,5827,5828,5838,5846,5854],"tbody",{},[5812,5829,5830,5834,5836],{},[5831,5832,5833],"td",{"align":5817},"0",[5831,5835,5833],{"align":5817},[5831,5837,5833],{"align":5817},[5812,5839,5840,5842,5844],{},[5831,5841,5833],{"align":5817},[5831,5843,5495],{"align":5817},[5831,5845,5495],{"align":5817},[5812,5847,5848,5850,5852],{},[5831,5849,5495],{"align":5817},[5831,5851,5833],{"align":5817},[5831,5853,5495],{"align":5817},[5812,5855,5856,5858,5860],{},[5831,5857,5495],{"align":5817},[5831,5859,5495],{"align":5817},[5831,5861,5495],{"align":5817},[5191,5863,5864,5867,5868,5871],{},[5198,5865,5866],{},"Питання:"," чи можна знайти такі ваги ",[5369,5869],{"tex":5870,":inline":5372},"w_1, w_2, b",", щоб персептрон правильно класифікував всі 4 приклади?",[5191,5873,5874,5877,5878,5799],{},[5198,5875,5876],{},"Відповідь:"," так! Наприклад, ",[5369,5879],{"tex":5880,":inline":5372},"w_1 = 1, w_2 = 1, b = -0.5",[5191,5882,5883],{},"Перевірка:",[5885,5886,5889],"jupyter-notebook",{"kernel":5887,"title":5888},"Python 3.11 (ipykernel)","perceptron_or.ipynb",[5890,5891,5892,6215],"jupyter-cell",{"execution-count":5495},[5523,5893,5897],{"className":5894,"code":5895,"language":5896,"meta":5528,"style":5528},"language-python shiki shiki-themes light-plus dark-plus dark-plus","import numpy as np\n\ndef step_function(z):\n    \"\"\"Функція кроку: 1 якщо z >= 0, інакше 0\"\"\"\n    return 1 if z >= 0 else 0\n\n# Ваги персептрона для OR\nw1, w2, b = 1.0, 1.0, -0.5\n\n# Перевірка всіх комбінацій\ninputs = [(0, 0), (0, 1), (1, 0), (1, 1)]\n\nprint(\"x₁  x₂  | z = w₁·x₁ + w₂·x₂ + b | σ(z) | Очікується\")\nprint(\"-\" * 55)\n\nfor x1, x2 in inputs:\n    z = w1 * x1 + w2 * x2 + b\n    output = step_function(z)\n    expected = int(x1 or x2)\n    status = \"✓\" if output == expected else \"✗\"\n    print(f\"{x1}   {x2}   |  {z:6.2f}               | {output}    | {expected}        {status}\")\n","python",[5530,5898,5899,5915,5919,5938,5944,5967,5971,5977,5996,6000,6005,6044,6048,6061,6078,6082,6096,6101,6106,6124,6143],{"__ignoreMap":5528},[5533,5900,5901,5905,5909,5912],{"class":5535,"line":5536},[5533,5902,5904],{"class":5903},"s8xlr","import",[5533,5906,5908],{"class":5907},"sHH4Y"," numpy ",[5533,5910,5911],{"class":5903},"as",[5533,5913,5914],{"class":5907}," np\n",[5533,5916,5917],{"class":5535,"line":5542},[5533,5918,5563],{"emptyLinePlaceholder":5205},[5533,5920,5921,5925,5929,5932,5935],{"class":5535,"line":5548},[5533,5922,5924],{"class":5923},"su1O8","def",[5533,5926,5928],{"class":5927},"s8Opu"," step_function",[5533,5930,5931],{"class":5907},"(",[5533,5933,5453],{"class":5934},"siwwj",[5533,5936,5937],{"class":5907},"):\n",[5533,5939,5940],{"class":5535,"line":5554},[5533,5941,5943],{"class":5942},"sbdoH","    \"\"\"Функція кроку: 1 якщо z >= 0, інакше 0\"\"\"\n",[5533,5945,5946,5949,5953,5956,5959,5961,5964],{"class":5535,"line":5560},[5533,5947,5948],{"class":5903},"    return",[5533,5950,5952],{"class":5951},"sJj4R"," 1",[5533,5954,5955],{"class":5903}," if",[5533,5957,5958],{"class":5907}," z >= ",[5533,5960,5833],{"class":5951},[5533,5962,5963],{"class":5903}," else",[5533,5965,5966],{"class":5951}," 0\n",[5533,5968,5969],{"class":5535,"line":5566},[5533,5970,5563],{"emptyLinePlaceholder":5205},[5533,5972,5973],{"class":5535,"line":5572},[5533,5974,5976],{"class":5975},"spJ8K","# Ваги персептрона для OR\n",[5533,5978,5979,5982,5985,5988,5990,5993],{"class":5535,"line":5578},[5533,5980,5981],{"class":5907},"w1, w2, b = ",[5533,5983,5984],{"class":5951},"1.0",[5533,5986,5987],{"class":5907},", ",[5533,5989,5984],{"class":5951},[5533,5991,5992],{"class":5907},", -",[5533,5994,5995],{"class":5951},"0.5\n",[5533,5997,5998],{"class":5535,"line":5584},[5533,5999,5563],{"emptyLinePlaceholder":5205},[5533,6001,6002],{"class":5535,"line":5589},[5533,6003,6004],{"class":5975},"# Перевірка всіх комбінацій\n",[5533,6006,6007,6010,6012,6014,6016,6019,6021,6023,6025,6027,6029,6031,6033,6035,6037,6039,6041],{"class":5535,"line":5595},[5533,6008,6009],{"class":5907},"inputs = [(",[5533,6011,5833],{"class":5951},[5533,6013,5987],{"class":5907},[5533,6015,5833],{"class":5951},[5533,6017,6018],{"class":5907},"), (",[5533,6020,5833],{"class":5951},[5533,6022,5987],{"class":5907},[5533,6024,5495],{"class":5951},[5533,6026,6018],{"class":5907},[5533,6028,5495],{"class":5951},[5533,6030,5987],{"class":5907},[5533,6032,5833],{"class":5951},[5533,6034,6018],{"class":5907},[5533,6036,5495],{"class":5951},[5533,6038,5987],{"class":5907},[5533,6040,5495],{"class":5951},[5533,6042,6043],{"class":5907},")]\n",[5533,6045,6046],{"class":5535,"line":5601},[5533,6047,5563],{"emptyLinePlaceholder":5205},[5533,6049,6050,6053,6055,6058],{"class":5535,"line":5607},[5533,6051,6052],{"class":5927},"print",[5533,6054,5931],{"class":5907},[5533,6056,6057],{"class":5942},"\"x₁  x₂  | z = w₁·x₁ + w₂·x₂ + b | σ(z) | Очікується\"",[5533,6059,6060],{"class":5907},")\n",[5533,6062,6063,6065,6067,6070,6073,6076],{"class":5535,"line":5613},[5533,6064,6052],{"class":5927},[5533,6066,5931],{"class":5907},[5533,6068,6069],{"class":5942},"\"-\"",[5533,6071,6072],{"class":5907}," * ",[5533,6074,6075],{"class":5951},"55",[5533,6077,6060],{"class":5907},[5533,6079,6080],{"class":5535,"line":5619},[5533,6081,5563],{"emptyLinePlaceholder":5205},[5533,6083,6084,6087,6090,6093],{"class":5535,"line":5625},[5533,6085,6086],{"class":5903},"for",[5533,6088,6089],{"class":5907}," x1, x2 ",[5533,6091,6092],{"class":5903},"in",[5533,6094,6095],{"class":5907}," inputs:\n",[5533,6097,6098],{"class":5535,"line":5630},[5533,6099,6100],{"class":5907},"    z = w1 * x1 + w2 * x2 + b\n",[5533,6102,6103],{"class":5535,"line":5636},[5533,6104,6105],{"class":5907},"    output = step_function(z)\n",[5533,6107,6108,6111,6115,6118,6121],{"class":5535,"line":5642},[5533,6109,6110],{"class":5907},"    expected = ",[5533,6112,6114],{"class":6113},"sN1BT","int",[5533,6116,6117],{"class":5907},"(x1 ",[5533,6119,6120],{"class":5903},"or",[5533,6122,6123],{"class":5907}," x2)\n",[5533,6125,6126,6129,6132,6134,6137,6140],{"class":5535,"line":5648},[5533,6127,6128],{"class":5907},"    status = ",[5533,6130,6131],{"class":5942},"\"✓\"",[5533,6133,5955],{"class":5903},[5533,6135,6136],{"class":5907}," output == expected ",[5533,6138,6139],{"class":5903},"else",[5533,6141,6142],{"class":5942}," \"✗\"\n",[5533,6144,6145,6148,6150,6153,6156,6159,6162,6165,6168,6171,6173,6176,6178,6180,6183,6186,6188,6191,6193,6196,6198,6201,6203,6206,6209,6211,6213],{"class":5535,"line":5654},[5533,6146,6147],{"class":5927},"    print",[5533,6149,5931],{"class":5907},[5533,6151,6152],{"class":5923},"f",[5533,6154,6155],{"class":5942},"\"",[5533,6157,6158],{"class":5923},"{",[5533,6160,6161],{"class":5907},"x1",[5533,6163,6164],{"class":5923},"}",[5533,6166,6167],{"class":5923},"   {",[5533,6169,6170],{"class":5907},"x2",[5533,6172,6164],{"class":5923},[5533,6174,6175],{"class":5942},"   |  ",[5533,6177,6158],{"class":5923},[5533,6179,5453],{"class":5907},[5533,6181,6182],{"class":5923},":6.2f}",[5533,6184,6185],{"class":5942},"               | ",[5533,6187,6158],{"class":5923},[5533,6189,6190],{"class":5907},"output",[5533,6192,6164],{"class":5923},[5533,6194,6195],{"class":5942},"    | ",[5533,6197,6158],{"class":5923},[5533,6199,6200],{"class":5907},"expected",[5533,6202,6164],{"class":5923},[5533,6204,6205],{"class":5923},"        {",[5533,6207,6208],{"class":5907},"status",[5533,6210,6164],{"class":5923},[5533,6212,6155],{"class":5942},[5533,6214,6060],{"class":5907},[6216,6217,6218],"template",{"v-slot:output":5528},[5806,6219,6220,6243],{},[5809,6221,6222],{},[5812,6223,6224,6227,6230,6233,6236,6239],{},[5815,6225,6226],{"align":5817},"$x_1$",[5815,6228,6229],{"align":5817},"$x_2$",[5815,6231,6232],{"align":5817},"$z = w_1 x_1 + w_2 x_2 + b$",[5815,6234,6235],{"align":5817},"$\\sigma(z)$ (вихід)",[5815,6237,6238],{"align":5817},"Очікуване (OR)",[5815,6240,6242],{"align":6241},"left","Статус тесту",[5826,6244,6245,6269,6293,6315],{},[5812,6246,6247,6251,6255,6260,6264,6266],{},[5831,6248,6249],{"align":5817},[5198,6250,5833],{},[5831,6252,6253],{"align":5817},[5198,6254,5833],{},[5831,6256,6257],{"align":5817},[5530,6258,6259],{},"-0.50",[5831,6261,6262],{"align":5817},[5198,6263,5833],{},[5831,6265,5833],{"align":5817},[5831,6267,6268],{"align":6241},"✅ Успішно (клас 0)",[5812,6270,6271,6275,6279,6284,6288,6290],{},[5831,6272,6273],{"align":5817},[5198,6274,5833],{},[5831,6276,6277],{"align":5817},[5198,6278,5495],{},[5831,6280,6281],{"align":5817},[5530,6282,6283],{},"+0.50",[5831,6285,6286],{"align":5817},[5198,6287,5495],{},[5831,6289,5495],{"align":5817},[5831,6291,6292],{"align":6241},"✅ Успішно (клас 1)",[5812,6294,6295,6299,6303,6307,6311,6313],{},[5831,6296,6297],{"align":5817},[5198,6298,5495],{},[5831,6300,6301],{"align":5817},[5198,6302,5833],{},[5831,6304,6305],{"align":5817},[5530,6306,6283],{},[5831,6308,6309],{"align":5817},[5198,6310,5495],{},[5831,6312,5495],{"align":5817},[5831,6314,6292],{"align":6241},[5812,6316,6317,6321,6325,6330,6334,6336],{},[5831,6318,6319],{"align":5817},[5198,6320,5495],{},[5831,6322,6323],{"align":5817},[5198,6324,5495],{},[5831,6326,6327],{"align":5817},[5530,6328,6329],{},"+1.50",[5831,6331,6332],{"align":5817},[5198,6333,5495],{},[5831,6335,5495],{"align":5817},[5831,6337,6292],{"align":6241},[6339,6340,6341,6344,6345,6348],"tip",{},[5198,6342,6343],{},"Геометрична інтерпретація:"," Персептрон для OR знаходить пряму лінію ",[5369,6346],{"tex":6347,":inline":5372},"w_1 x_1 + w_2 x_2 + b = 0",", яка розділяє простір на два класи. Точки вище лінії — клас 1, нижче — клас 0.",[5191,6350,6351],{},[5224,6352],{"alt":6353,"className":6354,"src":6355},"Геометрична інтерпретація лінійної роздільності персептрона для логічних операцій OR та AND",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F02.png",[5329,6357,6359],{"alt":6358},"Лінійна роздільність персептрона для логічних вентилів OR та AND",[5523,6360,6362],{"className":5525,"code":6361,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define INPUT_COLOR DBEAFE\n!define GATE_COLOR FEF3C7\n!define OUTPUT_COLOR DCFCE7\n\nrectangle \"Логічний вентиль OR (АБО)\" as or_gate #GATE_COLOR {\n  card \"w₁ = 1.0, w₂ = 1.0\\nb = -0.5\" as or_weights\n  card \"Межа розділення:\\nx₁ + x₂ - 0.5 = 0\" as or_line\n}\n\nrectangle \"Логічний вентиль AND (І)\" as and_gate #GATE_COLOR {\n  card \"w₁ = 1.0, w₂ = 1.0\\nb = -1.5\" as and_weights\n  card \"Межа розділення:\\nx₁ + x₂ - 1.5 = 0\" as and_line\n}\n\nnode \"(0,0) → 0\\n(0,1) → 1\\n(1,0) → 1\\n(1,1) → 1\" as or_truth #INPUT_COLOR\nnode \"(0,0) → 0\\n(0,1) → 0\\n(1,0) → 0\\n(1,1) → 1\" as and_truth #INPUT_COLOR\n\nor_truth -down-> or_gate : лінійно роздільні\nand_truth -down-> and_gate : лінійно роздільні\n\ncard \"Висновок: обидві задачі успішно розв'язуються\\nоднією прямою гіперплощиною\" as conclusion #OUTPUT_COLOR\nor_gate -down-> conclusion\nand_gate -down-> conclusion\n\n@enduml\n",[5530,6363,6364,6368,6372,6376,6380,6384,6388,6393,6397,6401,6406,6411,6416,6420,6424,6429,6434,6439,6443,6447,6452,6457,6461,6466,6471,6475,6480,6485,6490,6494],{"__ignoreMap":5528},[5533,6365,6366],{"class":5535,"line":5536},[5533,6367,5539],{},[5533,6369,6370],{"class":5535,"line":5542},[5533,6371,5545],{},[5533,6373,6374],{"class":5535,"line":5548},[5533,6375,5551],{},[5533,6377,6378],{"class":5535,"line":5554},[5533,6379,5557],{},[5533,6381,6382],{"class":5535,"line":5560},[5533,6383,5563],{"emptyLinePlaceholder":5205},[5533,6385,6386],{"class":5535,"line":5566},[5533,6387,5569],{},[5533,6389,6390],{"class":5535,"line":5572},[5533,6391,6392],{},"!define GATE_COLOR FEF3C7\n",[5533,6394,6395],{"class":5535,"line":5578},[5533,6396,5581],{},[5533,6398,6399],{"class":5535,"line":5584},[5533,6400,5563],{"emptyLinePlaceholder":5205},[5533,6402,6403],{"class":5535,"line":5589},[5533,6404,6405],{},"rectangle \"Логічний вентиль OR (АБО)\" as or_gate #GATE_COLOR {\n",[5533,6407,6408],{"class":5535,"line":5595},[5533,6409,6410],{},"  card \"w₁ = 1.0, w₂ = 1.0\\nb = -0.5\" as or_weights\n",[5533,6412,6413],{"class":5535,"line":5601},[5533,6414,6415],{},"  card \"Межа розділення:\\nx₁ + x₂ - 0.5 = 0\" as or_line\n",[5533,6417,6418],{"class":5535,"line":5607},[5533,6419,5622],{},[5533,6421,6422],{"class":5535,"line":5613},[5533,6423,5563],{"emptyLinePlaceholder":5205},[5533,6425,6426],{"class":5535,"line":5619},[5533,6427,6428],{},"rectangle \"Логічний вентиль AND (І)\" as and_gate #GATE_COLOR {\n",[5533,6430,6431],{"class":5535,"line":5625},[5533,6432,6433],{},"  card \"w₁ = 1.0, w₂ = 1.0\\nb = -1.5\" as and_weights\n",[5533,6435,6436],{"class":5535,"line":5630},[5533,6437,6438],{},"  card \"Межа розділення:\\nx₁ + x₂ - 1.5 = 0\" as and_line\n",[5533,6440,6441],{"class":5535,"line":5636},[5533,6442,5622],{},[5533,6444,6445],{"class":5535,"line":5642},[5533,6446,5563],{"emptyLinePlaceholder":5205},[5533,6448,6449],{"class":5535,"line":5648},[5533,6450,6451],{},"node \"(0,0) → 0\\n(0,1) → 1\\n(1,0) → 1\\n(1,1) → 1\" as or_truth #INPUT_COLOR\n",[5533,6453,6454],{"class":5535,"line":5654},[5533,6455,6456],{},"node \"(0,0) → 0\\n(0,1) → 0\\n(1,0) → 0\\n(1,1) → 1\" as and_truth #INPUT_COLOR\n",[5533,6458,6459],{"class":5535,"line":5659},[5533,6460,5563],{"emptyLinePlaceholder":5205},[5533,6462,6463],{"class":5535,"line":5664},[5533,6464,6465],{},"or_truth -down-> or_gate : лінійно роздільні\n",[5533,6467,6468],{"class":5535,"line":5670},[5533,6469,6470],{},"and_truth -down-> and_gate : лінійно роздільні\n",[5533,6472,6473],{"class":5535,"line":5676},[5533,6474,5563],{"emptyLinePlaceholder":5205},[5533,6476,6477],{"class":5535,"line":5681},[5533,6478,6479],{},"card \"Висновок: обидві задачі успішно розв'язуються\\nоднією прямою гіперплощиною\" as conclusion #OUTPUT_COLOR\n",[5533,6481,6482],{"class":5535,"line":5686},[5533,6483,6484],{},"or_gate -down-> conclusion\n",[5533,6486,6487],{"class":5535,"line":5692},[5533,6488,6489],{},"and_gate -down-> conclusion\n",[5533,6491,6492],{"class":5535,"line":5698},[5533,6493,5563],{"emptyLinePlaceholder":5205},[5533,6495,6496],{"class":5535,"line":5704},[5533,6497,5786],{},[5309,6499],{},[5186,6501,6503],{"id":6502},"проблема-xor-межа-лінійної-роздільності","Проблема XOR — межа лінійної роздільності",[5191,6505,6506,6507,6510,6511,5799],{},"Персептрон успішно вирішує логічні операції AND, OR, NOT. Але існує одна проста операція, яка ",[5198,6508,6509],{},"повністю розбиває"," одношаровий персептрон: ",[5198,6512,6513],{},"XOR (виключне АБО)",[5191,6515,6516],{},[5198,6517,6518],{},"Таблиця істинності XOR:",[5806,6520,6521,6532],{},[5809,6522,6523],{},[5812,6524,6525,6527,6529],{},[5815,6526,5818],{"align":5817},[5815,6528,5821],{"align":5817},[5815,6530,6531],{"align":5817},"y (XOR)",[5826,6533,6534,6542,6550,6558],{},[5812,6535,6536,6538,6540],{},[5831,6537,5833],{"align":5817},[5831,6539,5833],{"align":5817},[5831,6541,5833],{"align":5817},[5812,6543,6544,6546,6548],{},[5831,6545,5833],{"align":5817},[5831,6547,5495],{"align":5817},[5831,6549,5495],{"align":5817},[5812,6551,6552,6554,6556],{},[5831,6553,5495],{"align":5817},[5831,6555,5833],{"align":5817},[5831,6557,5495],{"align":5817},[5812,6559,6560,6562,6564],{},[5831,6561,5495],{"align":5817},[5831,6563,5495],{"align":5817},[5831,6565,5833],{"align":5817},[5191,6567,6568,6570,6571,6573],{},[5198,6569,5866],{}," чи можна знайти ваги ",[5369,6572],{"tex":5870,":inline":5372}," для персептрона, щоб правильно класифікувати XOR?",[5191,6575,6576,5479,6578,6581],{},[5198,6577,5876],{},[5198,6579,6580],{},"НІ!"," Це математично неможливо.",[5309,6583],{},[5351,6585,6587],{"id":6586},"чому-персептрон-не-може-розвязати-xor","Чому персептрон не може розв'язати XOR?",[5191,6589,6590,6591,6594,6595,6598],{},"Персептрон — це ",[5198,6592,6593],{},"лінійний класифікатор",". Він може провести лише ",[5198,6596,6597],{},"одну пряму лінію"," для розділення класів. Подивимося на візуалізацію XOR:",[5885,6600,6602],{"kernel":5887,"title":6601},"xor_visualization.ipynb",[5890,6603,6606,7120],{"execution-count":6604,"execution-time":6605},"2","0.31s",[5523,6607,6609],{"className":5894,"code":6608,"language":5896,"meta":5528,"style":5528},"import matplotlib.pyplot as plt\nimport numpy as np\n\n# Дані XOR\nx_coords = [0, 0, 1, 1]\ny_coords = [0, 1, 0, 1]\ncolors = ['red', 'blue', 'blue', 'red']  # клас 0 — червоний, клас 1 — синій\nlabels = [0, 1, 1, 0]\n\nplt.figure(figsize=(8, 6))\nplt.scatter(x_coords, y_coords, c=colors, s=300, edgecolors='black', linewidths=2, alpha=0.7)\n\n# Додаємо підписи точок\nfor i, (x, y, label) in enumerate(zip(x_coords, y_coords, labels)):\n    plt.text(x, y, f'  ({x}, {y})\\n  y={label}', fontsize=12, ha='left')\n\n# Спроба провести лінію розділення (завжди помилиться)\nplt.axline((0.5, 0), slope=1, color='gray', linestyle='--', linewidth=2, alpha=0.5, label='Неможлива лінія розділення')\n\nplt.xlim(-0.3, 1.5)\nplt.ylim(-0.3, 1.5)\nplt.xlabel('x₁', fontsize=14)\nplt.ylabel('x₂', fontsize=14)\nplt.title('Проблема XOR: класи не є лінійно роздільними', fontsize=16, fontweight='bold')\nplt.legend(fontsize=12)\nplt.grid(alpha=0.3)\nplt.tight_layout()\nplt.show()\n",[5530,6610,6611,6623,6633,6637,6642,6664,6685,6712,6733,6737,6759,6810,6814,6819,6839,6907,6911,6916,6986,6990,7005,7018,7037,7055,7084,7097,7110,7115],{"__ignoreMap":5528},[5533,6612,6613,6615,6618,6620],{"class":5535,"line":5536},[5533,6614,5904],{"class":5903},[5533,6616,6617],{"class":5907}," matplotlib.pyplot ",[5533,6619,5911],{"class":5903},[5533,6621,6622],{"class":5907}," plt\n",[5533,6624,6625,6627,6629,6631],{"class":5535,"line":5542},[5533,6626,5904],{"class":5903},[5533,6628,5908],{"class":5907},[5533,6630,5911],{"class":5903},[5533,6632,5914],{"class":5907},[5533,6634,6635],{"class":5535,"line":5548},[5533,6636,5563],{"emptyLinePlaceholder":5205},[5533,6638,6639],{"class":5535,"line":5554},[5533,6640,6641],{"class":5975},"# Дані XOR\n",[5533,6643,6644,6647,6649,6651,6653,6655,6657,6659,6661],{"class":5535,"line":5560},[5533,6645,6646],{"class":5907},"x_coords = [",[5533,6648,5833],{"class":5951},[5533,6650,5987],{"class":5907},[5533,6652,5833],{"class":5951},[5533,6654,5987],{"class":5907},[5533,6656,5495],{"class":5951},[5533,6658,5987],{"class":5907},[5533,6660,5495],{"class":5951},[5533,6662,6663],{"class":5907},"]\n",[5533,6665,6666,6669,6671,6673,6675,6677,6679,6681,6683],{"class":5535,"line":5566},[5533,6667,6668],{"class":5907},"y_coords = [",[5533,6670,5833],{"class":5951},[5533,6672,5987],{"class":5907},[5533,6674,5495],{"class":5951},[5533,6676,5987],{"class":5907},[5533,6678,5833],{"class":5951},[5533,6680,5987],{"class":5907},[5533,6682,5495],{"class":5951},[5533,6684,6663],{"class":5907},[5533,6686,6687,6690,6693,6695,6698,6700,6702,6704,6706,6709],{"class":5535,"line":5572},[5533,6688,6689],{"class":5907},"colors = [",[5533,6691,6692],{"class":5942},"'red'",[5533,6694,5987],{"class":5907},[5533,6696,6697],{"class":5942},"'blue'",[5533,6699,5987],{"class":5907},[5533,6701,6697],{"class":5942},[5533,6703,5987],{"class":5907},[5533,6705,6692],{"class":5942},[5533,6707,6708],{"class":5907},"]  ",[5533,6710,6711],{"class":5975},"# клас 0 — червоний, клас 1 — синій\n",[5533,6713,6714,6717,6719,6721,6723,6725,6727,6729,6731],{"class":5535,"line":5578},[5533,6715,6716],{"class":5907},"labels = [",[5533,6718,5833],{"class":5951},[5533,6720,5987],{"class":5907},[5533,6722,5495],{"class":5951},[5533,6724,5987],{"class":5907},[5533,6726,5495],{"class":5951},[5533,6728,5987],{"class":5907},[5533,6730,5833],{"class":5951},[5533,6732,6663],{"class":5907},[5533,6734,6735],{"class":5535,"line":5584},[5533,6736,5563],{"emptyLinePlaceholder":5205},[5533,6738,6739,6742,6745,6748,6751,6753,6756],{"class":5535,"line":5589},[5533,6740,6741],{"class":5907},"plt.figure(",[5533,6743,6744],{"class":5934},"figsize",[5533,6746,6747],{"class":5907},"=(",[5533,6749,6750],{"class":5951},"8",[5533,6752,5987],{"class":5907},[5533,6754,6755],{"class":5951},"6",[5533,6757,6758],{"class":5907},"))\n",[5533,6760,6761,6764,6767,6770,6773,6776,6779,6781,6784,6786,6789,6791,6794,6796,6798,6800,6803,6805,6808],{"class":5535,"line":5595},[5533,6762,6763],{"class":5907},"plt.scatter(x_coords, y_coords, ",[5533,6765,6766],{"class":5934},"c",[5533,6768,6769],{"class":5907},"=colors, ",[5533,6771,6772],{"class":5934},"s",[5533,6774,6775],{"class":5907},"=",[5533,6777,6778],{"class":5951},"300",[5533,6780,5987],{"class":5907},[5533,6782,6783],{"class":5934},"edgecolors",[5533,6785,6775],{"class":5907},[5533,6787,6788],{"class":5942},"'black'",[5533,6790,5987],{"class":5907},[5533,6792,6793],{"class":5934},"linewidths",[5533,6795,6775],{"class":5907},[5533,6797,6604],{"class":5951},[5533,6799,5987],{"class":5907},[5533,6801,6802],{"class":5934},"alpha",[5533,6804,6775],{"class":5907},[5533,6806,6807],{"class":5951},"0.7",[5533,6809,6060],{"class":5907},[5533,6811,6812],{"class":5535,"line":5601},[5533,6813,5563],{"emptyLinePlaceholder":5205},[5533,6815,6816],{"class":5535,"line":5607},[5533,6817,6818],{"class":5975},"# Додаємо підписи точок\n",[5533,6820,6821,6823,6826,6828,6831,6833,6836],{"class":5535,"line":5613},[5533,6822,6086],{"class":5903},[5533,6824,6825],{"class":5907}," i, (x, y, label) ",[5533,6827,6092],{"class":5903},[5533,6829,6830],{"class":5927}," enumerate",[5533,6832,5931],{"class":5907},[5533,6834,6835],{"class":5927},"zip",[5533,6837,6838],{"class":5907},"(x_coords, y_coords, labels)):\n",[5533,6840,6841,6844,6846,6849,6851,6854,6856,6858,6860,6863,6865,6868,6872,6875,6877,6880,6882,6885,6887,6890,6892,6895,6897,6900,6902,6905],{"class":5535,"line":5619},[5533,6842,6843],{"class":5907},"    plt.text(x, y, ",[5533,6845,6152],{"class":5923},[5533,6847,6848],{"class":5942},"'  (",[5533,6850,6158],{"class":5923},[5533,6852,6853],{"class":5907},"x",[5533,6855,6164],{"class":5923},[5533,6857,5987],{"class":5942},[5533,6859,6158],{"class":5923},[5533,6861,6862],{"class":5907},"y",[5533,6864,6164],{"class":5923},[5533,6866,6867],{"class":5942},")",[5533,6869,6871],{"class":6870},"sjcCO","\\n",[5533,6873,6874],{"class":5942},"  y=",[5533,6876,6158],{"class":5923},[5533,6878,6879],{"class":5907},"label",[5533,6881,6164],{"class":5923},[5533,6883,6884],{"class":5942},"'",[5533,6886,5987],{"class":5907},[5533,6888,6889],{"class":5934},"fontsize",[5533,6891,6775],{"class":5907},[5533,6893,6894],{"class":5951},"12",[5533,6896,5987],{"class":5907},[5533,6898,6899],{"class":5934},"ha",[5533,6901,6775],{"class":5907},[5533,6903,6904],{"class":5942},"'left'",[5533,6906,6060],{"class":5907},[5533,6908,6909],{"class":5535,"line":5625},[5533,6910,5563],{"emptyLinePlaceholder":5205},[5533,6912,6913],{"class":5535,"line":5630},[5533,6914,6915],{"class":5975},"# Спроба провести лінію розділення (завжди помилиться)\n",[5533,6917,6918,6921,6924,6926,6928,6931,6934,6936,6938,6940,6943,6945,6948,6950,6953,6955,6958,6960,6963,6965,6967,6969,6971,6973,6975,6977,6979,6981,6984],{"class":5535,"line":5636},[5533,6919,6920],{"class":5907},"plt.axline((",[5533,6922,6923],{"class":5951},"0.5",[5533,6925,5987],{"class":5907},[5533,6927,5833],{"class":5951},[5533,6929,6930],{"class":5907},"), ",[5533,6932,6933],{"class":5934},"slope",[5533,6935,6775],{"class":5907},[5533,6937,5495],{"class":5951},[5533,6939,5987],{"class":5907},[5533,6941,6942],{"class":5934},"color",[5533,6944,6775],{"class":5907},[5533,6946,6947],{"class":5942},"'gray'",[5533,6949,5987],{"class":5907},[5533,6951,6952],{"class":5934},"linestyle",[5533,6954,6775],{"class":5907},[5533,6956,6957],{"class":5942},"'--'",[5533,6959,5987],{"class":5907},[5533,6961,6962],{"class":5934},"linewidth",[5533,6964,6775],{"class":5907},[5533,6966,6604],{"class":5951},[5533,6968,5987],{"class":5907},[5533,6970,6802],{"class":5934},[5533,6972,6775],{"class":5907},[5533,6974,6923],{"class":5951},[5533,6976,5987],{"class":5907},[5533,6978,6879],{"class":5934},[5533,6980,6775],{"class":5907},[5533,6982,6983],{"class":5942},"'Неможлива лінія розділення'",[5533,6985,6060],{"class":5907},[5533,6987,6988],{"class":5535,"line":5642},[5533,6989,5563],{"emptyLinePlaceholder":5205},[5533,6991,6992,6995,6998,7000,7003],{"class":5535,"line":5648},[5533,6993,6994],{"class":5907},"plt.xlim(-",[5533,6996,6997],{"class":5951},"0.3",[5533,6999,5987],{"class":5907},[5533,7001,7002],{"class":5951},"1.5",[5533,7004,6060],{"class":5907},[5533,7006,7007,7010,7012,7014,7016],{"class":5535,"line":5654},[5533,7008,7009],{"class":5907},"plt.ylim(-",[5533,7011,6997],{"class":5951},[5533,7013,5987],{"class":5907},[5533,7015,7002],{"class":5951},[5533,7017,6060],{"class":5907},[5533,7019,7020,7023,7026,7028,7030,7032,7035],{"class":5535,"line":5659},[5533,7021,7022],{"class":5907},"plt.xlabel(",[5533,7024,7025],{"class":5942},"'x₁'",[5533,7027,5987],{"class":5907},[5533,7029,6889],{"class":5934},[5533,7031,6775],{"class":5907},[5533,7033,7034],{"class":5951},"14",[5533,7036,6060],{"class":5907},[5533,7038,7039,7042,7045,7047,7049,7051,7053],{"class":5535,"line":5664},[5533,7040,7041],{"class":5907},"plt.ylabel(",[5533,7043,7044],{"class":5942},"'x₂'",[5533,7046,5987],{"class":5907},[5533,7048,6889],{"class":5934},[5533,7050,6775],{"class":5907},[5533,7052,7034],{"class":5951},[5533,7054,6060],{"class":5907},[5533,7056,7057,7060,7063,7065,7067,7069,7072,7074,7077,7079,7082],{"class":5535,"line":5670},[5533,7058,7059],{"class":5907},"plt.title(",[5533,7061,7062],{"class":5942},"'Проблема XOR: класи не є лінійно роздільними'",[5533,7064,5987],{"class":5907},[5533,7066,6889],{"class":5934},[5533,7068,6775],{"class":5907},[5533,7070,7071],{"class":5951},"16",[5533,7073,5987],{"class":5907},[5533,7075,7076],{"class":5934},"fontweight",[5533,7078,6775],{"class":5907},[5533,7080,7081],{"class":5942},"'bold'",[5533,7083,6060],{"class":5907},[5533,7085,7086,7089,7091,7093,7095],{"class":5535,"line":5676},[5533,7087,7088],{"class":5907},"plt.legend(",[5533,7090,6889],{"class":5934},[5533,7092,6775],{"class":5907},[5533,7094,6894],{"class":5951},[5533,7096,6060],{"class":5907},[5533,7098,7099,7102,7104,7106,7108],{"class":5535,"line":5681},[5533,7100,7101],{"class":5907},"plt.grid(",[5533,7103,6802],{"class":5934},[5533,7105,6775],{"class":5907},[5533,7107,6997],{"class":5951},[5533,7109,6060],{"class":5907},[5533,7111,7112],{"class":5535,"line":5686},[5533,7113,7114],{"class":5907},"plt.tight_layout()\n",[5533,7116,7117],{"class":5535,"line":5692},[5533,7118,7119],{"class":5907},"plt.show()\n",[6216,7121,7122],{"v-slot:output":5528},[5224,7123],{"alt":7124,"className":7125,"src":7126},"Проблема нелінійної роздільності XOR: неможливість лінійного розділення класів однією прямою",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F03.png",[7128,7129,7130,7135],"warning",{},[5191,7131,7132],{},[5198,7133,7134],{},"Критичне обмеження персептрона:",[5249,7136,7137,7144],{},[5252,7138,7139,7140,7143],{},"Персептрон може розв'язувати ",[5198,7141,7142],{},"лише лінійно роздільні"," задачі — ті, де класи можна розділити гіперплощиною (у 2D — прямою лінією, у 3D — площиною).",[5252,7145,7146,7147,7150,7151,7154],{},"Для XOR червоні точки (клас 0) розташовані діагонально від синіх (клас 1). Жодна пряма лінія не може їх розділити — потрібна ",[5198,7148,7149],{},"крива"," або ",[5198,7152,7153],{},"дві лінії",". Одношаровий персептрон на це не здатний.",[5329,7156,7158],{"alt":7157},"Неможливість розділення XOR однією прямою лінією",[5523,7159,7161],{"className":5525,"code":7160,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define CLASS0_COLOR FEE2E2\n!define CLASS1_COLOR DBEAFE\n!define LIMIT_COLOR FEF3C7\n\npackage \"Простір входів XOR (x₁, x₂)\" {\n  node \"(0, 0)\\ny = 0\" as p00 #CLASS0_COLOR\n  node \"(1, 1)\\ny = 0\" as p11 #CLASS0_COLOR\n  node \"(0, 1)\\ny = 1\" as p01 #CLASS1_COLOR\n  node \"(1, 0)\\ny = 1\" as p10 #CLASS1_COLOR\n}\n\npackage \"Обмеження одношарового персептрона\" as limit #LIMIT_COLOR {\n  card \"Лінійна модель: w₁·x₁ + w₂·x₂ + b = 0\" as model\n  card \"Пряма лінія може розділити лише сусідні точки,\\nале точки однакових класів розташовані діагонально!\" as conflict\n}\n\np00 ..> conflict : діагональ 1\np11 ..> conflict : діагональ 1\np01 ..> conflict : діагональ 2\np10 ..> conflict : діагональ 2\n\ncard \"Рішення: Багатошаровий персептрон (MLP)\\nіз нелінійною активацією\" as solution #DCFCE7\nconflict -down-> solution : подолання обмеження\n@enduml\n",[5530,7162,7163,7167,7171,7175,7179,7183,7188,7193,7198,7202,7207,7212,7217,7222,7227,7231,7235,7240,7245,7250,7254,7258,7263,7268,7273,7278,7282,7287,7292],{"__ignoreMap":5528},[5533,7164,7165],{"class":5535,"line":5536},[5533,7166,5539],{},[5533,7168,7169],{"class":5535,"line":5542},[5533,7170,5545],{},[5533,7172,7173],{"class":5535,"line":5548},[5533,7174,5551],{},[5533,7176,7177],{"class":5535,"line":5554},[5533,7178,5557],{},[5533,7180,7181],{"class":5535,"line":5560},[5533,7182,5563],{"emptyLinePlaceholder":5205},[5533,7184,7185],{"class":5535,"line":5566},[5533,7186,7187],{},"!define CLASS0_COLOR FEE2E2\n",[5533,7189,7190],{"class":5535,"line":5572},[5533,7191,7192],{},"!define CLASS1_COLOR DBEAFE\n",[5533,7194,7195],{"class":5535,"line":5578},[5533,7196,7197],{},"!define LIMIT_COLOR FEF3C7\n",[5533,7199,7200],{"class":5535,"line":5584},[5533,7201,5563],{"emptyLinePlaceholder":5205},[5533,7203,7204],{"class":5535,"line":5589},[5533,7205,7206],{},"package \"Простір входів XOR (x₁, x₂)\" {\n",[5533,7208,7209],{"class":5535,"line":5595},[5533,7210,7211],{},"  node \"(0, 0)\\ny = 0\" as p00 #CLASS0_COLOR\n",[5533,7213,7214],{"class":5535,"line":5601},[5533,7215,7216],{},"  node \"(1, 1)\\ny = 0\" as p11 #CLASS0_COLOR\n",[5533,7218,7219],{"class":5535,"line":5607},[5533,7220,7221],{},"  node \"(0, 1)\\ny = 1\" as p01 #CLASS1_COLOR\n",[5533,7223,7224],{"class":5535,"line":5613},[5533,7225,7226],{},"  node \"(1, 0)\\ny = 1\" as p10 #CLASS1_COLOR\n",[5533,7228,7229],{"class":5535,"line":5619},[5533,7230,5622],{},[5533,7232,7233],{"class":5535,"line":5625},[5533,7234,5563],{"emptyLinePlaceholder":5205},[5533,7236,7237],{"class":5535,"line":5630},[5533,7238,7239],{},"package \"Обмеження одношарового персептрона\" as limit #LIMIT_COLOR {\n",[5533,7241,7242],{"class":5535,"line":5636},[5533,7243,7244],{},"  card \"Лінійна модель: w₁·x₁ + w₂·x₂ + b = 0\" as model\n",[5533,7246,7247],{"class":5535,"line":5642},[5533,7248,7249],{},"  card \"Пряма лінія може розділити лише сусідні точки,\\nале точки однакових класів розташовані діагонально!\" as conflict\n",[5533,7251,7252],{"class":5535,"line":5648},[5533,7253,5622],{},[5533,7255,7256],{"class":5535,"line":5654},[5533,7257,5563],{"emptyLinePlaceholder":5205},[5533,7259,7260],{"class":5535,"line":5659},[5533,7261,7262],{},"p00 ..> conflict : діагональ 1\n",[5533,7264,7265],{"class":5535,"line":5664},[5533,7266,7267],{},"p11 ..> conflict : діагональ 1\n",[5533,7269,7270],{"class":5535,"line":5670},[5533,7271,7272],{},"p01 ..> conflict : діагональ 2\n",[5533,7274,7275],{"class":5535,"line":5676},[5533,7276,7277],{},"p10 ..> conflict : діагональ 2\n",[5533,7279,7280],{"class":5535,"line":5681},[5533,7281,5563],{"emptyLinePlaceholder":5205},[5533,7283,7284],{"class":5535,"line":5686},[5533,7285,7286],{},"card \"Рішення: Багатошаровий персептрон (MLP)\\nіз нелінійною активацією\" as solution #DCFCE7\n",[5533,7288,7289],{"class":5535,"line":5692},[5533,7290,7291],{},"conflict -down-> solution : подолання обмеження\n",[5533,7293,7294],{"class":5535,"line":5698},[5533,7295,5786],{},[5309,7297],{},[5351,7299,7301],{"id":7300},"історичний-контекст-зима-ai-через-xor","Історичний контекст: «зима AI» через XOR",[5191,7303,7304,7305,7308,7309,7312],{},"У 1969 році математики Марвін Мінський та Сеймур Паперт опублікували книгу ",[5198,7306,7307],{},"«Персептрони»",", де математично довели, що одношаровий персептрон ",[5198,7310,7311],{},"принципово не може"," розв'язати XOR.",[5191,7314,7315,7316,7319],{},"Це викликало ",[5198,7317,7318],{},"першу «зиму штучного інтелекту»"," (1970–1980-ті роки) — різке скорочення фінансування досліджень AI, бо вважалося, що нейронні мережі — тупиковий шлях.",[7321,7322,7323,7328],"blockquote",{},[5191,7324,7325],{},[5198,7326,7327],{},"Аналогія з будівництвом:",[5191,7329,7330,7331,7334,7335,7338,7339,7342,7343,7346],{},"Уявіть, що ви маєте лише ",[5198,7332,7333],{},"прямокутні цеглини",". З них можна збудувати стіни, але неможливо створити ",[5198,7336,7337],{},"арку"," чи ",[5198,7340,7341],{},"купол"," — потрібні цеглини інших форм. Одношаровий персептрон — це «прямокутні цеглини». Для складних форм (нелінійних задач) потрібні ",[5198,7344,7345],{},"багатошарові мережі"," — цеглини різних форм і розмірів.",[5191,7348,7349,7352,7353,7356,7357,5799],{},[5198,7350,7351],{},"Рішення проблеми:"," додати ",[5198,7354,7355],{},"приховані шари"," нейронів між входом і виходом. Так з'являються ",[5198,7358,7359],{},"багатошарові нейронні мережі (Multi-Layer Perceptron, MLP)",[5191,7361,7362],{},[5224,7363],{"alt":7364,"className":7365,"src":7366},"Криза персептрона та настання першої «Зими ШІ» (AI Winter) через проблему нелінійної роздільності XOR",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F04.png",[5329,7368,7370,7372,7375,7378,7381,7384],{"alt":7369},"Хронологія та наслідки проблеми XOR для розвитку ШІ",[5191,7371,5334],{},[5191,7373,7374],{},"skinparam state {\nBackgroundColor #F8FAFC\nBorderColor #94A3B8\nFontColor #0F172A\nFontSize 12\nArrowColor #64748B\n}",[5191,7376,7377],{},"title Еволюційний шлях: від ейфорії персептрона до подолання AI Winter",[5191,7379,7380],{},"state \"1957: Ейфорія (Френк Розенблатт)\" as S1 #EFF6FF : Винахід персептрона\\nУспіх на лінійно роздільних задачах (OR, AND)\nstate \"1969: Криза (Мінський і Пейперт)\" as S2 #FEF2F2 : Математичний доказ:\\nодношаровий персептрон не може розв'язати XOR\nstate \"1970-і: Перша «Зима ШІ» (AI Winter)\" as S3 #F1F5F9 : Замороження фінансування\\nСкептицизм академічної спільноти\nstate \"1986: Відродження (Rumelhart, Hinton, Williams)\" as S4 #ECFDF5 : Багатошаровий персептрон (MLP)\\n+ Алгоритм Backpropagation розв'язують XOR",[5191,7382,7383],{},"S1 -down-> S2 : Виявлення межі лінійності\nS2 -down-> S3 : Втрата інтересу та грантів\nS3 -down-> S4 : Поява прихованих шарів та градієнтного спуску",[5191,7385,5349],{},[5309,7387],{},[5186,7389,7391],{"id":7390},"багатошаровий-персептрон-mlp-прорив-у-нелінійності","Багатошаровий персептрон (MLP) — прорив у нелінійності",[5191,7393,7394,7395,7398,7399,5799],{},"Якщо один персептрон — це одна пряма лінія, то ",[5198,7396,7397],{},"кілька персептронів, з'єднаних у мережу",", можуть створювати ",[5198,7400,7401],{},"складні нелінійні межі розділення",[5191,7403,7404],{},[5224,7405],{"alt":7406,"className":7407,"src":7408},"Архітектура багатошарового персептрона (MLP) з прихованими шарами для обчислення складних нелінійних залежностей",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F05.png",[5329,7410,7412,7414,7417,7420,7443,7446,7460],{"alt":7411},"Архітектурні рівні багатошарового персептрона (MLP)",[5191,7413,5334],{},[5191,7415,7416],{},"skinparam rectangle {\nRoundCorner 8\nBorderColor #94A3B8\nFontSize 12\n}",[5191,7418,7419],{},"rectangle \"Вхідний шар (Input Layer)\" as in_layer #EFF6FF {\ncard \"Ознаки x₁...xₙ\\n(Сирі числові дані)\" as in_nodes\n}",[5191,7421,7422,7423,7425,7426,7428,7429,7431,7432,7425,7434,7436,7437,7439,7440,7442],{},"rectangle \"Приховані шари (Hidden Layers)\" as hid_layer #FEF3C7 {\ncard \"Прихований шар 1\\nНелінійне комбінування: a^",[5533,7424,5495],{}," = σ(W^",[5533,7427,5495],{},"x + b^",[5533,7430,5495],{},")\" as h1\ncard \"Прихований шар 2\\nІєрархічні абстрактні ознаки: a^",[5533,7433,6604],{},[5533,7435,6604],{},"a^",[5533,7438,5495],{}," + b^",[5533,7441,6604],{},")\" as h2\nh1 -right-> h2 : активації\n}",[5191,7444,7445],{},"rectangle \"Вихідний шар (Output Layer)\" as out_layer #ECFDF5 {\ncard \"Фінальний вихід ŷ\\nЙмовірність класу \u002F регресійне число\" as out_nodes\n}",[5191,7447,7448,7449,7451,7452,7454,7455,7451,7458],{},"in_nodes -right-> h1 : W^",[5533,7450,5495],{},", b^",[5533,7453,5495],{},"\nh2 -right-> out_nodes : W^",[5533,7456,7457],{},"3",[5533,7459,7457],{},[5191,7461,5349],{},[5351,7463,7465],{"id":7464},"архітектура-mlp","Архітектура MLP",[5191,7467,7468,7471],{},[5198,7469,7470],{},"Multi-Layer Perceptron (MLP)"," — це нейронна мережа, що складається з:",[7473,7474,7475,7481,7487],"ol",{},[5252,7476,7477,7480],{},[5198,7478,7479],{},"Вхідного шару (Input Layer):"," приймає ознаки об'єкта (не виконує обчислень, лише передає дані далі)",[5252,7482,7483,7486],{},[5198,7484,7485],{},"Прихованих шарів (Hidden Layers):"," один або кілька шарів нейронів, що виконують нелінійні перетворення",[5252,7488,7489,7492],{},[5198,7490,7491],{},"Вихідного шару (Output Layer):"," повертає передбачення (одне число для регресії, ймовірності класів для класифікації)",[5309,7494],{},[5351,7496,7498],{"id":7497},"приклад-mlp-для-розвязання-xor","Приклад: MLP для розв'язання XOR",[5191,7500,7501],{},"Найпростіша архітектура для XOR:",[5249,7503,7504,7513,7519],{},[5252,7505,7506,7509,7510,6867],{},[5198,7507,7508],{},"Вхідний шар:"," 2 нейрони (",[5369,7511],{"tex":7512,":inline":5372},"x_1, x_2",[5252,7514,7515,7518],{},[5198,7516,7517],{},"Прихований шар:"," 2 нейрони (дозволяють створити дві лінії розділення)",[5252,7520,7521,7524],{},[5198,7522,7523],{},"Вихідний шар:"," 1 нейрон (передбачення 0 або 1)",[5329,7526,7528],{"alt":7527},"Архітектура MLP для XOR",[5523,7529,7531],{"className":5525,"code":7530,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define INPUT_COLOR DBEAFE\n!define HIDDEN_COLOR FEF3C7\n!define OUTPUT_COLOR DCFCE7\n\nleft to right direction\n\npackage \"Вхідний шар\\n(Input Layer)\" as input #INPUT_COLOR {\n  circle x1 as \"x₁\"\n  circle x2 as \"x₂\"\n}\n\npackage \"Прихований шар\\n(Hidden Layer)\" as hidden #HIDDEN_COLOR {\n  circle h1 as \"h₁\"\n  circle h2 as \"h₂\"\n}\n\npackage \"Вихідний шар\\n(Output Layer)\" as output #OUTPUT_COLOR {\n  circle y as \"ŷ\"\n}\n\nx1 -right-> h1\nx1 -right-> h2\nx2 -right-> h1\nx2 -right-> h2\n\nh1 -right-> y\nh2 -right-> y\n\nnote bottom of hidden\n  Кожен нейрон обчислює:\n  **hᵢ = σ(w·x + b)**\n  де σ — функція активації\nend note\n\n@enduml\n",[5530,7532,7533,7537,7541,7545,7549,7553,7557,7562,7566,7570,7575,7579,7584,7589,7594,7598,7602,7607,7612,7617,7621,7625,7630,7635,7639,7643,7648,7653,7658,7663,7667,7672,7677,7681,7686,7691,7696,7701,7705,7709],{"__ignoreMap":5528},[5533,7534,7535],{"class":5535,"line":5536},[5533,7536,5539],{},[5533,7538,7539],{"class":5535,"line":5542},[5533,7540,5545],{},[5533,7542,7543],{"class":5535,"line":5548},[5533,7544,5551],{},[5533,7546,7547],{"class":5535,"line":5554},[5533,7548,5557],{},[5533,7550,7551],{"class":5535,"line":5560},[5533,7552,5563],{"emptyLinePlaceholder":5205},[5533,7554,7555],{"class":5535,"line":5566},[5533,7556,5569],{},[5533,7558,7559],{"class":5535,"line":5572},[5533,7560,7561],{},"!define HIDDEN_COLOR FEF3C7\n",[5533,7563,7564],{"class":5535,"line":5578},[5533,7565,5581],{},[5533,7567,7568],{"class":5535,"line":5584},[5533,7569,5563],{"emptyLinePlaceholder":5205},[5533,7571,7572],{"class":5535,"line":5589},[5533,7573,7574],{},"left to right direction\n",[5533,7576,7577],{"class":5535,"line":5595},[5533,7578,5563],{"emptyLinePlaceholder":5205},[5533,7580,7581],{"class":5535,"line":5601},[5533,7582,7583],{},"package \"Вхідний шар\\n(Input Layer)\" as input #INPUT_COLOR {\n",[5533,7585,7586],{"class":5535,"line":5607},[5533,7587,7588],{},"  circle x1 as \"x₁\"\n",[5533,7590,7591],{"class":5535,"line":5613},[5533,7592,7593],{},"  circle x2 as \"x₂\"\n",[5533,7595,7596],{"class":5535,"line":5619},[5533,7597,5622],{},[5533,7599,7600],{"class":5535,"line":5625},[5533,7601,5563],{"emptyLinePlaceholder":5205},[5533,7603,7604],{"class":5535,"line":5630},[5533,7605,7606],{},"package \"Прихований шар\\n(Hidden Layer)\" as hidden #HIDDEN_COLOR {\n",[5533,7608,7609],{"class":5535,"line":5636},[5533,7610,7611],{},"  circle h1 as \"h₁\"\n",[5533,7613,7614],{"class":5535,"line":5642},[5533,7615,7616],{},"  circle h2 as \"h₂\"\n",[5533,7618,7619],{"class":5535,"line":5648},[5533,7620,5622],{},[5533,7622,7623],{"class":5535,"line":5654},[5533,7624,5563],{"emptyLinePlaceholder":5205},[5533,7626,7627],{"class":5535,"line":5659},[5533,7628,7629],{},"package \"Вихідний шар\\n(Output Layer)\" as output #OUTPUT_COLOR {\n",[5533,7631,7632],{"class":5535,"line":5664},[5533,7633,7634],{},"  circle y as \"ŷ\"\n",[5533,7636,7637],{"class":5535,"line":5670},[5533,7638,5622],{},[5533,7640,7641],{"class":5535,"line":5676},[5533,7642,5563],{"emptyLinePlaceholder":5205},[5533,7644,7645],{"class":5535,"line":5681},[5533,7646,7647],{},"x1 -right-> h1\n",[5533,7649,7650],{"class":5535,"line":5686},[5533,7651,7652],{},"x1 -right-> h2\n",[5533,7654,7655],{"class":5535,"line":5692},[5533,7656,7657],{},"x2 -right-> h1\n",[5533,7659,7660],{"class":5535,"line":5698},[5533,7661,7662],{},"x2 -right-> h2\n",[5533,7664,7665],{"class":5535,"line":5704},[5533,7666,5563],{"emptyLinePlaceholder":5205},[5533,7668,7669],{"class":5535,"line":5710},[5533,7670,7671],{},"h1 -right-> y\n",[5533,7673,7674],{"class":5535,"line":5715},[5533,7675,7676],{},"h2 -right-> y\n",[5533,7678,7679],{"class":5535,"line":5721},[5533,7680,5563],{"emptyLinePlaceholder":5205},[5533,7682,7683],{"class":5535,"line":5726},[5533,7684,7685],{},"note bottom of hidden\n",[5533,7687,7688],{"class":5535,"line":5732},[5533,7689,7690],{},"  Кожен нейрон обчислює:\n",[5533,7692,7693],{"class":5535,"line":5738},[5533,7694,7695],{},"  **hᵢ = σ(w·x + b)**\n",[5533,7697,7698],{"class":5535,"line":5744},[5533,7699,7700],{},"  де σ — функція активації\n",[5533,7702,7703],{"class":5535,"line":5750},[5533,7704,5747],{},[5533,7706,7707],{"class":5535,"line":5755},[5533,7708,5563],{"emptyLinePlaceholder":5205},[5533,7710,7711],{"class":5535,"line":5761},[5533,7712,5786],{},[5351,7714,7716],{"id":7715},"як-mlp-розвязує-xor-покрокове-пояснення","Як MLP розв'язує XOR: покрокове пояснення",[5191,7718,7719],{},"Розберемо, як працює MLP з 2 входами → 2 прихованих нейронів → 1 вихід для задачі XOR.",[5885,7721,7723,7752,8406],{"kernel":5887,"title":7722},"mlp_xor_solution.ipynb",[5890,7724,7726,7731,7742],{"type":7725},"markdown",[7727,7728,7730],"h4",{"id":7729},"крок-1-прихований-шар-створює-проміжні-ознаки","Крок 1: Прихований шар створює проміжні ознаки",[5191,7732,7733,7734,7737,7738,7741],{},"Перший прихований нейрон ",[5369,7735],{"tex":7736,":inline":5372},"h_1"," навчається розпізнавати ",[5198,7739,7740],{},"«хоча б один вхід дорівнює 1»"," (логічне OR).",[5191,7743,7744,7745,7737,7748,7751],{},"Другий прихований нейрон ",[5369,7746],{"tex":7747,":inline":5372},"h_2",[5198,7749,7750],{},"«обидва входи дорівнюють 1»"," (логічне AND).",[5890,7753,7754,8233],{"execution-count":7457},[5523,7755,7757],{"className":5894,"code":7756,"language":5896,"meta":5528,"style":5528},"import numpy as np\n\ndef sigmoid(z):\n    \"\"\"Сигмоїда: σ(z) = 1 \u002F (1 + e^(-z))\"\"\"\n    return 1 \u002F (1 + np.exp(-z))\n\n# Ваги для прихованого шару (підібрані вручну для демонстрації)\nW1 = np.array([\n    [1.0, 1.0],   # h1: реагує на OR (x1 + x2)\n    [1.0, 1.0]    # h2: реагує на AND (x1 * x2 при правильному bias)\n])\nb1 = np.array([-0.5, -1.5])  # Порогові значення\n\n# Ваги для вихідного шару\nW2 = np.array([1.0, -2.0])   # y = h1 - 2*h2\nb2 = np.array([0.0])\n\n# Вхідні дані XOR\nX = np.array([\n    [0, 0],\n    [0, 1],\n    [1, 0],\n    [1, 1]\n])\n\nprint(\"Обчислення MLP для XOR:\\n\")\nprint(\"x₁  x₂  | h₁ (OR-подібний) | h₂ (AND-подібний) | z_out      | ŷ (σ(z)) | Очікується\")\nprint(\"-\" * 90)\n\nfor x in X:\n    # Прихований шар\n    z_hidden = W1 @ x + b1\n    h = sigmoid(z_hidden)\n\n    # Вихідний шар\n    z_out = W2 @ h + b2\n    y_pred = sigmoid(z_out)\n\n    expected = int(x[0] != x[1])  # XOR: 1 якщо входи різні\n    status = \"✓\" if round(y_pred[0]) == expected else \"✗\"\n\n    print(f\"{x[0]}   {x[1]}   |      {h[0]:.3f}       |      {h[1]:.3f}        | {z_out[0]:7.3f}   | {y_pred[0]:7.3f}  | {expected}        {status}\")\n",[5530,7758,7759,7769,7773,7786,7791,7805,7809,7814,7819,7836,7852,7857,7874,7878,7883,7901,7911,7915,7920,7925,7938,7950,7962,7974,7978,7982,7997,8008,8023,8027,8039,8044,8049,8054,8058,8063,8068,8073,8077,8098,8121,8125],{"__ignoreMap":5528},[5533,7760,7761,7763,7765,7767],{"class":5535,"line":5536},[5533,7762,5904],{"class":5903},[5533,7764,5908],{"class":5907},[5533,7766,5911],{"class":5903},[5533,7768,5914],{"class":5907},[5533,7770,7771],{"class":5535,"line":5542},[5533,7772,5563],{"emptyLinePlaceholder":5205},[5533,7774,7775,7777,7780,7782,7784],{"class":5535,"line":5548},[5533,7776,5924],{"class":5923},[5533,7778,7779],{"class":5927}," sigmoid",[5533,7781,5931],{"class":5907},[5533,7783,5453],{"class":5934},[5533,7785,5937],{"class":5907},[5533,7787,7788],{"class":5535,"line":5554},[5533,7789,7790],{"class":5942},"    \"\"\"Сигмоїда: σ(z) = 1 \u002F (1 + e^(-z))\"\"\"\n",[5533,7792,7793,7795,7797,7800,7802],{"class":5535,"line":5560},[5533,7794,5948],{"class":5903},[5533,7796,5952],{"class":5951},[5533,7798,7799],{"class":5907}," \u002F (",[5533,7801,5495],{"class":5951},[5533,7803,7804],{"class":5907}," + np.exp(-z))\n",[5533,7806,7807],{"class":5535,"line":5566},[5533,7808,5563],{"emptyLinePlaceholder":5205},[5533,7810,7811],{"class":5535,"line":5572},[5533,7812,7813],{"class":5975},"# Ваги для прихованого шару (підібрані вручну для демонстрації)\n",[5533,7815,7816],{"class":5535,"line":5578},[5533,7817,7818],{"class":5907},"W1 = np.array([\n",[5533,7820,7821,7824,7826,7828,7830,7833],{"class":5535,"line":5584},[5533,7822,7823],{"class":5907},"    [",[5533,7825,5984],{"class":5951},[5533,7827,5987],{"class":5907},[5533,7829,5984],{"class":5951},[5533,7831,7832],{"class":5907},"],   ",[5533,7834,7835],{"class":5975},"# h1: реагує на OR (x1 + x2)\n",[5533,7837,7838,7840,7842,7844,7846,7849],{"class":5535,"line":5589},[5533,7839,7823],{"class":5907},[5533,7841,5984],{"class":5951},[5533,7843,5987],{"class":5907},[5533,7845,5984],{"class":5951},[5533,7847,7848],{"class":5907},"]    ",[5533,7850,7851],{"class":5975},"# h2: реагує на AND (x1 * x2 при правильному bias)\n",[5533,7853,7854],{"class":5535,"line":5595},[5533,7855,7856],{"class":5907},"])\n",[5533,7858,7859,7862,7864,7866,7868,7871],{"class":5535,"line":5601},[5533,7860,7861],{"class":5907},"b1 = np.array([-",[5533,7863,6923],{"class":5951},[5533,7865,5992],{"class":5907},[5533,7867,7002],{"class":5951},[5533,7869,7870],{"class":5907},"])  ",[5533,7872,7873],{"class":5975},"# Порогові значення\n",[5533,7875,7876],{"class":5535,"line":5607},[5533,7877,5563],{"emptyLinePlaceholder":5205},[5533,7879,7880],{"class":5535,"line":5613},[5533,7881,7882],{"class":5975},"# Ваги для вихідного шару\n",[5533,7884,7885,7888,7890,7892,7895,7898],{"class":5535,"line":5619},[5533,7886,7887],{"class":5907},"W2 = np.array([",[5533,7889,5984],{"class":5951},[5533,7891,5992],{"class":5907},[5533,7893,7894],{"class":5951},"2.0",[5533,7896,7897],{"class":5907},"])   ",[5533,7899,7900],{"class":5975},"# y = h1 - 2*h2\n",[5533,7902,7903,7906,7909],{"class":5535,"line":5625},[5533,7904,7905],{"class":5907},"b2 = np.array([",[5533,7907,7908],{"class":5951},"0.0",[5533,7910,7856],{"class":5907},[5533,7912,7913],{"class":5535,"line":5630},[5533,7914,5563],{"emptyLinePlaceholder":5205},[5533,7916,7917],{"class":5535,"line":5636},[5533,7918,7919],{"class":5975},"# Вхідні дані XOR\n",[5533,7921,7922],{"class":5535,"line":5642},[5533,7923,7924],{"class":5907},"X = np.array([\n",[5533,7926,7927,7929,7931,7933,7935],{"class":5535,"line":5648},[5533,7928,7823],{"class":5907},[5533,7930,5833],{"class":5951},[5533,7932,5987],{"class":5907},[5533,7934,5833],{"class":5951},[5533,7936,7937],{"class":5907},"],\n",[5533,7939,7940,7942,7944,7946,7948],{"class":5535,"line":5654},[5533,7941,7823],{"class":5907},[5533,7943,5833],{"class":5951},[5533,7945,5987],{"class":5907},[5533,7947,5495],{"class":5951},[5533,7949,7937],{"class":5907},[5533,7951,7952,7954,7956,7958,7960],{"class":5535,"line":5659},[5533,7953,7823],{"class":5907},[5533,7955,5495],{"class":5951},[5533,7957,5987],{"class":5907},[5533,7959,5833],{"class":5951},[5533,7961,7937],{"class":5907},[5533,7963,7964,7966,7968,7970,7972],{"class":5535,"line":5664},[5533,7965,7823],{"class":5907},[5533,7967,5495],{"class":5951},[5533,7969,5987],{"class":5907},[5533,7971,5495],{"class":5951},[5533,7973,6663],{"class":5907},[5533,7975,7976],{"class":5535,"line":5670},[5533,7977,7856],{"class":5907},[5533,7979,7980],{"class":5535,"line":5676},[5533,7981,5563],{"emptyLinePlaceholder":5205},[5533,7983,7984,7986,7988,7991,7993,7995],{"class":5535,"line":5681},[5533,7985,6052],{"class":5927},[5533,7987,5931],{"class":5907},[5533,7989,7990],{"class":5942},"\"Обчислення MLP для XOR:",[5533,7992,6871],{"class":6870},[5533,7994,6155],{"class":5942},[5533,7996,6060],{"class":5907},[5533,7998,7999,8001,8003,8006],{"class":5535,"line":5686},[5533,8000,6052],{"class":5927},[5533,8002,5931],{"class":5907},[5533,8004,8005],{"class":5942},"\"x₁  x₂  | h₁ (OR-подібний) | h₂ (AND-подібний) | z_out      | ŷ (σ(z)) | Очікується\"",[5533,8007,6060],{"class":5907},[5533,8009,8010,8012,8014,8016,8018,8021],{"class":5535,"line":5692},[5533,8011,6052],{"class":5927},[5533,8013,5931],{"class":5907},[5533,8015,6069],{"class":5942},[5533,8017,6072],{"class":5907},[5533,8019,8020],{"class":5951},"90",[5533,8022,6060],{"class":5907},[5533,8024,8025],{"class":5535,"line":5698},[5533,8026,5563],{"emptyLinePlaceholder":5205},[5533,8028,8029,8031,8034,8036],{"class":5535,"line":5704},[5533,8030,6086],{"class":5903},[5533,8032,8033],{"class":5907}," x ",[5533,8035,6092],{"class":5903},[5533,8037,8038],{"class":5907}," X:\n",[5533,8040,8041],{"class":5535,"line":5710},[5533,8042,8043],{"class":5975},"    # Прихований шар\n",[5533,8045,8046],{"class":5535,"line":5715},[5533,8047,8048],{"class":5907},"    z_hidden = W1 @ x + b1\n",[5533,8050,8051],{"class":5535,"line":5721},[5533,8052,8053],{"class":5907},"    h = sigmoid(z_hidden)\n",[5533,8055,8056],{"class":5535,"line":5726},[5533,8057,5563],{"emptyLinePlaceholder":5205},[5533,8059,8060],{"class":5535,"line":5732},[5533,8061,8062],{"class":5975},"    # Вихідний шар\n",[5533,8064,8065],{"class":5535,"line":5738},[5533,8066,8067],{"class":5907},"    z_out = W2 @ h + b2\n",[5533,8069,8070],{"class":5535,"line":5744},[5533,8071,8072],{"class":5907},"    y_pred = sigmoid(z_out)\n",[5533,8074,8075],{"class":5535,"line":5750},[5533,8076,5563],{"emptyLinePlaceholder":5205},[5533,8078,8079,8081,8083,8086,8088,8091,8093,8095],{"class":5535,"line":5755},[5533,8080,6110],{"class":5907},[5533,8082,6114],{"class":6113},[5533,8084,8085],{"class":5907},"(x[",[5533,8087,5833],{"class":5951},[5533,8089,8090],{"class":5907},"] != x[",[5533,8092,5495],{"class":5951},[5533,8094,7870],{"class":5907},[5533,8096,8097],{"class":5975},"# XOR: 1 якщо входи різні\n",[5533,8099,8100,8102,8104,8106,8109,8112,8114,8117,8119],{"class":5535,"line":5761},[5533,8101,6128],{"class":5907},[5533,8103,6131],{"class":5942},[5533,8105,5955],{"class":5903},[5533,8107,8108],{"class":5927}," round",[5533,8110,8111],{"class":5907},"(y_pred[",[5533,8113,5833],{"class":5951},[5533,8115,8116],{"class":5907},"]) == expected ",[5533,8118,6139],{"class":5903},[5533,8120,6142],{"class":5942},[5533,8122,8123],{"class":5535,"line":5767},[5533,8124,5563],{"emptyLinePlaceholder":5205},[5533,8126,8127,8129,8131,8133,8135,8137,8140,8142,8145,8147,8149,8151,8153,8155,8157,8160,8162,8165,8167,8169,8172,8175,8177,8179,8181,8183,8185,8188,8190,8193,8195,8197,8200,8203,8205,8208,8210,8212,8214,8217,8219,8221,8223,8225,8227,8229,8231],{"class":5535,"line":5773},[5533,8128,6147],{"class":5927},[5533,8130,5931],{"class":5907},[5533,8132,6152],{"class":5923},[5533,8134,6155],{"class":5942},[5533,8136,6158],{"class":5923},[5533,8138,8139],{"class":5907},"x[",[5533,8141,5833],{"class":5951},[5533,8143,8144],{"class":5907},"]",[5533,8146,6164],{"class":5923},[5533,8148,6167],{"class":5923},[5533,8150,8139],{"class":5907},[5533,8152,5495],{"class":5951},[5533,8154,8144],{"class":5907},[5533,8156,6164],{"class":5923},[5533,8158,8159],{"class":5942},"   |      ",[5533,8161,6158],{"class":5923},[5533,8163,8164],{"class":5907},"h[",[5533,8166,5833],{"class":5951},[5533,8168,8144],{"class":5907},[5533,8170,8171],{"class":5923},":.3f}",[5533,8173,8174],{"class":5942},"       |      ",[5533,8176,6158],{"class":5923},[5533,8178,8164],{"class":5907},[5533,8180,5495],{"class":5951},[5533,8182,8144],{"class":5907},[5533,8184,8171],{"class":5923},[5533,8186,8187],{"class":5942},"        | ",[5533,8189,6158],{"class":5923},[5533,8191,8192],{"class":5907},"z_out[",[5533,8194,5833],{"class":5951},[5533,8196,8144],{"class":5907},[5533,8198,8199],{"class":5923},":7.3f}",[5533,8201,8202],{"class":5942},"   | ",[5533,8204,6158],{"class":5923},[5533,8206,8207],{"class":5907},"y_pred[",[5533,8209,5833],{"class":5951},[5533,8211,8144],{"class":5907},[5533,8213,8199],{"class":5923},[5533,8215,8216],{"class":5942},"  | ",[5533,8218,6158],{"class":5923},[5533,8220,6200],{"class":5907},[5533,8222,6164],{"class":5923},[5533,8224,6205],{"class":5923},[5533,8226,6208],{"class":5907},[5533,8228,6164],{"class":5923},[5533,8230,6155],{"class":5942},[5533,8232,6060],{"class":5907},[6216,8234,8235],{"v-slot:output":5528},[5806,8236,8237,8263],{},[5809,8238,8239],{},[5812,8240,8241,8243,8245,8248,8251,8254,8257,8260],{},[5815,8242,6226],{"align":5817},[5815,8244,6229],{"align":5817},[5815,8246,8247],{"align":5817},"$h_1$ (OR-подібний)",[5815,8249,8250],{"align":5817},"$h_2$ (AND-подібний)",[5815,8252,8253],{"align":5817},"$z_{\\text{out}}$",[5815,8255,8256],{"align":5817},"$\\hat{y} = \\sigma(z)$",[5815,8258,8259],{"align":5817},"Очікуване (XOR)",[5815,8261,8262],{"align":6241},"Результат класифікації",[5826,8264,8265,8302,8338,8370],{},[5812,8266,8267,8271,8275,8280,8285,8290,8295,8299],{},[5831,8268,8269],{"align":5817},[5198,8270,5833],{},[5831,8272,8273],{"align":5817},[5198,8274,5833],{},[5831,8276,8277],{"align":5817},[5530,8278,8279],{},"0.378",[5831,8281,8282],{"align":5817},[5530,8283,8284],{},"0.182",[5831,8286,8287],{"align":5817},[5530,8288,8289],{},"-0.014",[5831,8291,8292],{"align":5817},[5530,8293,8294],{},"0.496",[5831,8296,8297],{"align":5817},[5198,8298,5833],{},[5831,8300,8301],{"align":6241},"✅ Вірно (нижче порогу 0.5)",[5812,8303,8304,8308,8312,8317,8321,8326,8331,8335],{},[5831,8305,8306],{"align":5817},[5198,8307,5833],{},[5831,8309,8310],{"align":5817},[5198,8311,5495],{},[5831,8313,8314],{"align":5817},[5530,8315,8316],{},"0.622",[5831,8318,8319],{"align":5817},[5530,8320,8279],{},[5831,8322,8323],{"align":5817},[5530,8324,8325],{},"-0.134",[5831,8327,8328],{"align":5817},[5530,8329,8330],{},"0.467",[5831,8332,8333],{"align":5817},[5198,8334,5495],{},[5831,8336,8337],{"align":6241},"✅ Вірно (активація $h_1$)",[5812,8339,8340,8344,8348,8352,8356,8360,8364,8368],{},[5831,8341,8342],{"align":5817},[5198,8343,5495],{},[5831,8345,8346],{"align":5817},[5198,8347,5833],{},[5831,8349,8350],{"align":5817},[5530,8351,8316],{},[5831,8353,8354],{"align":5817},[5530,8355,8279],{},[5831,8357,8358],{"align":5817},[5530,8359,8325],{},[5831,8361,8362],{"align":5817},[5530,8363,8330],{},[5831,8365,8366],{"align":5817},[5198,8367,5495],{},[5831,8369,8337],{"align":6241},[5812,8371,8372,8376,8380,8385,8389,8394,8399,8403],{},[5831,8373,8374],{"align":5817},[5198,8375,5495],{},[5831,8377,8378],{"align":5817},[5198,8379,5495],{},[5831,8381,8382],{"align":5817},[5530,8383,8384],{},"0.818",[5831,8386,8387],{"align":5817},[5530,8388,8316],{},[5831,8390,8391],{"align":5817},[5530,8392,8393],{},"-0.426",[5831,8395,8396],{"align":5817},[5530,8397,8398],{},"0.395",[5831,8400,8401],{"align":5817},[5198,8402,5833],{},[5831,8404,8405],{"align":6241},"✅ Вірно (гальмування $h_2$)",[5890,8407,8408,8412,8418,8421],{"type":7725},[7727,8409,8411],{"id":8410},"крок-2-вихідний-нейрон-комбінує-проміжні-ознаки","Крок 2: Вихідний нейрон комбінує проміжні ознаки",[5191,8413,8414,8415,5462],{},"Вихідний нейрон $\\hat{y}$ обчислює ",[5198,8416,8417],{},"XOR = OR AND NOT AND",[5191,8419,8420],{},"$$\\text{XOR}(x_1, x_2) = \\text{OR}(x_1, x_2) ; \\text{AND NOT} ; \\text{AND}(x_1, x_2)$$",[5191,8422,8423],{},"Саме це робить формула $\\hat{y} = h_1 - 2 \\cdot h_2$: якщо обидва входи активні ($h_2$ велике), то сильне від'ємне значення від $-2 \\cdot h_2$ «вимикає» вихід.",[5191,8425,8426],{},[5224,8427],{"alt":8428,"className":8429,"src":8430},"Трансформація простору ознак у багатошаровому персептроні: перехід від нелінійної задачі XOR до лінійно роздільної у прихованому просторі",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F06.png",[5329,8432,8434],{"alt":8433},"Трансформація простору ознак у MLP",[5523,8435,8437],{"className":5525,"code":8436,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define INPUT_COLOR DBEAFE\n!define HIDDEN_COLOR FEF3C7\n!define OUTPUT_COLOR DCFCE7\n\nrectangle \"1. Вхідний простір (x₁, x₂)\" as input_space #INPUT_COLOR {\n  card \"Точки нелінійні:\\n(0,0)=0, (1,1)=0\\n(0,1)=1, (1,0)=1\" as raw_pts\n  card \"Потрібні дві лінії розділення:\\n• h₁: x₁ + x₂ = 0.5 (OR)\\n• h₂: x₁ + x₂ = 1.5 (AND)\" as lines\n}\n\nrectangle \"2. Нелінійна активація σ(z)\" as activation #HIDDEN_COLOR {\n  card \"Прихований шар деформує простір:\\nточки (0,1) та (1,0) зближуються,\\nа (0,0) та (1,1) розсуваються\" as transform\n}\n\nrectangle \"3. Прихований простір (h₁, h₂)\" as hidden_space #OUTPUT_COLOR {\n  card \"Точки стають лінійно роздільними!\" as sep_pts\n  card \"Вихідний нейрон проводить пряму:\\nh₁ - 2·h₂ = 0\" as final_line\n}\n\ninput_space -right-> activation : W₁, b₁\nactivation -right-> hidden_space : W₂, b₂\n@enduml\n",[5530,8438,8439,8443,8447,8451,8455,8459,8463,8467,8471,8475,8480,8485,8490,8494,8498,8503,8508,8512,8516,8521,8526,8531,8535,8539,8544,8549],{"__ignoreMap":5528},[5533,8440,8441],{"class":5535,"line":5536},[5533,8442,5539],{},[5533,8444,8445],{"class":5535,"line":5542},[5533,8446,5545],{},[5533,8448,8449],{"class":5535,"line":5548},[5533,8450,5551],{},[5533,8452,8453],{"class":5535,"line":5554},[5533,8454,5557],{},[5533,8456,8457],{"class":5535,"line":5560},[5533,8458,5563],{"emptyLinePlaceholder":5205},[5533,8460,8461],{"class":5535,"line":5566},[5533,8462,5569],{},[5533,8464,8465],{"class":5535,"line":5572},[5533,8466,7561],{},[5533,8468,8469],{"class":5535,"line":5578},[5533,8470,5581],{},[5533,8472,8473],{"class":5535,"line":5584},[5533,8474,5563],{"emptyLinePlaceholder":5205},[5533,8476,8477],{"class":5535,"line":5589},[5533,8478,8479],{},"rectangle \"1. Вхідний простір (x₁, x₂)\" as input_space #INPUT_COLOR {\n",[5533,8481,8482],{"class":5535,"line":5595},[5533,8483,8484],{},"  card \"Точки нелінійні:\\n(0,0)=0, (1,1)=0\\n(0,1)=1, (1,0)=1\" as raw_pts\n",[5533,8486,8487],{"class":5535,"line":5601},[5533,8488,8489],{},"  card \"Потрібні дві лінії розділення:\\n• h₁: x₁ + x₂ = 0.5 (OR)\\n• h₂: x₁ + x₂ = 1.5 (AND)\" as lines\n",[5533,8491,8492],{"class":5535,"line":5607},[5533,8493,5622],{},[5533,8495,8496],{"class":5535,"line":5613},[5533,8497,5563],{"emptyLinePlaceholder":5205},[5533,8499,8500],{"class":5535,"line":5619},[5533,8501,8502],{},"rectangle \"2. Нелінійна активація σ(z)\" as activation #HIDDEN_COLOR {\n",[5533,8504,8505],{"class":5535,"line":5625},[5533,8506,8507],{},"  card \"Прихований шар деформує простір:\\nточки (0,1) та (1,0) зближуються,\\nа (0,0) та (1,1) розсуваються\" as transform\n",[5533,8509,8510],{"class":5535,"line":5630},[5533,8511,5622],{},[5533,8513,8514],{"class":5535,"line":5636},[5533,8515,5563],{"emptyLinePlaceholder":5205},[5533,8517,8518],{"class":5535,"line":5642},[5533,8519,8520],{},"rectangle \"3. Прихований простір (h₁, h₂)\" as hidden_space #OUTPUT_COLOR {\n",[5533,8522,8523],{"class":5535,"line":5648},[5533,8524,8525],{},"  card \"Точки стають лінійно роздільними!\" as sep_pts\n",[5533,8527,8528],{"class":5535,"line":5654},[5533,8529,8530],{},"  card \"Вихідний нейрон проводить пряму:\\nh₁ - 2·h₂ = 0\" as final_line\n",[5533,8532,8533],{"class":5535,"line":5659},[5533,8534,5622],{},[5533,8536,8537],{"class":5535,"line":5664},[5533,8538,5563],{"emptyLinePlaceholder":5205},[5533,8540,8541],{"class":5535,"line":5670},[5533,8542,8543],{},"input_space -right-> activation : W₁, b₁\n",[5533,8545,8546],{"class":5535,"line":5676},[5533,8547,8548],{},"activation -right-> hidden_space : W₂, b₂\n",[5533,8550,8551],{"class":5535,"line":5681},[5533,8552,5786],{},[6339,8554,8555,8560,8567,8588],{},[5191,8556,8557],{},[5198,8558,8559],{},"Головна ідея MLP:",[5191,8561,8562,8563,8566],{},"Приховані шари створюють ",[5198,8564,8565],{},"нові, більш інформативні ознаки"," з вихідних. У випадку XOR:",[5249,8568,8569,8575,8582],{},[5252,8570,8571,8572,8574],{},"Вхід: ",[5369,8573],{"tex":7512,":inline":5372}," (лінійно нероздільні)",[5252,8576,8577,8578,8581],{},"Після прихованого шару: ",[5369,8579],{"tex":8580,":inline":5372},"h_1, h_2"," (вже лінійно роздільні!)",[5252,8583,8584,8585],{},"Вихідний шар просто проводить лінію розділення у новому просторі ",[5369,8586],{"tex":8587,":inline":5372},"(h_1, h_2)",[5191,8589,8590],{},"Це як перейти з 2D у вищий вимір, де задача стає простішою.",[5309,8592],{},[5186,8594,8596],{"id":8595},"функції-активації-ключ-до-нелінійності","Функції активації — ключ до нелінійності",[5191,8598,8599,8600,8603],{},"Ми вже бачили функцію кроку та сигмоїду. Але чому взагалі потрібна ",[5198,8601,8602],{},"будь-яка"," функція активації? Що станеться, якщо її не буде?",[5351,8605,8607],{"id":8606},"чому-без-активації-мережа-колапсує-до-лінійної-моделі","Чому без активації мережа колапсує до лінійної моделі",[5191,8609,8610,8611,8614],{},"Уявімо MLP ",[5198,8612,8613],{},"без"," функцій активації (тобто кожен нейрон просто обчислює зважену суму):",[5369,8616],{"tex":8617},"h = W_1 x + b_1 \\quad \\text{(без активації)}",[5369,8619],{"tex":8620},"\\hat{y} = W_2 h + b_2 = W_2 (W_1 x + b_1) + b_2",[5191,8622,8623],{},"Розкриємо дужки:",[5369,8625],{"tex":8626},"\\hat{y} = (W_2 W_1) x + (W_2 b_1 + b_2)",[5191,8628,8629,8630,8633,8634,5462],{},"Позначимо ",[5369,8631],{"tex":8632,":inline":5372},"W' = W_2 W_1"," та ",[5369,8635],{"tex":8636,":inline":5372},"b' = W_2 b_1 + b_2",[5369,8638],{"tex":8639},"\\hat{y} = W' x + b'",[5191,8641,8642,8645,8646,5799],{},[5198,8643,8644],{},"Результат:"," отримали просту лінійну модель! Неважливо, скільки шарів ви додасте — без нелінійної активації вся мережа ",[5198,8647,8648],{},"редукується до однієї лінійної функції",[7128,8650,8651,8656,8663],{},[5191,8652,8653],{},[5198,8654,8655],{},"Критичний висновок:",[5191,8657,8658,8659,8662],{},"Без функції активації багатошарова нейронна мережа ",[5198,8660,8661],{},"еквівалентна"," одношаровому персептрону. Всі приховані шари стають марними — їх можна «склеїти» в одну матрицю.",[5249,8664,8665],{},[5252,8666,8667],{},[5198,8668,8669],{},"Функція активації — це те, що дає мережі можливість моделювати нелінійні залежності.",[5309,8671],{},[5351,8673,8675],{"id":8674},"огляд-популярних-функцій-активації","Огляд популярних функцій активації",[5191,8677,8678],{},"Розглянемо найважливіші функції активації, їхні переваги та недоліки.",[7727,8680,8682],{"id":8681},"_1-сигмоїда-sigmoid","1. Сигмоїда (Sigmoid)",[5191,8684,8685],{},[5198,8686,8687],{},"Формула:",[5369,8689],{"tex":8690},"\\sigma(z) = \\frac{1}{1 + e^{-z}}",[5191,8692,8693,5479,8696],{},[5198,8694,8695],{},"Діапазон виходу:",[5369,8697],{"tex":8698,":inline":5372},"(0, 1)",[5191,8700,8701],{},[5198,8702,8703],{},"Властивості:",[5249,8705,8706,8709,8712],{},[5252,8707,8708],{},"Плавна S-подібна крива",[5252,8710,8711],{},"Інтерпретується як ймовірність",[5252,8713,8714],{},"Виходи завжди додатні",[5885,8716,8718],{"kernel":5887,"title":8717},"activation_functions.ipynb",[5890,8719,8722,9828],{"execution-count":8720,"execution-time":8721},"4","0.28s",[5523,8723,8725],{"className":5894,"code":8724,"language":5896,"meta":5528,"style":5528},"import numpy as np\nimport matplotlib.pyplot as plt\n\n# Визначення функцій активації\ndef sigmoid(z):\n    return 1 \u002F (1 + np.exp(-z))\n\ndef tanh(z):\n    return np.tanh(z)\n\ndef relu(z):\n    return np.maximum(0, z)\n\ndef leaky_relu(z, alpha=0.01):\n    return np.where(z > 0, z, alpha * z)\n\n# Діапазон значень\nz = np.linspace(-5, 5, 200)\n\n# Візуалізація\nfig, axes = plt.subplots(2, 2, figsize=(14, 10))\n\n# Сигмоїда\naxes[0, 0].plot(z, sigmoid(z), color='#3b82f6', linewidth=3)\naxes[0, 0].axhline(0, color='gray', linestyle='--', alpha=0.3)\naxes[0, 0].axvline(0, color='gray', linestyle='--', alpha=0.3)\naxes[0, 0].grid(alpha=0.3)\naxes[0, 0].set_title('Сигмоїда: σ(z) = 1\u002F(1+e⁻ᶻ)', fontsize=14, fontweight='bold')\naxes[0, 0].set_ylabel('σ(z)', fontsize=12)\naxes[0, 0].set_ylim(-0.2, 1.2)\n\n# Tanh\naxes[0, 1].plot(z, tanh(z), color='#8b5cf6', linewidth=3)\naxes[0, 1].axhline(0, color='gray', linestyle='--', alpha=0.3)\naxes[0, 1].axvline(0, color='gray', linestyle='--', alpha=0.3)\naxes[0, 1].grid(alpha=0.3)\naxes[0, 1].set_title('Tanh: tanh(z)', fontsize=14, fontweight='bold')\naxes[0, 1].set_ylabel('tanh(z)', fontsize=12)\n\n# ReLU\naxes[1, 0].plot(z, relu(z), color='#10b981', linewidth=3)\naxes[1, 0].axhline(0, color='gray', linestyle='--', alpha=0.3)\naxes[1, 0].axvline(0, color='gray', linestyle='--', alpha=0.3)\naxes[1, 0].grid(alpha=0.3)\naxes[1, 0].set_title('ReLU: max(0, z)', fontsize=14, fontweight='bold')\naxes[1, 0].set_xlabel('z', fontsize=12)\naxes[1, 0].set_ylabel('ReLU(z)', fontsize=12)\n\n# Leaky ReLU\naxes[1, 1].plot(z, leaky_relu(z), color='#f59e0b', linewidth=3)\naxes[1, 1].axhline(0, color='gray', linestyle='--', alpha=0.3)\naxes[1, 1].axvline(0, color='gray', linestyle='--', alpha=0.3)\naxes[1, 1].grid(alpha=0.3)\naxes[1, 1].set_title('Leaky ReLU: max(0.01z, z)', fontsize=14, fontweight='bold')\naxes[1, 1].set_xlabel('z', fontsize=12)\naxes[1, 1].set_ylabel('Leaky ReLU(z)', fontsize=12)\n\nplt.tight_layout()\nplt.show()\n",[5530,8726,8727,8737,8747,8751,8756,8768,8780,8784,8797,8804,8808,8821,8833,8837,8859,8871,8875,8880,8899,8903,8908,8934,8938,8943,8974,9015,9056,9077,9111,9137,9160,9164,9169,9199,9239,9279,9299,9332,9357,9361,9366,9396,9436,9476,9496,9530,9557,9583,9588,9594,9625,9666,9707,9728,9762,9787,9813,9818,9823],{"__ignoreMap":5528},[5533,8728,8729,8731,8733,8735],{"class":5535,"line":5536},[5533,8730,5904],{"class":5903},[5533,8732,5908],{"class":5907},[5533,8734,5911],{"class":5903},[5533,8736,5914],{"class":5907},[5533,8738,8739,8741,8743,8745],{"class":5535,"line":5542},[5533,8740,5904],{"class":5903},[5533,8742,6617],{"class":5907},[5533,8744,5911],{"class":5903},[5533,8746,6622],{"class":5907},[5533,8748,8749],{"class":5535,"line":5548},[5533,8750,5563],{"emptyLinePlaceholder":5205},[5533,8752,8753],{"class":5535,"line":5554},[5533,8754,8755],{"class":5975},"# Визначення функцій активації\n",[5533,8757,8758,8760,8762,8764,8766],{"class":5535,"line":5560},[5533,8759,5924],{"class":5923},[5533,8761,7779],{"class":5927},[5533,8763,5931],{"class":5907},[5533,8765,5453],{"class":5934},[5533,8767,5937],{"class":5907},[5533,8769,8770,8772,8774,8776,8778],{"class":5535,"line":5566},[5533,8771,5948],{"class":5903},[5533,8773,5952],{"class":5951},[5533,8775,7799],{"class":5907},[5533,8777,5495],{"class":5951},[5533,8779,7804],{"class":5907},[5533,8781,8782],{"class":5535,"line":5572},[5533,8783,5563],{"emptyLinePlaceholder":5205},[5533,8785,8786,8788,8791,8793,8795],{"class":5535,"line":5578},[5533,8787,5924],{"class":5923},[5533,8789,8790],{"class":5927}," tanh",[5533,8792,5931],{"class":5907},[5533,8794,5453],{"class":5934},[5533,8796,5937],{"class":5907},[5533,8798,8799,8801],{"class":5535,"line":5584},[5533,8800,5948],{"class":5903},[5533,8802,8803],{"class":5907}," np.tanh(z)\n",[5533,8805,8806],{"class":5535,"line":5589},[5533,8807,5563],{"emptyLinePlaceholder":5205},[5533,8809,8810,8812,8815,8817,8819],{"class":5535,"line":5595},[5533,8811,5924],{"class":5923},[5533,8813,8814],{"class":5927}," relu",[5533,8816,5931],{"class":5907},[5533,8818,5453],{"class":5934},[5533,8820,5937],{"class":5907},[5533,8822,8823,8825,8828,8830],{"class":5535,"line":5601},[5533,8824,5948],{"class":5903},[5533,8826,8827],{"class":5907}," np.maximum(",[5533,8829,5833],{"class":5951},[5533,8831,8832],{"class":5907},", z)\n",[5533,8834,8835],{"class":5535,"line":5607},[5533,8836,5563],{"emptyLinePlaceholder":5205},[5533,8838,8839,8841,8844,8846,8848,8850,8852,8854,8857],{"class":5535,"line":5613},[5533,8840,5924],{"class":5923},[5533,8842,8843],{"class":5927}," leaky_relu",[5533,8845,5931],{"class":5907},[5533,8847,5453],{"class":5934},[5533,8849,5987],{"class":5907},[5533,8851,6802],{"class":5934},[5533,8853,6775],{"class":5907},[5533,8855,8856],{"class":5951},"0.01",[5533,8858,5937],{"class":5907},[5533,8860,8861,8863,8866,8868],{"class":5535,"line":5619},[5533,8862,5948],{"class":5903},[5533,8864,8865],{"class":5907}," np.where(z > ",[5533,8867,5833],{"class":5951},[5533,8869,8870],{"class":5907},", z, alpha * z)\n",[5533,8872,8873],{"class":5535,"line":5625},[5533,8874,5563],{"emptyLinePlaceholder":5205},[5533,8876,8877],{"class":5535,"line":5630},[5533,8878,8879],{"class":5975},"# Діапазон значень\n",[5533,8881,8882,8885,8888,8890,8892,8894,8897],{"class":5535,"line":5636},[5533,8883,8884],{"class":5907},"z = np.linspace(-",[5533,8886,8887],{"class":5951},"5",[5533,8889,5987],{"class":5907},[5533,8891,8887],{"class":5951},[5533,8893,5987],{"class":5907},[5533,8895,8896],{"class":5951},"200",[5533,8898,6060],{"class":5907},[5533,8900,8901],{"class":5535,"line":5642},[5533,8902,5563],{"emptyLinePlaceholder":5205},[5533,8904,8905],{"class":5535,"line":5648},[5533,8906,8907],{"class":5975},"# Візуалізація\n",[5533,8909,8910,8913,8915,8917,8919,8921,8923,8925,8927,8929,8932],{"class":5535,"line":5654},[5533,8911,8912],{"class":5907},"fig, axes = plt.subplots(",[5533,8914,6604],{"class":5951},[5533,8916,5987],{"class":5907},[5533,8918,6604],{"class":5951},[5533,8920,5987],{"class":5907},[5533,8922,6744],{"class":5934},[5533,8924,6747],{"class":5907},[5533,8926,7034],{"class":5951},[5533,8928,5987],{"class":5907},[5533,8930,8931],{"class":5951},"10",[5533,8933,6758],{"class":5907},[5533,8935,8936],{"class":5535,"line":5659},[5533,8937,5563],{"emptyLinePlaceholder":5205},[5533,8939,8940],{"class":5535,"line":5664},[5533,8941,8942],{"class":5975},"# Сигмоїда\n",[5533,8944,8945,8948,8950,8952,8954,8957,8959,8961,8964,8966,8968,8970,8972],{"class":5535,"line":5670},[5533,8946,8947],{"class":5907},"axes[",[5533,8949,5833],{"class":5951},[5533,8951,5987],{"class":5907},[5533,8953,5833],{"class":5951},[5533,8955,8956],{"class":5907},"].plot(z, sigmoid(z), ",[5533,8958,6942],{"class":5934},[5533,8960,6775],{"class":5907},[5533,8962,8963],{"class":5942},"'#3b82f6'",[5533,8965,5987],{"class":5907},[5533,8967,6962],{"class":5934},[5533,8969,6775],{"class":5907},[5533,8971,7457],{"class":5951},[5533,8973,6060],{"class":5907},[5533,8975,8976,8978,8980,8982,8984,8987,8989,8991,8993,8995,8997,8999,9001,9003,9005,9007,9009,9011,9013],{"class":5535,"line":5676},[5533,8977,8947],{"class":5907},[5533,8979,5833],{"class":5951},[5533,8981,5987],{"class":5907},[5533,8983,5833],{"class":5951},[5533,8985,8986],{"class":5907},"].axhline(",[5533,8988,5833],{"class":5951},[5533,8990,5987],{"class":5907},[5533,8992,6942],{"class":5934},[5533,8994,6775],{"class":5907},[5533,8996,6947],{"class":5942},[5533,8998,5987],{"class":5907},[5533,9000,6952],{"class":5934},[5533,9002,6775],{"class":5907},[5533,9004,6957],{"class":5942},[5533,9006,5987],{"class":5907},[5533,9008,6802],{"class":5934},[5533,9010,6775],{"class":5907},[5533,9012,6997],{"class":5951},[5533,9014,6060],{"class":5907},[5533,9016,9017,9019,9021,9023,9025,9028,9030,9032,9034,9036,9038,9040,9042,9044,9046,9048,9050,9052,9054],{"class":5535,"line":5681},[5533,9018,8947],{"class":5907},[5533,9020,5833],{"class":5951},[5533,9022,5987],{"class":5907},[5533,9024,5833],{"class":5951},[5533,9026,9027],{"class":5907},"].axvline(",[5533,9029,5833],{"class":5951},[5533,9031,5987],{"class":5907},[5533,9033,6942],{"class":5934},[5533,9035,6775],{"class":5907},[5533,9037,6947],{"class":5942},[5533,9039,5987],{"class":5907},[5533,9041,6952],{"class":5934},[5533,9043,6775],{"class":5907},[5533,9045,6957],{"class":5942},[5533,9047,5987],{"class":5907},[5533,9049,6802],{"class":5934},[5533,9051,6775],{"class":5907},[5533,9053,6997],{"class":5951},[5533,9055,6060],{"class":5907},[5533,9057,9058,9060,9062,9064,9066,9069,9071,9073,9075],{"class":5535,"line":5686},[5533,9059,8947],{"class":5907},[5533,9061,5833],{"class":5951},[5533,9063,5987],{"class":5907},[5533,9065,5833],{"class":5951},[5533,9067,9068],{"class":5907},"].grid(",[5533,9070,6802],{"class":5934},[5533,9072,6775],{"class":5907},[5533,9074,6997],{"class":5951},[5533,9076,6060],{"class":5907},[5533,9078,9079,9081,9083,9085,9087,9090,9093,9095,9097,9099,9101,9103,9105,9107,9109],{"class":5535,"line":5692},[5533,9080,8947],{"class":5907},[5533,9082,5833],{"class":5951},[5533,9084,5987],{"class":5907},[5533,9086,5833],{"class":5951},[5533,9088,9089],{"class":5907},"].set_title(",[5533,9091,9092],{"class":5942},"'Сигмоїда: σ(z) = 1\u002F(1+e⁻ᶻ)'",[5533,9094,5987],{"class":5907},[5533,9096,6889],{"class":5934},[5533,9098,6775],{"class":5907},[5533,9100,7034],{"class":5951},[5533,9102,5987],{"class":5907},[5533,9104,7076],{"class":5934},[5533,9106,6775],{"class":5907},[5533,9108,7081],{"class":5942},[5533,9110,6060],{"class":5907},[5533,9112,9113,9115,9117,9119,9121,9124,9127,9129,9131,9133,9135],{"class":5535,"line":5698},[5533,9114,8947],{"class":5907},[5533,9116,5833],{"class":5951},[5533,9118,5987],{"class":5907},[5533,9120,5833],{"class":5951},[5533,9122,9123],{"class":5907},"].set_ylabel(",[5533,9125,9126],{"class":5942},"'σ(z)'",[5533,9128,5987],{"class":5907},[5533,9130,6889],{"class":5934},[5533,9132,6775],{"class":5907},[5533,9134,6894],{"class":5951},[5533,9136,6060],{"class":5907},[5533,9138,9139,9141,9143,9145,9147,9150,9153,9155,9158],{"class":5535,"line":5704},[5533,9140,8947],{"class":5907},[5533,9142,5833],{"class":5951},[5533,9144,5987],{"class":5907},[5533,9146,5833],{"class":5951},[5533,9148,9149],{"class":5907},"].set_ylim(-",[5533,9151,9152],{"class":5951},"0.2",[5533,9154,5987],{"class":5907},[5533,9156,9157],{"class":5951},"1.2",[5533,9159,6060],{"class":5907},[5533,9161,9162],{"class":5535,"line":5710},[5533,9163,5563],{"emptyLinePlaceholder":5205},[5533,9165,9166],{"class":5535,"line":5715},[5533,9167,9168],{"class":5975},"# Tanh\n",[5533,9170,9171,9173,9175,9177,9179,9182,9184,9186,9189,9191,9193,9195,9197],{"class":5535,"line":5721},[5533,9172,8947],{"class":5907},[5533,9174,5833],{"class":5951},[5533,9176,5987],{"class":5907},[5533,9178,5495],{"class":5951},[5533,9180,9181],{"class":5907},"].plot(z, tanh(z), ",[5533,9183,6942],{"class":5934},[5533,9185,6775],{"class":5907},[5533,9187,9188],{"class":5942},"'#8b5cf6'",[5533,9190,5987],{"class":5907},[5533,9192,6962],{"class":5934},[5533,9194,6775],{"class":5907},[5533,9196,7457],{"class":5951},[5533,9198,6060],{"class":5907},[5533,9200,9201,9203,9205,9207,9209,9211,9213,9215,9217,9219,9221,9223,9225,9227,9229,9231,9233,9235,9237],{"class":5535,"line":5726},[5533,9202,8947],{"class":5907},[5533,9204,5833],{"class":5951},[5533,9206,5987],{"class":5907},[5533,9208,5495],{"class":5951},[5533,9210,8986],{"class":5907},[5533,9212,5833],{"class":5951},[5533,9214,5987],{"class":5907},[5533,9216,6942],{"class":5934},[5533,9218,6775],{"class":5907},[5533,9220,6947],{"class":5942},[5533,9222,5987],{"class":5907},[5533,9224,6952],{"class":5934},[5533,9226,6775],{"class":5907},[5533,9228,6957],{"class":5942},[5533,9230,5987],{"class":5907},[5533,9232,6802],{"class":5934},[5533,9234,6775],{"class":5907},[5533,9236,6997],{"class":5951},[5533,9238,6060],{"class":5907},[5533,9240,9241,9243,9245,9247,9249,9251,9253,9255,9257,9259,9261,9263,9265,9267,9269,9271,9273,9275,9277],{"class":5535,"line":5732},[5533,9242,8947],{"class":5907},[5533,9244,5833],{"class":5951},[5533,9246,5987],{"class":5907},[5533,9248,5495],{"class":5951},[5533,9250,9027],{"class":5907},[5533,9252,5833],{"class":5951},[5533,9254,5987],{"class":5907},[5533,9256,6942],{"class":5934},[5533,9258,6775],{"class":5907},[5533,9260,6947],{"class":5942},[5533,9262,5987],{"class":5907},[5533,9264,6952],{"class":5934},[5533,9266,6775],{"class":5907},[5533,9268,6957],{"class":5942},[5533,9270,5987],{"class":5907},[5533,9272,6802],{"class":5934},[5533,9274,6775],{"class":5907},[5533,9276,6997],{"class":5951},[5533,9278,6060],{"class":5907},[5533,9280,9281,9283,9285,9287,9289,9291,9293,9295,9297],{"class":5535,"line":5738},[5533,9282,8947],{"class":5907},[5533,9284,5833],{"class":5951},[5533,9286,5987],{"class":5907},[5533,9288,5495],{"class":5951},[5533,9290,9068],{"class":5907},[5533,9292,6802],{"class":5934},[5533,9294,6775],{"class":5907},[5533,9296,6997],{"class":5951},[5533,9298,6060],{"class":5907},[5533,9300,9301,9303,9305,9307,9309,9311,9314,9316,9318,9320,9322,9324,9326,9328,9330],{"class":5535,"line":5744},[5533,9302,8947],{"class":5907},[5533,9304,5833],{"class":5951},[5533,9306,5987],{"class":5907},[5533,9308,5495],{"class":5951},[5533,9310,9089],{"class":5907},[5533,9312,9313],{"class":5942},"'Tanh: tanh(z)'",[5533,9315,5987],{"class":5907},[5533,9317,6889],{"class":5934},[5533,9319,6775],{"class":5907},[5533,9321,7034],{"class":5951},[5533,9323,5987],{"class":5907},[5533,9325,7076],{"class":5934},[5533,9327,6775],{"class":5907},[5533,9329,7081],{"class":5942},[5533,9331,6060],{"class":5907},[5533,9333,9334,9336,9338,9340,9342,9344,9347,9349,9351,9353,9355],{"class":5535,"line":5750},[5533,9335,8947],{"class":5907},[5533,9337,5833],{"class":5951},[5533,9339,5987],{"class":5907},[5533,9341,5495],{"class":5951},[5533,9343,9123],{"class":5907},[5533,9345,9346],{"class":5942},"'tanh(z)'",[5533,9348,5987],{"class":5907},[5533,9350,6889],{"class":5934},[5533,9352,6775],{"class":5907},[5533,9354,6894],{"class":5951},[5533,9356,6060],{"class":5907},[5533,9358,9359],{"class":5535,"line":5755},[5533,9360,5563],{"emptyLinePlaceholder":5205},[5533,9362,9363],{"class":5535,"line":5761},[5533,9364,9365],{"class":5975},"# ReLU\n",[5533,9367,9368,9370,9372,9374,9376,9379,9381,9383,9386,9388,9390,9392,9394],{"class":5535,"line":5767},[5533,9369,8947],{"class":5907},[5533,9371,5495],{"class":5951},[5533,9373,5987],{"class":5907},[5533,9375,5833],{"class":5951},[5533,9377,9378],{"class":5907},"].plot(z, relu(z), ",[5533,9380,6942],{"class":5934},[5533,9382,6775],{"class":5907},[5533,9384,9385],{"class":5942},"'#10b981'",[5533,9387,5987],{"class":5907},[5533,9389,6962],{"class":5934},[5533,9391,6775],{"class":5907},[5533,9393,7457],{"class":5951},[5533,9395,6060],{"class":5907},[5533,9397,9398,9400,9402,9404,9406,9408,9410,9412,9414,9416,9418,9420,9422,9424,9426,9428,9430,9432,9434],{"class":5535,"line":5773},[5533,9399,8947],{"class":5907},[5533,9401,5495],{"class":5951},[5533,9403,5987],{"class":5907},[5533,9405,5833],{"class":5951},[5533,9407,8986],{"class":5907},[5533,9409,5833],{"class":5951},[5533,9411,5987],{"class":5907},[5533,9413,6942],{"class":5934},[5533,9415,6775],{"class":5907},[5533,9417,6947],{"class":5942},[5533,9419,5987],{"class":5907},[5533,9421,6952],{"class":5934},[5533,9423,6775],{"class":5907},[5533,9425,6957],{"class":5942},[5533,9427,5987],{"class":5907},[5533,9429,6802],{"class":5934},[5533,9431,6775],{"class":5907},[5533,9433,6997],{"class":5951},[5533,9435,6060],{"class":5907},[5533,9437,9438,9440,9442,9444,9446,9448,9450,9452,9454,9456,9458,9460,9462,9464,9466,9468,9470,9472,9474],{"class":5535,"line":5778},[5533,9439,8947],{"class":5907},[5533,9441,5495],{"class":5951},[5533,9443,5987],{"class":5907},[5533,9445,5833],{"class":5951},[5533,9447,9027],{"class":5907},[5533,9449,5833],{"class":5951},[5533,9451,5987],{"class":5907},[5533,9453,6942],{"class":5934},[5533,9455,6775],{"class":5907},[5533,9457,6947],{"class":5942},[5533,9459,5987],{"class":5907},[5533,9461,6952],{"class":5934},[5533,9463,6775],{"class":5907},[5533,9465,6957],{"class":5942},[5533,9467,5987],{"class":5907},[5533,9469,6802],{"class":5934},[5533,9471,6775],{"class":5907},[5533,9473,6997],{"class":5951},[5533,9475,6060],{"class":5907},[5533,9477,9478,9480,9482,9484,9486,9488,9490,9492,9494],{"class":5535,"line":5783},[5533,9479,8947],{"class":5907},[5533,9481,5495],{"class":5951},[5533,9483,5987],{"class":5907},[5533,9485,5833],{"class":5951},[5533,9487,9068],{"class":5907},[5533,9489,6802],{"class":5934},[5533,9491,6775],{"class":5907},[5533,9493,6997],{"class":5951},[5533,9495,6060],{"class":5907},[5533,9497,9499,9501,9503,9505,9507,9509,9512,9514,9516,9518,9520,9522,9524,9526,9528],{"class":5535,"line":9498},45,[5533,9500,8947],{"class":5907},[5533,9502,5495],{"class":5951},[5533,9504,5987],{"class":5907},[5533,9506,5833],{"class":5951},[5533,9508,9089],{"class":5907},[5533,9510,9511],{"class":5942},"'ReLU: max(0, z)'",[5533,9513,5987],{"class":5907},[5533,9515,6889],{"class":5934},[5533,9517,6775],{"class":5907},[5533,9519,7034],{"class":5951},[5533,9521,5987],{"class":5907},[5533,9523,7076],{"class":5934},[5533,9525,6775],{"class":5907},[5533,9527,7081],{"class":5942},[5533,9529,6060],{"class":5907},[5533,9531,9533,9535,9537,9539,9541,9544,9547,9549,9551,9553,9555],{"class":5535,"line":9532},46,[5533,9534,8947],{"class":5907},[5533,9536,5495],{"class":5951},[5533,9538,5987],{"class":5907},[5533,9540,5833],{"class":5951},[5533,9542,9543],{"class":5907},"].set_xlabel(",[5533,9545,9546],{"class":5942},"'z'",[5533,9548,5987],{"class":5907},[5533,9550,6889],{"class":5934},[5533,9552,6775],{"class":5907},[5533,9554,6894],{"class":5951},[5533,9556,6060],{"class":5907},[5533,9558,9560,9562,9564,9566,9568,9570,9573,9575,9577,9579,9581],{"class":5535,"line":9559},47,[5533,9561,8947],{"class":5907},[5533,9563,5495],{"class":5951},[5533,9565,5987],{"class":5907},[5533,9567,5833],{"class":5951},[5533,9569,9123],{"class":5907},[5533,9571,9572],{"class":5942},"'ReLU(z)'",[5533,9574,5987],{"class":5907},[5533,9576,6889],{"class":5934},[5533,9578,6775],{"class":5907},[5533,9580,6894],{"class":5951},[5533,9582,6060],{"class":5907},[5533,9584,9586],{"class":5535,"line":9585},48,[5533,9587,5563],{"emptyLinePlaceholder":5205},[5533,9589,9591],{"class":5535,"line":9590},49,[5533,9592,9593],{"class":5975},"# Leaky ReLU\n",[5533,9595,9597,9599,9601,9603,9605,9608,9610,9612,9615,9617,9619,9621,9623],{"class":5535,"line":9596},50,[5533,9598,8947],{"class":5907},[5533,9600,5495],{"class":5951},[5533,9602,5987],{"class":5907},[5533,9604,5495],{"class":5951},[5533,9606,9607],{"class":5907},"].plot(z, leaky_relu(z), ",[5533,9609,6942],{"class":5934},[5533,9611,6775],{"class":5907},[5533,9613,9614],{"class":5942},"'#f59e0b'",[5533,9616,5987],{"class":5907},[5533,9618,6962],{"class":5934},[5533,9620,6775],{"class":5907},[5533,9622,7457],{"class":5951},[5533,9624,6060],{"class":5907},[5533,9626,9628,9630,9632,9634,9636,9638,9640,9642,9644,9646,9648,9650,9652,9654,9656,9658,9660,9662,9664],{"class":5535,"line":9627},51,[5533,9629,8947],{"class":5907},[5533,9631,5495],{"class":5951},[5533,9633,5987],{"class":5907},[5533,9635,5495],{"class":5951},[5533,9637,8986],{"class":5907},[5533,9639,5833],{"class":5951},[5533,9641,5987],{"class":5907},[5533,9643,6942],{"class":5934},[5533,9645,6775],{"class":5907},[5533,9647,6947],{"class":5942},[5533,9649,5987],{"class":5907},[5533,9651,6952],{"class":5934},[5533,9653,6775],{"class":5907},[5533,9655,6957],{"class":5942},[5533,9657,5987],{"class":5907},[5533,9659,6802],{"class":5934},[5533,9661,6775],{"class":5907},[5533,9663,6997],{"class":5951},[5533,9665,6060],{"class":5907},[5533,9667,9669,9671,9673,9675,9677,9679,9681,9683,9685,9687,9689,9691,9693,9695,9697,9699,9701,9703,9705],{"class":5535,"line":9668},52,[5533,9670,8947],{"class":5907},[5533,9672,5495],{"class":5951},[5533,9674,5987],{"class":5907},[5533,9676,5495],{"class":5951},[5533,9678,9027],{"class":5907},[5533,9680,5833],{"class":5951},[5533,9682,5987],{"class":5907},[5533,9684,6942],{"class":5934},[5533,9686,6775],{"class":5907},[5533,9688,6947],{"class":5942},[5533,9690,5987],{"class":5907},[5533,9692,6952],{"class":5934},[5533,9694,6775],{"class":5907},[5533,9696,6957],{"class":5942},[5533,9698,5987],{"class":5907},[5533,9700,6802],{"class":5934},[5533,9702,6775],{"class":5907},[5533,9704,6997],{"class":5951},[5533,9706,6060],{"class":5907},[5533,9708,9710,9712,9714,9716,9718,9720,9722,9724,9726],{"class":5535,"line":9709},53,[5533,9711,8947],{"class":5907},[5533,9713,5495],{"class":5951},[5533,9715,5987],{"class":5907},[5533,9717,5495],{"class":5951},[5533,9719,9068],{"class":5907},[5533,9721,6802],{"class":5934},[5533,9723,6775],{"class":5907},[5533,9725,6997],{"class":5951},[5533,9727,6060],{"class":5907},[5533,9729,9731,9733,9735,9737,9739,9741,9744,9746,9748,9750,9752,9754,9756,9758,9760],{"class":5535,"line":9730},54,[5533,9732,8947],{"class":5907},[5533,9734,5495],{"class":5951},[5533,9736,5987],{"class":5907},[5533,9738,5495],{"class":5951},[5533,9740,9089],{"class":5907},[5533,9742,9743],{"class":5942},"'Leaky ReLU: max(0.01z, z)'",[5533,9745,5987],{"class":5907},[5533,9747,6889],{"class":5934},[5533,9749,6775],{"class":5907},[5533,9751,7034],{"class":5951},[5533,9753,5987],{"class":5907},[5533,9755,7076],{"class":5934},[5533,9757,6775],{"class":5907},[5533,9759,7081],{"class":5942},[5533,9761,6060],{"class":5907},[5533,9763,9765,9767,9769,9771,9773,9775,9777,9779,9781,9783,9785],{"class":5535,"line":9764},55,[5533,9766,8947],{"class":5907},[5533,9768,5495],{"class":5951},[5533,9770,5987],{"class":5907},[5533,9772,5495],{"class":5951},[5533,9774,9543],{"class":5907},[5533,9776,9546],{"class":5942},[5533,9778,5987],{"class":5907},[5533,9780,6889],{"class":5934},[5533,9782,6775],{"class":5907},[5533,9784,6894],{"class":5951},[5533,9786,6060],{"class":5907},[5533,9788,9790,9792,9794,9796,9798,9800,9803,9805,9807,9809,9811],{"class":5535,"line":9789},56,[5533,9791,8947],{"class":5907},[5533,9793,5495],{"class":5951},[5533,9795,5987],{"class":5907},[5533,9797,5495],{"class":5951},[5533,9799,9123],{"class":5907},[5533,9801,9802],{"class":5942},"'Leaky ReLU(z)'",[5533,9804,5987],{"class":5907},[5533,9806,6889],{"class":5934},[5533,9808,6775],{"class":5907},[5533,9810,6894],{"class":5951},[5533,9812,6060],{"class":5907},[5533,9814,9816],{"class":5535,"line":9815},57,[5533,9817,5563],{"emptyLinePlaceholder":5205},[5533,9819,9821],{"class":5535,"line":9820},58,[5533,9822,7114],{"class":5907},[5533,9824,9826],{"class":5535,"line":9825},59,[5533,9827,7119],{"class":5907},[6216,9829,9830],{"v-slot:output":5528},[5224,9831],{"alt":9832,"className":9833,"src":9834},"Порівняльний аналіз ключових функцій активації: Sigmoid, Tanh, ReLU та Leaky ReLU",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F07.png",[5329,9836,9838],{"alt":9837},"Класифікація та характеристики функцій активації",[5523,9839,9841],{"className":5525,"code":9840,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define SIG_COLOR #DBEAFE\n!define TANH_COLOR #FEF3C7\n!define RELU_COLOR #DCFCE7\n!define LEAKY_COLOR #F1F5F9\n\npackage \"Функції активації (Activation Functions)\" {\n  class \"Sigmoid: σ(z) = 1\u002F(1+e⁻ᶻ)\" as sig #SIG_COLOR {\n    + Діапазон: (0, 1)\n    + Похідна: max 0.25 (зникаючий градієнт)\n    + Роль: вихід бінарної класифікації\n  }\n  class \"Tanh: (eᶻ - e⁻ᶻ)\u002F(eᶻ + e⁻ᶻ)\" as tanh #TANH_COLOR {\n    + Діапазон: (-1, 1)\n    + Центрована навколо нуля\n    + Роль: приховані шари RNN \u002F NLP\n  }\n  class \"ReLU: max(0, z)\" as relu #RELU_COLOR {\n    + Діапазон: [0, +∞)\n    + Похідна: 1 при z > 0\n    + Роль: дефолтний стандарт глибоких мереж\n  }\n  class \"Leaky ReLU: max(αz, z)\" as leaky #LEAKY_COLOR {\n    + Діапазон: (-∞, +∞)\n    + Похідна: α = 0.01 при z \u003C 0\n    + Роль: запобігання \"мертвим нейронам\"\n  }\n}\n@enduml\n",[5530,9842,9843,9847,9851,9855,9859,9863,9868,9873,9878,9883,9887,9892,9897,9902,9907,9912,9917,9922,9927,9932,9937,9941,9946,9951,9956,9961,9965,9970,9975,9980,9985,9989,9993],{"__ignoreMap":5528},[5533,9844,9845],{"class":5535,"line":5536},[5533,9846,5539],{},[5533,9848,9849],{"class":5535,"line":5542},[5533,9850,5545],{},[5533,9852,9853],{"class":5535,"line":5548},[5533,9854,5551],{},[5533,9856,9857],{"class":5535,"line":5554},[5533,9858,5557],{},[5533,9860,9861],{"class":5535,"line":5560},[5533,9862,5563],{"emptyLinePlaceholder":5205},[5533,9864,9865],{"class":5535,"line":5566},[5533,9866,9867],{},"!define SIG_COLOR #DBEAFE\n",[5533,9869,9870],{"class":5535,"line":5572},[5533,9871,9872],{},"!define TANH_COLOR #FEF3C7\n",[5533,9874,9875],{"class":5535,"line":5578},[5533,9876,9877],{},"!define RELU_COLOR #DCFCE7\n",[5533,9879,9880],{"class":5535,"line":5584},[5533,9881,9882],{},"!define LEAKY_COLOR #F1F5F9\n",[5533,9884,9885],{"class":5535,"line":5589},[5533,9886,5563],{"emptyLinePlaceholder":5205},[5533,9888,9889],{"class":5535,"line":5595},[5533,9890,9891],{},"package \"Функції активації (Activation Functions)\" {\n",[5533,9893,9894],{"class":5535,"line":5601},[5533,9895,9896],{},"  class \"Sigmoid: σ(z) = 1\u002F(1+e⁻ᶻ)\" as sig #SIG_COLOR {\n",[5533,9898,9899],{"class":5535,"line":5607},[5533,9900,9901],{},"    + Діапазон: (0, 1)\n",[5533,9903,9904],{"class":5535,"line":5613},[5533,9905,9906],{},"    + Похідна: max 0.25 (зникаючий градієнт)\n",[5533,9908,9909],{"class":5535,"line":5619},[5533,9910,9911],{},"    + Роль: вихід бінарної класифікації\n",[5533,9913,9914],{"class":5535,"line":5625},[5533,9915,9916],{},"  }\n",[5533,9918,9919],{"class":5535,"line":5630},[5533,9920,9921],{},"  class \"Tanh: (eᶻ - e⁻ᶻ)\u002F(eᶻ + e⁻ᶻ)\" as tanh #TANH_COLOR {\n",[5533,9923,9924],{"class":5535,"line":5636},[5533,9925,9926],{},"    + Діапазон: (-1, 1)\n",[5533,9928,9929],{"class":5535,"line":5642},[5533,9930,9931],{},"    + Центрована навколо нуля\n",[5533,9933,9934],{"class":5535,"line":5648},[5533,9935,9936],{},"    + Роль: приховані шари RNN \u002F NLP\n",[5533,9938,9939],{"class":5535,"line":5654},[5533,9940,9916],{},[5533,9942,9943],{"class":5535,"line":5659},[5533,9944,9945],{},"  class \"ReLU: max(0, z)\" as relu #RELU_COLOR {\n",[5533,9947,9948],{"class":5535,"line":5664},[5533,9949,9950],{},"    + Діапазон: [0, +∞)\n",[5533,9952,9953],{"class":5535,"line":5670},[5533,9954,9955],{},"    + Похідна: 1 при z > 0\n",[5533,9957,9958],{"class":5535,"line":5676},[5533,9959,9960],{},"    + Роль: дефолтний стандарт глибоких мереж\n",[5533,9962,9963],{"class":5535,"line":5681},[5533,9964,9916],{},[5533,9966,9967],{"class":5535,"line":5686},[5533,9968,9969],{},"  class \"Leaky ReLU: max(αz, z)\" as leaky #LEAKY_COLOR {\n",[5533,9971,9972],{"class":5535,"line":5692},[5533,9973,9974],{},"    + Діапазон: (-∞, +∞)\n",[5533,9976,9977],{"class":5535,"line":5698},[5533,9978,9979],{},"    + Похідна: α = 0.01 при z \u003C 0\n",[5533,9981,9982],{"class":5535,"line":5704},[5533,9983,9984],{},"    + Роль: запобігання \"мертвим нейронам\"\n",[5533,9986,9987],{"class":5535,"line":5710},[5533,9988,9916],{},[5533,9990,9991],{"class":5535,"line":5715},[5533,9992,5622],{},[5533,9994,9995],{"class":5535,"line":5721},[5533,9996,5786],{},[5191,9998,9999],{},[5198,10000,10001],{},"Проблеми сигмоїди:",[5241,10003,10004,10017],{},[5244,10005,10008,10009,10012,10013,10016],{"icon":10006,"title":10007},"i-lucide-alert-triangle","⚠️ Vanishing Gradient Problem","При ",[5369,10010],{"tex":10011,":inline":5372},"z \\to \\pm\\infty"," сигмоїда наближається до 0 або 1, а її похідна прямує до нуля. У глибоких мережах це призводить до ",[5198,10014,10015],{},"зникнення градієнтів"," — ваги перших шарів практично не навчаються.",[5244,10018,10020,10021,10024],{"icon":10006,"title":10019},"⚠️ Не центрована навколо нуля","Виходи завжди додатні (",[5369,10022],{"tex":10023,":inline":5372},"0 \u003C \\sigma(z) \u003C 1","). Це уповільнює навчання, бо градієнти для всіх ваг одного нейрона мають однаковий знак.",[5191,10026,10027,10030,10031,10034],{},[5198,10028,10029],{},"Коли використовувати:"," лише для ",[5198,10032,10033],{},"вихідного шару"," в бінарній класифікації (інтерпретація як ймовірність класу 1).",[5309,10036],{},[7727,10038,10040],{"id":10039},"_2-гіперболічний-тангенс-tanh","2. Гіперболічний тангенс (Tanh)",[5191,10042,10043],{},[5198,10044,8687],{},[5369,10046],{"tex":10047},"\\text{tanh}(z) = \\frac{e^z - e^{-z}}{e^z + e^{-z}} = 2\\sigma(2z) - 1",[5191,10049,10050,5479,10052],{},[5198,10051,8695],{},[5369,10053],{"tex":10054,":inline":5372},"(-1, 1)",[5191,10056,10057],{},[5198,10058,10059],{},"Переваги над сигмоїдою:",[5249,10061,10062,10068],{},[5252,10063,10064,10067],{},[5198,10065,10066],{},"Центрована навколо нуля",": виходи симетричні відносно нуля, що прискорює збіжність",[5252,10069,10070],{},"Більший діапазон градієнтів",[5191,10072,10073],{},[5198,10074,10075],{},"Недоліки:",[5249,10077,10078],{},[5252,10079,10080],{},"Також страждає від проблеми зникаючих градієнтів (хоча меншою мірою, ніж сигмоїда)",[5191,10082,10083,10085,10086,10089],{},[5198,10084,10029],{}," для ",[5198,10087,10088],{},"прихованих шарів"," у рекурентних нейронних мережах (RNN, LSTM).",[7321,10091,10092,10097],{},[5191,10093,10094],{},[5198,10095,10096],{},"Аналогія:",[5191,10098,10099],{},"Сигмоїда — як термометр, що показує від 0°C до 100°C. Tanh — як термометр із шкалою від -50°C до +50°C (центрований навколо нормальної температури). Другий термометр точніше реагує на невеликі зміни навколо середнього значення.",[5309,10101],{},[7727,10103,10105],{"id":10104},"_3-relu-rectified-linear-unit","3. ReLU (Rectified Linear Unit)",[5191,10107,10108],{},[5198,10109,8687],{},[5369,10111,10112],{},"\\text{ReLU}(z) = \\max(0, z) = \\begin{cases}\nz, & \\text{якщо } z > 0 \\\n0, & \\text{якщо } z \\leq 0\n\\end{cases}",[5191,10114,10115,5479,10117],{},[5198,10116,8695],{},[5369,10118],{"tex":10119,":inline":5372},"[0, +\\infty)",[5191,10121,10122],{},[5198,10123,10124],{},"Чому ReLU стала революцією (2010-ті роки):",[5241,10126,10127,10140,10144],{},[5244,10128,10131,10132,10135,10136,10139],{"icon":10129,"title":10130},"i-lucide-check-circle","✅ Немає зникаючих градієнтів","Для ",[5369,10133],{"tex":10134,":inline":5372},"z > 0"," похідна ",[5369,10137],{"tex":10138,":inline":5372},"\\text{ReLU}'(z) = 1"," — константа! Градієнт не зменшується при проходженні через шари.",[5244,10141,10143],{"icon":92,"title":10142},"✅ Обчислювальна простота","Немає експонент чи ділення — лише одна операція порівняння. Швидше на 6–10× за сигмоїду.",[5244,10145,10148,10149,10152],{"icon":10146,"title":10147},"i-lucide-sparkles","✅ Розріджена активація","Приблизно 50% нейронів «вимкнені» (виводять 0) для будь-якого входу. Це створює ",[5198,10150,10151],{},"розріджені представлення"," — мережа стає ефективнішою.",[5191,10154,10155],{},[5198,10156,10157],{},"Проблема: \"мертві нейрони\" (Dying ReLU)",[5191,10159,10160,10161,10164],{},"Якщо нейрон отримує лише від'ємні входи, ReLU завжди повертає 0, градієнт також 0, і нейрон ",[5198,10162,10163],{},"назавжди перестає навчатися",". Це відбувається при:",[5249,10166,10167,10170],{},[5252,10168,10169],{},"Дуже високому learning rate (ваги «перестрибують» в область, де вхід завжди від'ємний)",[5252,10171,10172],{},"Поганій ініціалізації ваг",[10174,10175,10176,10181],"note",{},[5191,10177,10178],{},[5198,10179,10180],{},"Практичний поради для запобігання \"мертвим нейронам\":",[7473,10182,10183,10186,10189],{},[5252,10184,10185],{},"Використовувати помірковані learning rate (0.001–0.01 для Adam)",[5252,10187,10188],{},"Правильно ініціалізувати ваги (He initialization для ReLU)",[5252,10190,10191],{},"Розглянути варіанти ReLU: Leaky ReLU або ELU",[5191,10193,10194,10085,10196,10198],{},[5198,10195,10029],{},[5198,10197,10088],{}," у більшості завдань — стандартний вибір за замовчуванням.",[5309,10200],{},[7727,10202,10204],{"id":10203},"_4-leaky-relu","4. Leaky ReLU",[5191,10206,10207],{},[5198,10208,8687],{},[5369,10210],{"tex":10211},"\\text{Leaky ReLU}(z) = \\max(\\alpha z, z), \\quad \\alpha = 0.01",[5191,10213,10214,10217,10218,10221],{},[5198,10215,10216],{},"Відмінність від ReLU:"," замість нуля для від'ємних значень використовується невеликий нахил ",[5369,10219],{"tex":10220,":inline":5372},"\\alpha"," (зазвичай 0.01).",[5191,10223,10224],{},[5198,10225,10226],{},"Переваги:",[5249,10228,10229,10243],{},[5252,10230,10231,10234,10235,10238,10239,10242],{},[5198,10232,10233],{},"Немає \"мертвих нейронів\"",": навіть для ",[5369,10236],{"tex":10237,":inline":5372},"z \u003C 0"," градієнт ",[5369,10240],{"tex":10241,":inline":5372},"\\alpha \\neq 0",", тому нейрон продовжує навчатися",[5252,10244,10245],{},"Всі переваги ReLU зберігаються",[5191,10247,10248,10250],{},[5198,10249,10029],{}," якщо ReLU призводить до великої кількості мертвих нейронів (експериментальна альтернатива).",[5309,10252],{},[7727,10254,10256],{"id":10255},"_5-softmax-для-багатокласової-класифікації","5. Softmax (для багатокласової класифікації)",[5191,10258,10259],{},[5198,10260,10261,10262,10265],{},"Формула (для вектора ",[5369,10263],{"tex":10264,":inline":5372},"z = [z_1, z_2, \\ldots, z_K]","):",[5369,10267],{"tex":10268},"\\text{softmax}(z*i) = \\frac{e^{z_i}}{\\sum*{j=1}^{K} e^{z_j}}",[5191,10270,10271],{},[5198,10272,8703],{},[5249,10274,10275,10285],{},[5252,10276,10277,10278,10281,10282,10284],{},"Перетворює довільний вектор у ",[5198,10279,10280],{},"розподіл ймовірностей",": всі виходи в діапазоні ",[5369,10283],{"tex":8698,":inline":5372},", їхня сума дорівнює 1",[5252,10286,10287,10288,10291],{},"Клас з найбільшим ",[5369,10289],{"tex":10290,":inline":5372},"z_i"," отримує найвищу ймовірність",[5191,10293,10294,5479,10296,10299],{},[5198,10295,10029],{},[5198,10297,10298],{},"виключно для вихідного шару"," в задачах багатокласової класифікації (наприклад, розпізнавання 10 цифр MNIST).",[5885,10301,10303],{"kernel":5887,"title":10302},"softmax_example.ipynb",[5890,10304,10305,10568],{"execution-count":8887},[5523,10306,10308],{"className":5894,"code":10307,"language":5896,"meta":5528,"style":5528},"import numpy as np\n\ndef softmax(z):\n    \"\"\"Обчислює softmax для вектора z\"\"\"\n    exp_z = np.exp(z - np.max(z))  # Віднімаємо max для числової стабільності\n    return exp_z \u002F np.sum(exp_z)\n\n# Приклад: мережа передбачає бали для 3 класів (кішка, собака, птах)\nlogits = np.array([2.0, 1.0, 0.1])  # Сирі виходи мережі (до softmax)\n\nprobabilities = softmax(logits)\n\nprint(\"Клас         | Логіт (z) | Ймовірність (softmax)\")\nprint(\"-\" * 55)\nclasses = [\"Кішка\", \"Собака\", \"Птах\"]\nfor cls, z, prob in zip(classes, logits, probabilities):\n    print(f\"{cls:12} |   {z:5.2f}   |   {prob:6.4f}  ({prob*100:5.2f}%)\")\n\nprint(f\"\\nСума ймовірностей: {probabilities.sum():.6f}\")\nprint(f\"Передбачений клас: {classes[np.argmax(probabilities)]}\")\n",[5530,10309,10310,10320,10324,10337,10342,10350,10357,10361,10366,10387,10391,10396,10400,10411,10425,10445,10463,10515,10519,10546],{"__ignoreMap":5528},[5533,10311,10312,10314,10316,10318],{"class":5535,"line":5536},[5533,10313,5904],{"class":5903},[5533,10315,5908],{"class":5907},[5533,10317,5911],{"class":5903},[5533,10319,5914],{"class":5907},[5533,10321,10322],{"class":5535,"line":5542},[5533,10323,5563],{"emptyLinePlaceholder":5205},[5533,10325,10326,10328,10331,10333,10335],{"class":5535,"line":5548},[5533,10327,5924],{"class":5923},[5533,10329,10330],{"class":5927}," softmax",[5533,10332,5931],{"class":5907},[5533,10334,5453],{"class":5934},[5533,10336,5937],{"class":5907},[5533,10338,10339],{"class":5535,"line":5554},[5533,10340,10341],{"class":5942},"    \"\"\"Обчислює softmax для вектора z\"\"\"\n",[5533,10343,10344,10347],{"class":5535,"line":5560},[5533,10345,10346],{"class":5907},"    exp_z = np.exp(z - np.max(z))  ",[5533,10348,10349],{"class":5975},"# Віднімаємо max для числової стабільності\n",[5533,10351,10352,10354],{"class":5535,"line":5566},[5533,10353,5948],{"class":5903},[5533,10355,10356],{"class":5907}," exp_z \u002F np.sum(exp_z)\n",[5533,10358,10359],{"class":5535,"line":5572},[5533,10360,5563],{"emptyLinePlaceholder":5205},[5533,10362,10363],{"class":5535,"line":5578},[5533,10364,10365],{"class":5975},"# Приклад: мережа передбачає бали для 3 класів (кішка, собака, птах)\n",[5533,10367,10368,10371,10373,10375,10377,10379,10382,10384],{"class":5535,"line":5584},[5533,10369,10370],{"class":5907},"logits = np.array([",[5533,10372,7894],{"class":5951},[5533,10374,5987],{"class":5907},[5533,10376,5984],{"class":5951},[5533,10378,5987],{"class":5907},[5533,10380,10381],{"class":5951},"0.1",[5533,10383,7870],{"class":5907},[5533,10385,10386],{"class":5975},"# Сирі виходи мережі (до softmax)\n",[5533,10388,10389],{"class":5535,"line":5589},[5533,10390,5563],{"emptyLinePlaceholder":5205},[5533,10392,10393],{"class":5535,"line":5595},[5533,10394,10395],{"class":5907},"probabilities = softmax(logits)\n",[5533,10397,10398],{"class":5535,"line":5601},[5533,10399,5563],{"emptyLinePlaceholder":5205},[5533,10401,10402,10404,10406,10409],{"class":5535,"line":5607},[5533,10403,6052],{"class":5927},[5533,10405,5931],{"class":5907},[5533,10407,10408],{"class":5942},"\"Клас         | Логіт (z) | Ймовірність (softmax)\"",[5533,10410,6060],{"class":5907},[5533,10412,10413,10415,10417,10419,10421,10423],{"class":5535,"line":5613},[5533,10414,6052],{"class":5927},[5533,10416,5931],{"class":5907},[5533,10418,6069],{"class":5942},[5533,10420,6072],{"class":5907},[5533,10422,6075],{"class":5951},[5533,10424,6060],{"class":5907},[5533,10426,10427,10430,10433,10435,10438,10440,10443],{"class":5535,"line":5619},[5533,10428,10429],{"class":5907},"classes = [",[5533,10431,10432],{"class":5942},"\"Кішка\"",[5533,10434,5987],{"class":5907},[5533,10436,10437],{"class":5942},"\"Собака\"",[5533,10439,5987],{"class":5907},[5533,10441,10442],{"class":5942},"\"Птах\"",[5533,10444,6663],{"class":5907},[5533,10446,10447,10449,10452,10455,10457,10460],{"class":5535,"line":5625},[5533,10448,6086],{"class":5903},[5533,10450,10451],{"class":5923}," cls",[5533,10453,10454],{"class":5907},", z, prob ",[5533,10456,6092],{"class":5903},[5533,10458,10459],{"class":5927}," zip",[5533,10461,10462],{"class":5907},"(classes, logits, probabilities):\n",[5533,10464,10465,10467,10469,10471,10473,10476,10479,10481,10483,10486,10489,10491,10494,10497,10500,10502,10505,10508,10510,10513],{"class":5535,"line":5630},[5533,10466,6147],{"class":5927},[5533,10468,5931],{"class":5907},[5533,10470,6152],{"class":5923},[5533,10472,6155],{"class":5942},[5533,10474,10475],{"class":5923},"{cls:12}",[5533,10477,10478],{"class":5942}," |   ",[5533,10480,6158],{"class":5923},[5533,10482,5453],{"class":5907},[5533,10484,10485],{"class":5923},":5.2f}",[5533,10487,10488],{"class":5942},"   |   ",[5533,10490,6158],{"class":5923},[5533,10492,10493],{"class":5907},"prob",[5533,10495,10496],{"class":5923},":6.4f}",[5533,10498,10499],{"class":5942},"  (",[5533,10501,6158],{"class":5923},[5533,10503,10504],{"class":5907},"prob*",[5533,10506,10507],{"class":5951},"100",[5533,10509,10485],{"class":5923},[5533,10511,10512],{"class":5942},"%)\"",[5533,10514,6060],{"class":5907},[5533,10516,10517],{"class":5535,"line":5636},[5533,10518,5563],{"emptyLinePlaceholder":5205},[5533,10520,10521,10523,10525,10527,10529,10531,10534,10536,10539,10542,10544],{"class":5535,"line":5642},[5533,10522,6052],{"class":5927},[5533,10524,5931],{"class":5907},[5533,10526,6152],{"class":5923},[5533,10528,6155],{"class":5942},[5533,10530,6871],{"class":6870},[5533,10532,10533],{"class":5942},"Сума ймовірностей: ",[5533,10535,6158],{"class":5923},[5533,10537,10538],{"class":5907},"probabilities.sum()",[5533,10540,10541],{"class":5923},":.6f}",[5533,10543,6155],{"class":5942},[5533,10545,6060],{"class":5907},[5533,10547,10548,10550,10552,10554,10557,10559,10562,10564,10566],{"class":5535,"line":5648},[5533,10549,6052],{"class":5927},[5533,10551,5931],{"class":5907},[5533,10553,6152],{"class":5923},[5533,10555,10556],{"class":5942},"\"Передбачений клас: ",[5533,10558,6158],{"class":5923},[5533,10560,10561],{"class":5907},"classes[np.argmax(probabilities)]",[5533,10563,6164],{"class":5923},[5533,10565,6155],{"class":5942},[5533,10567,6060],{"class":5907},[6216,10569,10570],{"v-slot:output":5528},[5806,10571,10572,10591],{},[5809,10573,10574],{},[5812,10575,10576,10579,10582,10585,10588],{},[5815,10577,10578],{"align":6241},"Клас об'єкта",[5815,10580,10581],{"align":5817},"Логіт ($z$)",[5815,10583,10584],{"align":5817},"Експонента ($e^z$)",[5815,10586,10587],{"align":5817},"Ймовірність Softmax",[5815,10589,10590],{"align":6241},"Розподіл впевненості",[5826,10592,10593,10618,10643,10668],{},[5812,10594,10595,10601,10606,10609,10615],{},[5831,10596,10597,10598],{"align":6241},"🐱 ",[5198,10599,10600],{},"Кішка",[5831,10602,10603],{"align":5817},[5530,10604,10605],{},"2.00",[5831,10607,10608],{"align":5817},"$7.389$",[5831,10610,10611,10614],{"align":5817},[5198,10612,10613],{},"0.6590"," ($65.90%$)",[5831,10616,10617],{"align":6241},"🟩🟩🟩🟩🟩🟩🟩 (Переможець)",[5812,10619,10620,10626,10631,10634,10640],{},[5831,10621,10622,10623],{"align":6241},"🐶 ",[5198,10624,10625],{},"Собака",[5831,10627,10628],{"align":5817},[5530,10629,10630],{},"1.00",[5831,10632,10633],{"align":5817},"$2.718$",[5831,10635,10636,10639],{"align":5817},[5198,10637,10638],{},"0.2424"," ($24.24%$)",[5831,10641,10642],{"align":6241},"🟨🟨",[5812,10644,10645,10651,10656,10659,10665],{},[5831,10646,10647,10648],{"align":6241},"🐦 ",[5198,10649,10650],{},"Птах",[5831,10652,10653],{"align":5817},[5530,10654,10655],{},"0.10",[5831,10657,10658],{"align":5817},"$1.105$",[5831,10660,10661,10664],{"align":5817},[5198,10662,10663],{},"0.0986"," ($9.86%$)",[5831,10666,10667],{"align":6241},"⬜",[5812,10669,10670,10675,10678,10683,10689],{},[5831,10671,10672],{"align":6241},[5198,10673,10674],{},"Сума ймовірностей",[5831,10676,10677],{"align":5817},"—",[5831,10679,10680],{"align":5817},[5198,10681,10682],{},"11.212",[5831,10684,10685,10688],{"align":5817},[5198,10686,10687],{},"1.0000"," ($100.0%$)",[5831,10690,10691,10692],{"align":6241},"🎯 Передбачено: ",[5198,10693,10600],{},[5309,10695],{},[5351,10697,10699],{"id":10698},"порівняльна-таблиця-функцій-активації","Порівняльна таблиця функцій активації",[5806,10701,10702,10727],{},[5809,10703,10704],{},[5812,10705,10706,10709,10712,10715,10718,10721,10724],{},[5815,10707,10708],{"align":6241},"Функція",[5815,10710,10711],{"align":6241},"Формула",[5815,10713,10714],{"align":6241},"Діапазон",[5815,10716,10717],{"align":5817},"Прих. шари",[5815,10719,10720],{"align":5817},"Вих. шар",[5815,10722,10723],{"align":6241},"Переваги",[5815,10725,10726],{"align":6241},"Недоліки",[5826,10728,10729,10754,10779,10804,10829],{},[5812,10730,10731,10736,10741,10743,10746,10749,10751],{},[5831,10732,10733],{"align":6241},[5198,10734,10735],{},"Sigmoid",[5831,10737,10738],{"align":6241},[5369,10739],{"tex":10740,":inline":5372},"\\frac{1}{1+e^{-z}}",[5831,10742,8698],{"align":6241},[5831,10744,10745],{"align":5817},"❌",[5831,10747,10748],{"align":5817},"✅",[5831,10750,8711],{"align":6241},[5831,10752,10753],{"align":6241},"Зникаючі градієнти, повільна",[5812,10755,10756,10761,10766,10768,10771,10773,10776],{},[5831,10757,10758],{"align":6241},[5198,10759,10760],{},"Tanh",[5831,10762,10763],{"align":6241},[5369,10764],{"tex":10765,":inline":5372},"\\frac{e^z - e^{-z}}{e^z + e^{-z}}",[5831,10767,10054],{"align":6241},[5831,10769,10770],{"align":5817},"⚠️",[5831,10772,10745],{"align":5817},[5831,10774,10775],{"align":6241},"Центрована навколо 0",[5831,10777,10778],{"align":6241},"Зникаючі градієнти",[5812,10780,10781,10786,10791,10794,10796,10798,10801],{},[5831,10782,10783],{"align":6241},[5198,10784,10785],{},"ReLU",[5831,10787,10788],{"align":6241},[5369,10789],{"tex":10790,":inline":5372},"\\max(0, z)",[5831,10792,10793],{"align":6241},"[0, ∞)",[5831,10795,10748],{"align":5817},[5831,10797,10745],{"align":5817},[5831,10799,10800],{"align":6241},"Швидка, немає зникаючих градієнтів",[5831,10802,10803],{"align":6241},"Мертві нейрони",[5812,10805,10806,10811,10816,10819,10821,10823,10826],{},[5831,10807,10808],{"align":6241},[5198,10809,10810],{},"Leaky ReLU",[5831,10812,10813],{"align":6241},[5369,10814],{"tex":10815,":inline":5372},"\\max(0.01z, z)",[5831,10817,10818],{"align":6241},"(-∞, ∞)",[5831,10820,10748],{"align":5817},[5831,10822,10745],{"align":5817},[5831,10824,10825],{"align":6241},"Вирішує проблему мертвих нейронів",[5831,10827,10828],{"align":6241},"Потребує налаштування α",[5812,10830,10831,10836,10841,10844,10846,10848,10851],{},[5831,10832,10833],{"align":6241},[5198,10834,10835],{},"Softmax",[5831,10837,10838],{"align":6241},[5369,10839],{"tex":10840,":inline":5372},"\\frac{e^{z_i}}{\\sum e^{z_j}}",[5831,10842,10843],{"align":6241},"(0, 1), Σ = 1",[5831,10845,10745],{"align":5817},[5831,10847,10748],{"align":5817},[5831,10849,10850],{"align":6241},"Розподіл ймовірностей для K класів",[5831,10852,10853],{"align":6241},"Лише для вихідного шару",[6339,10855,10856,10861],{},[5191,10857,10858],{},[5198,10859,10860],{},"Емпіричне правило вибору функції активації:",[7473,10862,10863,10869],{},[5252,10864,10865,10868],{},[5198,10866,10867],{},"Приховані шари:"," ReLU (за замовчуванням) або Leaky ReLU",[5252,10870,10871,10873],{},[5198,10872,7523],{},[5249,10874,10875,10878,10881],{},[5252,10876,10877],{},"Бінарна класифікація → Sigmoid",[5252,10879,10880],{},"Багатокласова класифікація → Softmax",[5252,10882,10883],{},"Регресія → без активації (лінійний вихід)",[5309,10885],{},[5186,10887,10889],{"id":10888},"прямий-прохід-forward-propagation-від-входу-до-виходу","Прямий прохід (Forward Propagation) — від входу до виходу",[5191,10891,10892],{},"Тепер, коли ми розуміємо архітектуру MLP та функції активації, розберемо покроково, як мережа обчислює своє передбачення.",[5191,10894,10895,10898],{},[5198,10896,10897],{},"Forward Propagation"," — це процес послідовного обчислення виходів кожного шару, починаючи від вхідного та закінчуючи вихідним.",[5351,10900,10902],{"id":10901},"загальна-формула-для-одного-шару","Загальна формула для одного шару",[5191,10904,10905,10906,10909,10910,10913],{},"Для шару ",[5369,10907],{"tex":10908,":inline":5372},"l"," з ",[5369,10911],{"tex":10912,":inline":5372},"n"," нейронами:",[5369,10915],{"tex":10916},"\\mathbf{z}^{[l]} = \\mathbf{W}^{[l]} \\mathbf{a}^{[l-1]} + \\mathbf{b}^{[l]}",[5369,10918],{"tex":10919},"\\mathbf{a}^{[l]} = \\sigma^{[l]}(\\mathbf{z}^{[l]})",[5191,10921,10922],{},"Де:",[5249,10924,10925,10934,10946,10954],{},[5252,10926,10927,10930,10931,6867],{},[5369,10928],{"tex":10929,":inline":5372},"\\mathbf{a}^{[l-1]}"," — активації попереднього шару (для першого шару це вхідні дані ",[5369,10932],{"tex":10933,":inline":5372},"\\mathbf{x}",[5252,10935,10936,10939,10940,10942,10943,6867],{},[5369,10937],{"tex":10938,":inline":5372},"\\mathbf{W}^{[l]}"," — матриця ваг шару ",[5369,10941],{"tex":10908,":inline":5372}," (розмір: ",[5369,10944],{"tex":10945,":inline":5372},"n^{[l]} \\times n^{[l-1]}",[5252,10947,10948,10951,10952],{},[5369,10949],{"tex":10950,":inline":5372},"\\mathbf{b}^{[l]}"," — вектор зсувів (bias) шару ",[5369,10953],{"tex":10908,":inline":5372},[5252,10955,10956,10959,10960],{},[5369,10957],{"tex":10958,":inline":5372},"\\sigma^{[l]}"," — функція активації шару ",[5369,10961],{"tex":10908,":inline":5372},[5309,10963],{},[5351,10965,10967],{"id":10966},"приклад-прямий-прохід-для-мережі-3-4-2-1","Приклад: прямий прохід для мережі 3 → 4 → 2 → 1",[5191,10969,10970],{},"Розглянемо конкретну архітектуру:",[5249,10972,10973,10982,10988,10994],{},[5252,10974,10975,10978,10979,6867],{},[5198,10976,10977],{},"Вхід:"," 3 ознаки (",[5369,10980],{"tex":10981,":inline":5372},"x_1, x_2, x_3",[5252,10983,10984,10987],{},[5198,10985,10986],{},"Прихований шар 1:"," 4 нейрони з ReLU",[5252,10989,10990,10993],{},[5198,10991,10992],{},"Прихований шар 2:"," 2 нейрони з ReLU",[5252,10995,10996,10999],{},[5198,10997,10998],{},"Вихід:"," 1 нейрон з sigmoid (бінарна класифікація)",[5191,11001,11002],{},[5224,11003],{"alt":11004,"className":11005,"src":11006},"Потік векторно-матричних обчислень та узгодження розмірностей тензорів у повнозв'язній мережі MLP",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F08.png",[5329,11008,11010],{"alt":11009},"Прямий прохід у MLP",[5523,11011,11013],{"className":5525,"code":11012,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define INPUT_COLOR DBEAFE\n!define HIDDEN1_COLOR FEF3C7\n!define HIDDEN2_COLOR FECACA\n!define OUTPUT_COLOR DCFCE7\n\nleft to right direction\n\npackage \"Вхід\\n(3 ознаки)\" as input #INPUT_COLOR {\n  circle \"x₁\" as x1\n  circle \"x₂\" as x2\n  circle \"x₃\" as x3\n}\n\npackage \"Прихований 1\\n(4 нейрони, ReLU)\" as h1 #HIDDEN1_COLOR {\n  circle \"h₁⁽¹⁾\" as h11\n  circle \"h₂⁽¹⁾\" as h12\n  circle \"h₃⁽¹⁾\" as h13\n  circle \"h₄⁽¹⁾\" as h14\n}\n\npackage \"Прихований 2\\n(2 нейрони, ReLU)\" as h2 #HIDDEN2_COLOR {\n  circle \"h₁⁽²⁾\" as h21\n  circle \"h₂⁽²⁾\" as h22\n}\n\npackage \"Вихід\\n(1 нейрон, Sigmoid)\" as output #OUTPUT_COLOR {\n  circle \"ŷ\" as y\n}\n\nx1 --> h11\nx1 --> h12\nx1 --> h13\nx1 --> h14\n\nx2 --> h11\nx2 --> h12\nx2 --> h13\nx2 --> h14\n\nx3 --> h11\nx3 --> h12\nx3 --> h13\nx3 --> h14\n\nh11 --> h21\nh11 --> h22\nh12 --> h21\nh12 --> h22\nh13 --> h21\nh13 --> h22\nh14 --> h21\nh14 --> h22\n\nh21 --> y\nh22 --> y\n\nnote bottom of input\n  **Крок 1:** Отримуємо вхідні дані\n  **x** = [x₁, x₂, x₃]ᵀ\nend note\n\nnote bottom of h1\n  **Крок 2:** Обчислюємо шар 1\n  **z⁽¹⁾** = W⁽¹⁾·x + b⁽¹⁾\n  **a⁽¹⁾** = ReLU(z⁽¹⁾)\nend note\n\nnote bottom of h2\n  **Крок 3:** Обчислюємо шар 2\n  **z⁽²⁾** = W⁽²⁾·a⁽¹⁾ + b⁽²⁾\n  **a⁽²⁾** = ReLU(z⁽²⁾)\nend note\n\nnote bottom of output\n  **Крок 4:** Вихідний шар\n  **z** = W⁽³⁾·a⁽²⁾ + b⁽³⁾\n  **ŷ** = σ(z)\nend note\n\n@enduml\n",[5530,11014,11015,11019,11023,11027,11031,11035,11039,11044,11049,11053,11057,11061,11065,11070,11075,11080,11085,11089,11093,11098,11103,11108,11113,11118,11122,11126,11131,11136,11141,11145,11149,11154,11159,11163,11167,11172,11177,11182,11187,11191,11196,11201,11206,11211,11215,11220,11225,11230,11235,11239,11244,11249,11254,11259,11264,11269,11274,11279,11283,11288,11294,11299,11305,11311,11317,11322,11327,11333,11339,11345,11351,11356,11361,11367,11373,11379,11385,11390,11395,11401,11407,11413,11419,11424,11429],{"__ignoreMap":5528},[5533,11016,11017],{"class":5535,"line":5536},[5533,11018,5539],{},[5533,11020,11021],{"class":5535,"line":5542},[5533,11022,5545],{},[5533,11024,11025],{"class":5535,"line":5548},[5533,11026,5551],{},[5533,11028,11029],{"class":5535,"line":5554},[5533,11030,5557],{},[5533,11032,11033],{"class":5535,"line":5560},[5533,11034,5563],{"emptyLinePlaceholder":5205},[5533,11036,11037],{"class":5535,"line":5566},[5533,11038,5569],{},[5533,11040,11041],{"class":5535,"line":5572},[5533,11042,11043],{},"!define HIDDEN1_COLOR FEF3C7\n",[5533,11045,11046],{"class":5535,"line":5578},[5533,11047,11048],{},"!define HIDDEN2_COLOR FECACA\n",[5533,11050,11051],{"class":5535,"line":5584},[5533,11052,5581],{},[5533,11054,11055],{"class":5535,"line":5589},[5533,11056,5563],{"emptyLinePlaceholder":5205},[5533,11058,11059],{"class":5535,"line":5595},[5533,11060,7574],{},[5533,11062,11063],{"class":5535,"line":5601},[5533,11064,5563],{"emptyLinePlaceholder":5205},[5533,11066,11067],{"class":5535,"line":5607},[5533,11068,11069],{},"package \"Вхід\\n(3 ознаки)\" as input #INPUT_COLOR {\n",[5533,11071,11072],{"class":5535,"line":5613},[5533,11073,11074],{},"  circle \"x₁\" as x1\n",[5533,11076,11077],{"class":5535,"line":5619},[5533,11078,11079],{},"  circle \"x₂\" as x2\n",[5533,11081,11082],{"class":5535,"line":5625},[5533,11083,11084],{},"  circle \"x₃\" as x3\n",[5533,11086,11087],{"class":5535,"line":5630},[5533,11088,5622],{},[5533,11090,11091],{"class":5535,"line":5636},[5533,11092,5563],{"emptyLinePlaceholder":5205},[5533,11094,11095],{"class":5535,"line":5642},[5533,11096,11097],{},"package \"Прихований 1\\n(4 нейрони, ReLU)\" as h1 #HIDDEN1_COLOR {\n",[5533,11099,11100],{"class":5535,"line":5648},[5533,11101,11102],{},"  circle \"h₁⁽¹⁾\" as h11\n",[5533,11104,11105],{"class":5535,"line":5654},[5533,11106,11107],{},"  circle \"h₂⁽¹⁾\" as h12\n",[5533,11109,11110],{"class":5535,"line":5659},[5533,11111,11112],{},"  circle \"h₃⁽¹⁾\" as h13\n",[5533,11114,11115],{"class":5535,"line":5664},[5533,11116,11117],{},"  circle \"h₄⁽¹⁾\" as h14\n",[5533,11119,11120],{"class":5535,"line":5670},[5533,11121,5622],{},[5533,11123,11124],{"class":5535,"line":5676},[5533,11125,5563],{"emptyLinePlaceholder":5205},[5533,11127,11128],{"class":5535,"line":5681},[5533,11129,11130],{},"package \"Прихований 2\\n(2 нейрони, ReLU)\" as h2 #HIDDEN2_COLOR {\n",[5533,11132,11133],{"class":5535,"line":5686},[5533,11134,11135],{},"  circle \"h₁⁽²⁾\" as h21\n",[5533,11137,11138],{"class":5535,"line":5692},[5533,11139,11140],{},"  circle \"h₂⁽²⁾\" as h22\n",[5533,11142,11143],{"class":5535,"line":5698},[5533,11144,5622],{},[5533,11146,11147],{"class":5535,"line":5704},[5533,11148,5563],{"emptyLinePlaceholder":5205},[5533,11150,11151],{"class":5535,"line":5710},[5533,11152,11153],{},"package \"Вихід\\n(1 нейрон, Sigmoid)\" as output #OUTPUT_COLOR {\n",[5533,11155,11156],{"class":5535,"line":5715},[5533,11157,11158],{},"  circle \"ŷ\" as y\n",[5533,11160,11161],{"class":5535,"line":5721},[5533,11162,5622],{},[5533,11164,11165],{"class":5535,"line":5726},[5533,11166,5563],{"emptyLinePlaceholder":5205},[5533,11168,11169],{"class":5535,"line":5732},[5533,11170,11171],{},"x1 --> h11\n",[5533,11173,11174],{"class":5535,"line":5738},[5533,11175,11176],{},"x1 --> h12\n",[5533,11178,11179],{"class":5535,"line":5744},[5533,11180,11181],{},"x1 --> h13\n",[5533,11183,11184],{"class":5535,"line":5750},[5533,11185,11186],{},"x1 --> h14\n",[5533,11188,11189],{"class":5535,"line":5755},[5533,11190,5563],{"emptyLinePlaceholder":5205},[5533,11192,11193],{"class":5535,"line":5761},[5533,11194,11195],{},"x2 --> h11\n",[5533,11197,11198],{"class":5535,"line":5767},[5533,11199,11200],{},"x2 --> h12\n",[5533,11202,11203],{"class":5535,"line":5773},[5533,11204,11205],{},"x2 --> h13\n",[5533,11207,11208],{"class":5535,"line":5778},[5533,11209,11210],{},"x2 --> h14\n",[5533,11212,11213],{"class":5535,"line":5783},[5533,11214,5563],{"emptyLinePlaceholder":5205},[5533,11216,11217],{"class":5535,"line":9498},[5533,11218,11219],{},"x3 --> h11\n",[5533,11221,11222],{"class":5535,"line":9532},[5533,11223,11224],{},"x3 --> h12\n",[5533,11226,11227],{"class":5535,"line":9559},[5533,11228,11229],{},"x3 --> h13\n",[5533,11231,11232],{"class":5535,"line":9585},[5533,11233,11234],{},"x3 --> h14\n",[5533,11236,11237],{"class":5535,"line":9590},[5533,11238,5563],{"emptyLinePlaceholder":5205},[5533,11240,11241],{"class":5535,"line":9596},[5533,11242,11243],{},"h11 --> h21\n",[5533,11245,11246],{"class":5535,"line":9627},[5533,11247,11248],{},"h11 --> h22\n",[5533,11250,11251],{"class":5535,"line":9668},[5533,11252,11253],{},"h12 --> h21\n",[5533,11255,11256],{"class":5535,"line":9709},[5533,11257,11258],{},"h12 --> h22\n",[5533,11260,11261],{"class":5535,"line":9730},[5533,11262,11263],{},"h13 --> h21\n",[5533,11265,11266],{"class":5535,"line":9764},[5533,11267,11268],{},"h13 --> h22\n",[5533,11270,11271],{"class":5535,"line":9789},[5533,11272,11273],{},"h14 --> h21\n",[5533,11275,11276],{"class":5535,"line":9815},[5533,11277,11278],{},"h14 --> h22\n",[5533,11280,11281],{"class":5535,"line":9820},[5533,11282,5563],{"emptyLinePlaceholder":5205},[5533,11284,11285],{"class":5535,"line":9825},[5533,11286,11287],{},"h21 --> y\n",[5533,11289,11291],{"class":5535,"line":11290},60,[5533,11292,11293],{},"h22 --> y\n",[5533,11295,11297],{"class":5535,"line":11296},61,[5533,11298,5563],{"emptyLinePlaceholder":5205},[5533,11300,11302],{"class":5535,"line":11301},62,[5533,11303,11304],{},"note bottom of input\n",[5533,11306,11308],{"class":5535,"line":11307},63,[5533,11309,11310],{},"  **Крок 1:** Отримуємо вхідні дані\n",[5533,11312,11314],{"class":5535,"line":11313},64,[5533,11315,11316],{},"  **x** = [x₁, x₂, x₃]ᵀ\n",[5533,11318,11320],{"class":5535,"line":11319},65,[5533,11321,5747],{},[5533,11323,11325],{"class":5535,"line":11324},66,[5533,11326,5563],{"emptyLinePlaceholder":5205},[5533,11328,11330],{"class":5535,"line":11329},67,[5533,11331,11332],{},"note bottom of h1\n",[5533,11334,11336],{"class":5535,"line":11335},68,[5533,11337,11338],{},"  **Крок 2:** Обчислюємо шар 1\n",[5533,11340,11342],{"class":5535,"line":11341},69,[5533,11343,11344],{},"  **z⁽¹⁾** = W⁽¹⁾·x + b⁽¹⁾\n",[5533,11346,11348],{"class":5535,"line":11347},70,[5533,11349,11350],{},"  **a⁽¹⁾** = ReLU(z⁽¹⁾)\n",[5533,11352,11354],{"class":5535,"line":11353},71,[5533,11355,5747],{},[5533,11357,11359],{"class":5535,"line":11358},72,[5533,11360,5563],{"emptyLinePlaceholder":5205},[5533,11362,11364],{"class":5535,"line":11363},73,[5533,11365,11366],{},"note bottom of h2\n",[5533,11368,11370],{"class":5535,"line":11369},74,[5533,11371,11372],{},"  **Крок 3:** Обчислюємо шар 2\n",[5533,11374,11376],{"class":5535,"line":11375},75,[5533,11377,11378],{},"  **z⁽²⁾** = W⁽²⁾·a⁽¹⁾ + b⁽²⁾\n",[5533,11380,11382],{"class":5535,"line":11381},76,[5533,11383,11384],{},"  **a⁽²⁾** = ReLU(z⁽²⁾)\n",[5533,11386,11388],{"class":5535,"line":11387},77,[5533,11389,5747],{},[5533,11391,11393],{"class":5535,"line":11392},78,[5533,11394,5563],{"emptyLinePlaceholder":5205},[5533,11396,11398],{"class":5535,"line":11397},79,[5533,11399,11400],{},"note bottom of output\n",[5533,11402,11404],{"class":5535,"line":11403},80,[5533,11405,11406],{},"  **Крок 4:** Вихідний шар\n",[5533,11408,11410],{"class":5535,"line":11409},81,[5533,11411,11412],{},"  **z** = W⁽³⁾·a⁽²⁾ + b⁽³⁾\n",[5533,11414,11416],{"class":5535,"line":11415},82,[5533,11417,11418],{},"  **ŷ** = σ(z)\n",[5533,11420,11422],{"class":5535,"line":11421},83,[5533,11423,5747],{},[5533,11425,11427],{"class":5535,"line":11426},84,[5533,11428,5563],{"emptyLinePlaceholder":5205},[5533,11430,11432],{"class":5535,"line":11431},85,[5533,11433,5786],{},[5309,11435],{},[5351,11437,11439],{"id":11438},"реалізація-прямого-проходу-на-numpy","Реалізація прямого проходу на NumPy",[5885,11441,11443],{"kernel":5887,"title":11442},"forward_propagation.ipynb",[5890,11444,11445,12060],{"execution-count":6755},[5523,11446,11448],{"className":5894,"code":11447,"language":5896,"meta":5528,"style":5528},"import numpy as np\n\ndef relu(z):\n    \"\"\"ReLU: max(0, z)\"\"\"\n    return np.maximum(0, z)\n\ndef sigmoid(z):\n    \"\"\"Sigmoid: 1 \u002F (1 + exp(-z))\"\"\"\n    return 1 \u002F (1 + np.exp(-z))\n\n# Ініціалізація ваг (випадкові значення для демонстрації)\nnp.random.seed(42)\n\n# Розміри шарів: 3 → 4 → 2 → 1\nW1 = np.random.randn(4, 3) * 0.1  # Шар 1: 4 нейрони, кожен приймає 3 входи\nb1 = np.zeros((4, 1))\n\nW2 = np.random.randn(2, 4) * 0.1  # Шар 2: 2 нейрони, кожен приймає 4 входи\nb2 = np.zeros((2, 1))\n\nW3 = np.random.randn(1, 2) * 0.1  # Вихід: 1 нейрон, приймає 2 входи\nb3 = np.zeros((1, 1))\n\n# Вхідні дані: один приклад з 3 ознаками\nx = np.array([[0.5], [0.3], [0.8]])  # Вектор-стовпець (3, 1)\n\nprint(\"ПРЯМИЙ ПРОХІД (Forward Propagation)\\n\")\nprint(\"=\" * 60)\n\n# Шар 1\nz1 = W1 @ x + b1\na1 = relu(z1)\nprint(f\"Шар 1 (Прихований):\")\nprint(f\"  z⁽¹⁾ = W⁽¹⁾·x + b⁽¹⁾ → shape: {z1.shape}\")\nprint(f\"  Зважені суми z⁽¹⁾: {z1.flatten()}\")\nprint(f\"  a⁽¹⁾ = ReLU(z⁽¹⁾): {a1.flatten()}\\n\")\n\n# Шар 2\nz2 = W2 @ a1 + b2\na2 = relu(z2)\nprint(f\"Шар 2 (Прихований):\")\nprint(f\"  z⁽²⁾ = W⁽²⁾·a⁽¹⁾ + b⁽²⁾ → shape: {z2.shape}\")\nprint(f\"  Зважені суми z⁽²⁾: {z2.flatten()}\")\nprint(f\"  a⁽²⁾ = ReLU(z⁽²⁾): {a2.flatten()}\\n\")\n\n# Вихідний шар\nz3 = W3 @ a2 + b3\ny_pred = sigmoid(z3)\nprint(f\"Вихідний шар:\")\nprint(f\"  z = W⁽³⁾·a⁽²⁾ + b⁽³⁾: {z3.flatten()}\")\nprint(f\"  ŷ = σ(z): {y_pred.flatten()[0]:.4f}\")\nprint(f\"\\n{'='*60}\")\nprint(f\"ПЕРЕДБАЧЕННЯ: ймовірність класу 1 = {y_pred[0, 0]:.2%}\")\n",[5530,11449,11450,11460,11464,11476,11481,11491,11495,11507,11512,11524,11528,11533,11543,11547,11552,11571,11584,11588,11606,11619,11623,11641,11654,11658,11663,11686,11690,11705,11721,11725,11730,11735,11740,11753,11775,11797,11821,11825,11830,11835,11840,11853,11875,11897,11921,11925,11930,11935,11940,11953,11975,12002,12030],{"__ignoreMap":5528},[5533,11451,11452,11454,11456,11458],{"class":5535,"line":5536},[5533,11453,5904],{"class":5903},[5533,11455,5908],{"class":5907},[5533,11457,5911],{"class":5903},[5533,11459,5914],{"class":5907},[5533,11461,11462],{"class":5535,"line":5542},[5533,11463,5563],{"emptyLinePlaceholder":5205},[5533,11465,11466,11468,11470,11472,11474],{"class":5535,"line":5548},[5533,11467,5924],{"class":5923},[5533,11469,8814],{"class":5927},[5533,11471,5931],{"class":5907},[5533,11473,5453],{"class":5934},[5533,11475,5937],{"class":5907},[5533,11477,11478],{"class":5535,"line":5554},[5533,11479,11480],{"class":5942},"    \"\"\"ReLU: max(0, z)\"\"\"\n",[5533,11482,11483,11485,11487,11489],{"class":5535,"line":5560},[5533,11484,5948],{"class":5903},[5533,11486,8827],{"class":5907},[5533,11488,5833],{"class":5951},[5533,11490,8832],{"class":5907},[5533,11492,11493],{"class":5535,"line":5566},[5533,11494,5563],{"emptyLinePlaceholder":5205},[5533,11496,11497,11499,11501,11503,11505],{"class":5535,"line":5572},[5533,11498,5924],{"class":5923},[5533,11500,7779],{"class":5927},[5533,11502,5931],{"class":5907},[5533,11504,5453],{"class":5934},[5533,11506,5937],{"class":5907},[5533,11508,11509],{"class":5535,"line":5578},[5533,11510,11511],{"class":5942},"    \"\"\"Sigmoid: 1 \u002F (1 + exp(-z))\"\"\"\n",[5533,11513,11514,11516,11518,11520,11522],{"class":5535,"line":5584},[5533,11515,5948],{"class":5903},[5533,11517,5952],{"class":5951},[5533,11519,7799],{"class":5907},[5533,11521,5495],{"class":5951},[5533,11523,7804],{"class":5907},[5533,11525,11526],{"class":5535,"line":5589},[5533,11527,5563],{"emptyLinePlaceholder":5205},[5533,11529,11530],{"class":5535,"line":5595},[5533,11531,11532],{"class":5975},"# Ініціалізація ваг (випадкові значення для демонстрації)\n",[5533,11534,11535,11538,11541],{"class":5535,"line":5601},[5533,11536,11537],{"class":5907},"np.random.seed(",[5533,11539,11540],{"class":5951},"42",[5533,11542,6060],{"class":5907},[5533,11544,11545],{"class":5535,"line":5607},[5533,11546,5563],{"emptyLinePlaceholder":5205},[5533,11548,11549],{"class":5535,"line":5613},[5533,11550,11551],{"class":5975},"# Розміри шарів: 3 → 4 → 2 → 1\n",[5533,11553,11554,11557,11559,11561,11563,11566,11568],{"class":5535,"line":5619},[5533,11555,11556],{"class":5907},"W1 = np.random.randn(",[5533,11558,8720],{"class":5951},[5533,11560,5987],{"class":5907},[5533,11562,7457],{"class":5951},[5533,11564,11565],{"class":5907},") * ",[5533,11567,10381],{"class":5951},[5533,11569,11570],{"class":5975},"  # Шар 1: 4 нейрони, кожен приймає 3 входи\n",[5533,11572,11573,11576,11578,11580,11582],{"class":5535,"line":5625},[5533,11574,11575],{"class":5907},"b1 = np.zeros((",[5533,11577,8720],{"class":5951},[5533,11579,5987],{"class":5907},[5533,11581,5495],{"class":5951},[5533,11583,6758],{"class":5907},[5533,11585,11586],{"class":5535,"line":5630},[5533,11587,5563],{"emptyLinePlaceholder":5205},[5533,11589,11590,11593,11595,11597,11599,11601,11603],{"class":5535,"line":5636},[5533,11591,11592],{"class":5907},"W2 = np.random.randn(",[5533,11594,6604],{"class":5951},[5533,11596,5987],{"class":5907},[5533,11598,8720],{"class":5951},[5533,11600,11565],{"class":5907},[5533,11602,10381],{"class":5951},[5533,11604,11605],{"class":5975},"  # Шар 2: 2 нейрони, кожен приймає 4 входи\n",[5533,11607,11608,11611,11613,11615,11617],{"class":5535,"line":5642},[5533,11609,11610],{"class":5907},"b2 = np.zeros((",[5533,11612,6604],{"class":5951},[5533,11614,5987],{"class":5907},[5533,11616,5495],{"class":5951},[5533,11618,6758],{"class":5907},[5533,11620,11621],{"class":5535,"line":5648},[5533,11622,5563],{"emptyLinePlaceholder":5205},[5533,11624,11625,11628,11630,11632,11634,11636,11638],{"class":5535,"line":5654},[5533,11626,11627],{"class":5907},"W3 = np.random.randn(",[5533,11629,5495],{"class":5951},[5533,11631,5987],{"class":5907},[5533,11633,6604],{"class":5951},[5533,11635,11565],{"class":5907},[5533,11637,10381],{"class":5951},[5533,11639,11640],{"class":5975},"  # Вихід: 1 нейрон, приймає 2 входи\n",[5533,11642,11643,11646,11648,11650,11652],{"class":5535,"line":5659},[5533,11644,11645],{"class":5907},"b3 = np.zeros((",[5533,11647,5495],{"class":5951},[5533,11649,5987],{"class":5907},[5533,11651,5495],{"class":5951},[5533,11653,6758],{"class":5907},[5533,11655,11656],{"class":5535,"line":5664},[5533,11657,5563],{"emptyLinePlaceholder":5205},[5533,11659,11660],{"class":5535,"line":5670},[5533,11661,11662],{"class":5975},"# Вхідні дані: один приклад з 3 ознаками\n",[5533,11664,11665,11668,11670,11673,11675,11677,11680,11683],{"class":5535,"line":5676},[5533,11666,11667],{"class":5907},"x = np.array([[",[5533,11669,6923],{"class":5951},[5533,11671,11672],{"class":5907},"], [",[5533,11674,6997],{"class":5951},[5533,11676,11672],{"class":5907},[5533,11678,11679],{"class":5951},"0.8",[5533,11681,11682],{"class":5907},"]])  ",[5533,11684,11685],{"class":5975},"# Вектор-стовпець (3, 1)\n",[5533,11687,11688],{"class":5535,"line":5681},[5533,11689,5563],{"emptyLinePlaceholder":5205},[5533,11691,11692,11694,11696,11699,11701,11703],{"class":5535,"line":5686},[5533,11693,6052],{"class":5927},[5533,11695,5931],{"class":5907},[5533,11697,11698],{"class":5942},"\"ПРЯМИЙ ПРОХІД (Forward Propagation)",[5533,11700,6871],{"class":6870},[5533,11702,6155],{"class":5942},[5533,11704,6060],{"class":5907},[5533,11706,11707,11709,11711,11714,11716,11719],{"class":5535,"line":5692},[5533,11708,6052],{"class":5927},[5533,11710,5931],{"class":5907},[5533,11712,11713],{"class":5942},"\"=\"",[5533,11715,6072],{"class":5907},[5533,11717,11718],{"class":5951},"60",[5533,11720,6060],{"class":5907},[5533,11722,11723],{"class":5535,"line":5698},[5533,11724,5563],{"emptyLinePlaceholder":5205},[5533,11726,11727],{"class":5535,"line":5704},[5533,11728,11729],{"class":5975},"# Шар 1\n",[5533,11731,11732],{"class":5535,"line":5710},[5533,11733,11734],{"class":5907},"z1 = W1 @ x + b1\n",[5533,11736,11737],{"class":5535,"line":5715},[5533,11738,11739],{"class":5907},"a1 = relu(z1)\n",[5533,11741,11742,11744,11746,11748,11751],{"class":5535,"line":5721},[5533,11743,6052],{"class":5927},[5533,11745,5931],{"class":5907},[5533,11747,6152],{"class":5923},[5533,11749,11750],{"class":5942},"\"Шар 1 (Прихований):\"",[5533,11752,6060],{"class":5907},[5533,11754,11755,11757,11759,11761,11764,11766,11769,11771,11773],{"class":5535,"line":5726},[5533,11756,6052],{"class":5927},[5533,11758,5931],{"class":5907},[5533,11760,6152],{"class":5923},[5533,11762,11763],{"class":5942},"\"  z⁽¹⁾ = W⁽¹⁾·x + b⁽¹⁾ → shape: ",[5533,11765,6158],{"class":5923},[5533,11767,11768],{"class":5907},"z1.shape",[5533,11770,6164],{"class":5923},[5533,11772,6155],{"class":5942},[5533,11774,6060],{"class":5907},[5533,11776,11777,11779,11781,11783,11786,11788,11791,11793,11795],{"class":5535,"line":5732},[5533,11778,6052],{"class":5927},[5533,11780,5931],{"class":5907},[5533,11782,6152],{"class":5923},[5533,11784,11785],{"class":5942},"\"  Зважені суми z⁽¹⁾: ",[5533,11787,6158],{"class":5923},[5533,11789,11790],{"class":5907},"z1.flatten()",[5533,11792,6164],{"class":5923},[5533,11794,6155],{"class":5942},[5533,11796,6060],{"class":5907},[5533,11798,11799,11801,11803,11805,11808,11810,11813,11815,11817,11819],{"class":5535,"line":5738},[5533,11800,6052],{"class":5927},[5533,11802,5931],{"class":5907},[5533,11804,6152],{"class":5923},[5533,11806,11807],{"class":5942},"\"  a⁽¹⁾ = ReLU(z⁽¹⁾): ",[5533,11809,6158],{"class":5923},[5533,11811,11812],{"class":5907},"a1.flatten()",[5533,11814,6164],{"class":5923},[5533,11816,6871],{"class":6870},[5533,11818,6155],{"class":5942},[5533,11820,6060],{"class":5907},[5533,11822,11823],{"class":5535,"line":5744},[5533,11824,5563],{"emptyLinePlaceholder":5205},[5533,11826,11827],{"class":5535,"line":5750},[5533,11828,11829],{"class":5975},"# Шар 2\n",[5533,11831,11832],{"class":5535,"line":5755},[5533,11833,11834],{"class":5907},"z2 = W2 @ a1 + b2\n",[5533,11836,11837],{"class":5535,"line":5761},[5533,11838,11839],{"class":5907},"a2 = relu(z2)\n",[5533,11841,11842,11844,11846,11848,11851],{"class":5535,"line":5767},[5533,11843,6052],{"class":5927},[5533,11845,5931],{"class":5907},[5533,11847,6152],{"class":5923},[5533,11849,11850],{"class":5942},"\"Шар 2 (Прихований):\"",[5533,11852,6060],{"class":5907},[5533,11854,11855,11857,11859,11861,11864,11866,11869,11871,11873],{"class":5535,"line":5773},[5533,11856,6052],{"class":5927},[5533,11858,5931],{"class":5907},[5533,11860,6152],{"class":5923},[5533,11862,11863],{"class":5942},"\"  z⁽²⁾ = W⁽²⁾·a⁽¹⁾ + b⁽²⁾ → shape: ",[5533,11865,6158],{"class":5923},[5533,11867,11868],{"class":5907},"z2.shape",[5533,11870,6164],{"class":5923},[5533,11872,6155],{"class":5942},[5533,11874,6060],{"class":5907},[5533,11876,11877,11879,11881,11883,11886,11888,11891,11893,11895],{"class":5535,"line":5778},[5533,11878,6052],{"class":5927},[5533,11880,5931],{"class":5907},[5533,11882,6152],{"class":5923},[5533,11884,11885],{"class":5942},"\"  Зважені суми z⁽²⁾: ",[5533,11887,6158],{"class":5923},[5533,11889,11890],{"class":5907},"z2.flatten()",[5533,11892,6164],{"class":5923},[5533,11894,6155],{"class":5942},[5533,11896,6060],{"class":5907},[5533,11898,11899,11901,11903,11905,11908,11910,11913,11915,11917,11919],{"class":5535,"line":5783},[5533,11900,6052],{"class":5927},[5533,11902,5931],{"class":5907},[5533,11904,6152],{"class":5923},[5533,11906,11907],{"class":5942},"\"  a⁽²⁾ = ReLU(z⁽²⁾): ",[5533,11909,6158],{"class":5923},[5533,11911,11912],{"class":5907},"a2.flatten()",[5533,11914,6164],{"class":5923},[5533,11916,6871],{"class":6870},[5533,11918,6155],{"class":5942},[5533,11920,6060],{"class":5907},[5533,11922,11923],{"class":5535,"line":9498},[5533,11924,5563],{"emptyLinePlaceholder":5205},[5533,11926,11927],{"class":5535,"line":9532},[5533,11928,11929],{"class":5975},"# Вихідний шар\n",[5533,11931,11932],{"class":5535,"line":9559},[5533,11933,11934],{"class":5907},"z3 = W3 @ a2 + b3\n",[5533,11936,11937],{"class":5535,"line":9585},[5533,11938,11939],{"class":5907},"y_pred = sigmoid(z3)\n",[5533,11941,11942,11944,11946,11948,11951],{"class":5535,"line":9590},[5533,11943,6052],{"class":5927},[5533,11945,5931],{"class":5907},[5533,11947,6152],{"class":5923},[5533,11949,11950],{"class":5942},"\"Вихідний шар:\"",[5533,11952,6060],{"class":5907},[5533,11954,11955,11957,11959,11961,11964,11966,11969,11971,11973],{"class":5535,"line":9596},[5533,11956,6052],{"class":5927},[5533,11958,5931],{"class":5907},[5533,11960,6152],{"class":5923},[5533,11962,11963],{"class":5942},"\"  z = W⁽³⁾·a⁽²⁾ + b⁽³⁾: ",[5533,11965,6158],{"class":5923},[5533,11967,11968],{"class":5907},"z3.flatten()",[5533,11970,6164],{"class":5923},[5533,11972,6155],{"class":5942},[5533,11974,6060],{"class":5907},[5533,11976,11977,11979,11981,11983,11986,11988,11991,11993,11995,11998,12000],{"class":5535,"line":9627},[5533,11978,6052],{"class":5927},[5533,11980,5931],{"class":5907},[5533,11982,6152],{"class":5923},[5533,11984,11985],{"class":5942},"\"  ŷ = σ(z): ",[5533,11987,6158],{"class":5923},[5533,11989,11990],{"class":5907},"y_pred.flatten()[",[5533,11992,5833],{"class":5951},[5533,11994,8144],{"class":5907},[5533,11996,11997],{"class":5923},":.4f}",[5533,11999,6155],{"class":5942},[5533,12001,6060],{"class":5907},[5533,12003,12004,12006,12008,12010,12012,12014,12016,12019,12022,12024,12026,12028],{"class":5535,"line":9668},[5533,12005,6052],{"class":5927},[5533,12007,5931],{"class":5907},[5533,12009,6152],{"class":5923},[5533,12011,6155],{"class":5942},[5533,12013,6871],{"class":6870},[5533,12015,6158],{"class":5923},[5533,12017,12018],{"class":5942},"'='",[5533,12020,12021],{"class":5907},"*",[5533,12023,11718],{"class":5951},[5533,12025,6164],{"class":5923},[5533,12027,6155],{"class":5942},[5533,12029,6060],{"class":5907},[5533,12031,12032,12034,12036,12038,12041,12043,12045,12047,12049,12051,12053,12056,12058],{"class":5535,"line":9709},[5533,12033,6052],{"class":5927},[5533,12035,5931],{"class":5907},[5533,12037,6152],{"class":5923},[5533,12039,12040],{"class":5942},"\"ПЕРЕДБАЧЕННЯ: ймовірність класу 1 = ",[5533,12042,6158],{"class":5923},[5533,12044,8207],{"class":5907},[5533,12046,5833],{"class":5951},[5533,12048,5987],{"class":5907},[5533,12050,5833],{"class":5951},[5533,12052,8144],{"class":5907},[5533,12054,12055],{"class":5923},":.2%}",[5533,12057,6155],{"class":5942},[5533,12059,6060],{"class":5907},[6216,12061,12062],{"v-slot:output":5528},[5806,12063,12064,12083],{},[5809,12065,12066],{},[5812,12067,12068,12071,12074,12077,12080],{},[5815,12069,12070],{"align":6241},"Шар мережі",[5815,12072,12073],{"align":6241},"Розмірність ваг",[5815,12075,12076],{"align":6241},"Вхідні дані",[5815,12078,12079],{"align":6241},"Зважена сума $z$",[5815,12081,12082],{"align":6241},"Активація $a$ (вихід шару)",[5826,12084,12085,12127,12163],{},[5812,12086,12087,12096,12102,12109,12115],{},[5831,12088,12089,5479,12092,12095],{"align":6241},[5198,12090,12091],{},"Шар 1 (Hidden)",[12093,12094],"br",{}," Linear $3 \\to 4$ + ReLU",[5831,12097,12098,12099,12101],{"align":6241},"$W^{(1)} \\in \\mathbb{R}^{4 \\times 3}$ ",[12093,12100],{}," $b^{(1)} \\in \\mathbb{R}^{4 \\times 1}$",[5831,12103,12104,12105,12108],{"align":6241},"$x = ",[5533,12106,12107],{},"0.5,; 0.3,; 0.8","^T$",[5831,12110,12111,12112,12108],{"align":6241},"$z^{(1)} = ",[5533,12113,12114],{},"0.0494,; 0.0717,; -0.0052,; 0.0135",[5831,12116,12117,12118,12121,12122,5479,12124],{"align":6241},"$a^{(1)} = ",[5533,12119,12120],{},"0.0494,; 0.0717,; 0.0000,; 0.0135","^T$ ",[12093,12123],{},[5493,12125,12126],{},"(3-й нейрон занулено через ReLU)",[5812,12128,12129,12137,12143,12146,12152],{},[5831,12130,12131,5479,12134,12136],{"align":6241},[5198,12132,12133],{},"Шар 2 (Hidden)",[12093,12135],{}," Linear $4 \\to 2$ + ReLU",[5831,12138,12139,12140,12142],{"align":6241},"$W^{(2)} \\in \\mathbb{R}^{2 \\times 4}$ ",[12093,12141],{}," $b^{(2)} \\in \\mathbb{R}^{2 \\times 1}$",[5831,12144,12145],{"align":6241},"$a^{(1)} \\in \\mathbb{R}^{4 \\times 1}$",[5831,12147,12148,12149,12108],{"align":6241},"$z^{(2)} = ",[5533,12150,12151],{},"0.0104,; -0.0051",[5831,12153,12154,12155,12121,12158,5479,12160],{"align":6241},"$a^{(2)} = ",[5533,12156,12157],{},"0.0104,; 0.0000",[12093,12159],{},[5493,12161,12162],{},"(2-й нейрон відсічено)",[5812,12164,12165,12173,12179,12182,12185],{},[5831,12166,12167,5479,12170,12172],{"align":6241},[5198,12168,12169],{},"Шар 3 (Output)",[12093,12171],{}," Linear $2 \\to 1$ + Sigmoid",[5831,12174,12175,12176,12178],{"align":6241},"$W^{(3)} \\in \\mathbb{R}^{1 \\times 2}$ ",[12093,12177],{}," $b^{(3)} \\in \\mathbb{R}^{1 \\times 1}$",[5831,12180,12181],{"align":6241},"$a^{(2)} \\in \\mathbb{R}^{2 \\times 1}$",[5831,12183,12184],{"align":6241},"$z^{(3)} = -0.00097$",[5831,12186,12187,12188,5479,12190],{"align":6241},"$\\hat{y} = \\sigma(z^{(3)}) = \\mathbf{0.4998}$ ",[12093,12189],{},[5198,12191,12192],{},"($49.98%$ ймовірність класу 1)",[10174,12194,12195,12200],{},[5191,12196,12197],{},[5198,12198,12199],{},"Ключові спостереження:",[7473,12201,12202,12208,12218,12228],{},[5252,12203,12204,12207],{},[5198,12205,12206],{},"Послідовне обчислення:"," Вихід кожного шару стає входом для наступного",[5252,12209,12210,12213,12214,12217],{},[5198,12211,12212],{},"ReLU «вимикає» від'ємні значення:"," У шарі 1 третій нейрон отримав ",[5369,12215],{"tex":12216,":inline":5372},"z_3 = -0.0052",", після ReLU → 0",[5252,12219,12220,12223,12224,12227],{},[5198,12221,12222],{},"Форма даних:"," Вектори мають форму ",[5369,12225],{"tex":12226,":inline":5372},"(n, 1)"," (стовпці), що дозволяє коректне множення матриць",[5252,12229,12230,12233,12234],{},[5198,12231,12232],{},"Sigmoid на виході:"," Перетворює довільне число в ймовірність ",[5369,12235],{"tex":8698,":inline":5372},[5309,12237],{},[5186,12239,12241],{"id":12240},"зворотний-прохід-backpropagation-як-мережа-навчається","Зворотний прохід (Backpropagation) — як мережа навчається",[5191,12243,12244,12245,12247,12248,12250,12251,12254],{},"Ми отримали передбачення ",[5369,12246],{"tex":5471,":inline":5372},". Тепер потрібно порівняти його з правильною відповіддю ",[5369,12249],{"tex":6862,":inline":5372},", обчислити помилку та ",[5198,12252,12253],{},"оновити ваги",", щоб наступного разу помилка була меншою.",[5191,12256,12257,12260,12261,5799],{},[5198,12258,12259],{},"Backpropagation (зворотне поширення помилки)"," — це алгоритм обчислення градієнтів функції втрат по всіх параметрах мережі за допомогою ",[5198,12262,12263],{},"ланцюгового правила диференціювання (chain rule)",[5351,12265,12267],{"id":12266},"інтуїтивне-пояснення","Інтуїтивне пояснення",[7321,12269,12270,12275,12278,12298,12304,12325],{},[5191,12271,12272],{},[5198,12273,12274],{},"Аналогія з виробничим конвеєром:",[5191,12276,12277],{},"Уявіть фабрику з 3 етапами виробництва печива:",[7473,12279,12280,12286,12292],{},[5252,12281,12282,12285],{},[5198,12283,12284],{},"Етап А:"," Замішування тіста (робітник Андрій)",[5252,12287,12288,12291],{},[5198,12289,12290],{},"Етап Б:"," Формування печива (робітник Богдан)",[5252,12293,12294,12297],{},[5198,12295,12296],{},"Етап В:"," Випікання (робітник Віктор)",[5191,12299,12300,12301,5462],{},"Печиво вийшло несмачним (висока функція втрат). Директор починає розслідування ",[5198,12302,12303],{},"у зворотному порядку",[5249,12305,12306,12313,12319],{},[5252,12307,12308,12309,12312],{},"Перевіряє ",[5198,12310,12311],{},"Віктора (вихідний шар)",": температура печі занадто висока → коригує налаштування",[5252,12314,12308,12315,12318],{},[5198,12316,12317],{},"Богдана (прихований шар 2)",": печиво занадто товсте → коригує товщину",[5252,12320,12308,12321,12324],{},[5198,12322,12323],{},"Андрія (прихований шар 1)",": недостатньо борошна → коригує рецепт",[5191,12326,12327],{},"Кожен етап отримує «частку провини» пропорційно свому впливу на кінцевий результат. Саме це робить backpropagation.",[5309,12329],{},[5351,12331,12333],{"id":12332},"ланцюгове-правило-chain-rule-математична-основа","Ланцюгове правило (Chain Rule) — математична основа",[5191,12335,12336],{},"Припустимо, функція втрат залежить від виходу останнього шару, який залежить від ваг:",[5369,12338],{"tex":12339},"L = L(\\hat{y}), \\quad \\hat{y} = \\sigma(z), \\quad z = Wx + b",[5191,12341,12342,12343,12346,12347,12350,12351,5462],{},"Щоб знайти, як зміна ваги ",[5369,12344],{"tex":12345,":inline":5372},"w"," впливає на втрати ",[5369,12348],{"tex":12349,":inline":5372},"L",", застосовуємо ",[5198,12352,12353],{},"ланцюгове правило",[5369,12355],{"tex":12356},"\\frac{\\partial L}{\\partial w} = \\frac{\\partial L}{\\partial \\hat{y}} \\cdot \\frac{\\partial \\hat{y}}{\\partial z} \\cdot \\frac{\\partial z}{\\partial w}",[5191,12358,12359],{},[5198,12360,12361],{},"Інтерпретація:",[5249,12363,12364,12370,12376],{},[5252,12365,12366,12369],{},[5369,12367],{"tex":12368,":inline":5372},"\\frac{\\partial L}{\\partial \\hat{y}}"," — наскільки втрати чутливі до зміни передбачення",[5252,12371,12372,12375],{},[5369,12373],{"tex":12374,":inline":5372},"\\frac{\\partial \\hat{y}}{\\partial z}"," — наскільки передбачення чутливе до зміни зваженої суми (похідна функції активації)",[5252,12377,12378,12381,12382,6867],{},[5369,12379],{"tex":12380,":inline":5372},"\\frac{\\partial z}{\\partial w}"," — наскільки зважена сума чутлива до зміни ваги (це просто ",[5369,12383],{"tex":6853,":inline":5372},[5191,12385,12386],{},[5224,12387],{"alt":12388,"className":12389,"src":12390},"Граф обчислень (Computational Graph): прямий потік значень та зворотний потік градієнтів за ланцюговим правилом",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F09.png",[5329,12392,12394],{"alt":12393},"Граф обчислень та потік градієнтів Backpropagation",[5523,12395,12397],{"className":5525,"code":12396,"language":5527,"meta":5528,"style":5528},"@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\nskinparam defaultFontName \"SF Pro Display, Arial\"\n\n!define FWD_COLOR DBEAFE\n!define BWD_COLOR FEE2E2\n!define NODE_COLOR F1F5F9\n\nrectangle \"Прямий прохід (Forward Pass: обчислення втрат)\" #FWD_COLOR {\n  card \"x, w\" as in_val\n  card \"z = w·x + b\" as sum_val\n  card \"ŷ = σ(z)\" as act_val\n  card \"Loss L(ŷ, y)\" as loss_val\n  in_val -right-> sum_val : лінійна сума\n  sum_val -right-> act_val : активація\n  act_val -right-> loss_val : функція втрат\n}\n\nrectangle \"Зворотний прохід (Backpropagation: ланцюгове правило)\" #BWD_COLOR {\n  card \"∂L\u002F∂w = ∂L\u002F∂z · x\" as grad_w\n  card \"∂L\u002F∂z = ∂L\u002F∂ŷ · σ'(z)\" as grad_z\n  card \"∂L\u002F∂ŷ\" as grad_y\n  loss_val ..> grad_y : 1. помилка на виході\n  grad_y -left-> grad_z : 2. через активацію\n  grad_z -left-> grad_w : 3. на ваги\n}\n\ncard \"Оновлення ваг: w := w - α · (∂L\u002F∂w)\" as update #DCFCE7\ngrad_w -down-> update : градієнтний спуск\n\n@enduml\n",[5530,12398,12399,12403,12407,12411,12415,12419,12424,12429,12434,12438,12443,12448,12453,12458,12463,12468,12473,12478,12482,12486,12491,12496,12501,12506,12511,12516,12521,12525,12529,12534,12539,12543],{"__ignoreMap":5528},[5533,12400,12401],{"class":5535,"line":5536},[5533,12402,5539],{},[5533,12404,12405],{"class":5535,"line":5542},[5533,12406,5545],{},[5533,12408,12409],{"class":5535,"line":5548},[5533,12410,5551],{},[5533,12412,12413],{"class":5535,"line":5554},[5533,12414,5557],{},[5533,12416,12417],{"class":5535,"line":5560},[5533,12418,5563],{"emptyLinePlaceholder":5205},[5533,12420,12421],{"class":5535,"line":5566},[5533,12422,12423],{},"!define FWD_COLOR DBEAFE\n",[5533,12425,12426],{"class":5535,"line":5572},[5533,12427,12428],{},"!define BWD_COLOR FEE2E2\n",[5533,12430,12431],{"class":5535,"line":5578},[5533,12432,12433],{},"!define NODE_COLOR F1F5F9\n",[5533,12435,12436],{"class":5535,"line":5584},[5533,12437,5563],{"emptyLinePlaceholder":5205},[5533,12439,12440],{"class":5535,"line":5589},[5533,12441,12442],{},"rectangle \"Прямий прохід (Forward Pass: обчислення втрат)\" #FWD_COLOR {\n",[5533,12444,12445],{"class":5535,"line":5595},[5533,12446,12447],{},"  card \"x, w\" as in_val\n",[5533,12449,12450],{"class":5535,"line":5601},[5533,12451,12452],{},"  card \"z = w·x + b\" as sum_val\n",[5533,12454,12455],{"class":5535,"line":5607},[5533,12456,12457],{},"  card \"ŷ = σ(z)\" as act_val\n",[5533,12459,12460],{"class":5535,"line":5613},[5533,12461,12462],{},"  card \"Loss L(ŷ, y)\" as loss_val\n",[5533,12464,12465],{"class":5535,"line":5619},[5533,12466,12467],{},"  in_val -right-> sum_val : лінійна сума\n",[5533,12469,12470],{"class":5535,"line":5625},[5533,12471,12472],{},"  sum_val -right-> act_val : активація\n",[5533,12474,12475],{"class":5535,"line":5630},[5533,12476,12477],{},"  act_val -right-> loss_val : функція втрат\n",[5533,12479,12480],{"class":5535,"line":5636},[5533,12481,5622],{},[5533,12483,12484],{"class":5535,"line":5642},[5533,12485,5563],{"emptyLinePlaceholder":5205},[5533,12487,12488],{"class":5535,"line":5648},[5533,12489,12490],{},"rectangle \"Зворотний прохід (Backpropagation: ланцюгове правило)\" #BWD_COLOR {\n",[5533,12492,12493],{"class":5535,"line":5654},[5533,12494,12495],{},"  card \"∂L\u002F∂w = ∂L\u002F∂z · x\" as grad_w\n",[5533,12497,12498],{"class":5535,"line":5659},[5533,12499,12500],{},"  card \"∂L\u002F∂z = ∂L\u002F∂ŷ · σ'(z)\" as grad_z\n",[5533,12502,12503],{"class":5535,"line":5664},[5533,12504,12505],{},"  card \"∂L\u002F∂ŷ\" as grad_y\n",[5533,12507,12508],{"class":5535,"line":5670},[5533,12509,12510],{},"  loss_val ..> grad_y : 1. помилка на виході\n",[5533,12512,12513],{"class":5535,"line":5676},[5533,12514,12515],{},"  grad_y -left-> grad_z : 2. через активацію\n",[5533,12517,12518],{"class":5535,"line":5681},[5533,12519,12520],{},"  grad_z -left-> grad_w : 3. на ваги\n",[5533,12522,12523],{"class":5535,"line":5686},[5533,12524,5622],{},[5533,12526,12527],{"class":5535,"line":5692},[5533,12528,5563],{"emptyLinePlaceholder":5205},[5533,12530,12531],{"class":5535,"line":5698},[5533,12532,12533],{},"card \"Оновлення ваг: w := w - α · (∂L\u002F∂w)\" as update #DCFCE7\n",[5533,12535,12536],{"class":5535,"line":5704},[5533,12537,12538],{},"grad_w -down-> update : градієнтний спуск\n",[5533,12540,12541],{"class":5535,"line":5710},[5533,12542,5563],{"emptyLinePlaceholder":5205},[5533,12544,12545],{"class":5535,"line":5715},[5533,12546,5786],{},[5309,12548],{},[5351,12550,12552],{"id":12551},"алгоритм-backpropagation-покроково","Алгоритм backpropagation покроково",[5191,12554,12555,12556,12558],{},"Для мережі з ",[5369,12557],{"tex":12349,":inline":5372}," шарами:",[5359,12560,12561,12565,12572,12576,12582,12585,12589,12592,12595,12598,12601,12605,12611,12616,12619,12624,12627,12632,12635,12646,12650,12653,12656],{},[5351,12562,12564],{"id":12563},"крок-1-forward-pass","Крок 1: Forward Pass",[5191,12566,12567,12568,12571],{},"Обчислюємо активації всіх шарів ",[5369,12569],{"tex":12570,":inline":5372},"a^{[1]}, a^{[2]}, \\ldots, a^{[L]}"," та зберігаємо їх (потрібні для backprop).",[5351,12573,12575],{"id":12574},"крок-2-обчислення-втрат","Крок 2: Обчислення втрат",[5191,12577,12578,12579,5462],{},"Для бінарної класифікації використовуємо ",[5198,12580,12581],{},"Binary Cross-Entropy",[5369,12583],{"tex":12584},"L = -\\left[ y \\log(\\hat{y}) + (1 - y) \\log(1 - \\hat{y}) \\right]",[5351,12586,12588],{"id":12587},"крок-3-градієнт-на-виході","Крок 3: Градієнт на виході",[5191,12590,12591],{},"Обчислюємо похідну втрат по виходу:",[5369,12593],{"tex":12594},"\\frac{\\partial L}{\\partial \\hat{y}} = -\\frac{y}{\\hat{y}} + \\frac{1 - y}{1 - \\hat{y}}",[5191,12596,12597],{},"Для sigmoid з Binary Cross-Entropy це спрощується до:",[5369,12599],{"tex":12600},"\\frac{\\partial L}{\\partial z^{[L]}} = \\hat{y} - y",[5351,12602,12604],{"id":12603},"крок-4-зворотний-прохід-по-шарах","Крок 4: Зворотний прохід по шарах",[5191,12606,12607,12608,5462],{},"Для кожного шару ",[5369,12609],{"tex":12610,":inline":5372},"l = L, L-1, \\ldots, 1",[5191,12612,12613],{},[5198,12614,12615],{},"Градієнт по вагах:",[5369,12617],{"tex":12618},"\\frac{\\partial L}{\\partial W^{[l]}} = \\frac{\\partial L}{\\partial z^{[l]}} \\cdot (a^{[l-1]})^T",[5191,12620,12621],{},[5198,12622,12623],{},"Градієнт по bias:",[5369,12625],{"tex":12626},"\\frac{\\partial L}{\\partial b^{[l]}} = \\frac{\\partial L}{\\partial z^{[l]}}",[5191,12628,12629],{},[5198,12630,12631],{},"Градієнт для попереднього шару:",[5369,12633],{"tex":12634},"\\frac{\\partial L}{\\partial z^{[l-1]}} = (W^{[l]})^T \\cdot \\frac{\\partial L}{\\partial z^{[l]}} \\odot \\sigma'(z^{[l-1]})",[5191,12636,12637,12638,12641,12642,12645],{},"Де ",[5369,12639],{"tex":12640,":inline":5372},"\\odot"," — поелементне множення, ",[5369,12643],{"tex":12644,":inline":5372},"\\sigma'"," — похідна функції активації.",[5351,12647,12649],{"id":12648},"крок-5-оновлення-параметрів","Крок 5: Оновлення параметрів",[5369,12651],{"tex":12652},"W^{[l]} := W^{[l]} - \\alpha \\frac{\\partial L}{\\partial W^{[l]}}",[5369,12654],{"tex":12655},"b^{[l]} := b^{[l]} - \\alpha \\frac{\\partial L}{\\partial b^{[l]}}",[5191,12657,12637,12658,12660],{},[5369,12659],{"tex":10220,":inline":5372}," — learning rate.",[5309,12662],{},[5351,12664,12666],{"id":12665},"похідні-функцій-активації","Похідні функцій активації",[5191,12668,12669],{},"Для backpropagation потрібні похідні функцій активації:",[5806,12671,12672,12688],{},[5809,12673,12674],{},[5812,12675,12676,12678,12682],{},[5815,12677,10708],{"align":6241},[5815,12679,12680],{"align":6241},[5369,12681],{"tex":5457,":inline":5372},[5815,12683,12684,12685],{"align":6241},"Похідна ",[5369,12686],{"tex":12687,":inline":5372},"\\sigma'(z)",[5826,12689,12690,12706,12722,12737],{},[5812,12691,12692,12696,12701],{},[5831,12693,12694],{"align":6241},[5198,12695,10735],{},[5831,12697,12698],{"align":6241},[5369,12699],{"tex":12700,":inline":5372},"\\frac{1}{1 + e^{-z}}",[5831,12702,12703],{"align":6241},[5369,12704],{"tex":12705,":inline":5372},"\\sigma(z) \\cdot (1 - \\sigma(z))",[5812,12707,12708,12712,12717],{},[5831,12709,12710],{"align":6241},[5198,12711,10760],{},[5831,12713,12714],{"align":6241},[5369,12715],{"tex":12716,":inline":5372},"\\tanh(z)",[5831,12718,12719],{"align":6241},[5369,12720],{"tex":12721,":inline":5372},"1 - \\tanh^2(z)",[5812,12723,12724,12728,12732],{},[5831,12725,12726],{"align":6241},[5198,12727,10785],{},[5831,12729,12730],{"align":6241},[5369,12731],{"tex":10790,":inline":5372},[5831,12733,12734],{"align":6241},[5369,12735],{"tex":12736,":inline":5372},"1 \\text{ якщо } z > 0 \\text{, інакше } 0",[5812,12738,12739,12743,12747],{},[5831,12740,12741],{"align":6241},[5198,12742,10810],{},[5831,12744,12745],{"align":6241},[5369,12746],{"tex":10815,":inline":5372},[5831,12748,12749],{"align":6241},[5369,12750],{"tex":12751,":inline":5372},"1 \\text{ якщо } z > 0 \\text{, інакше } 0.01",[5191,12753,12754],{},[5224,12755],{"alt":12756,"className":12757,"src":12758},"Похідні функцій активації та механіка зникнення градієнтів у глибоких мережах",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F10.png",[5329,12760,12762,12764,12767,12770,12776,12788,12800],{"alt":12761},"Згасання градієнтів у глибоких мережах: Sigmoid проти ReLU",[5191,12763,5334],{},[5191,12765,12766],{},"skinparam state {\nBackgroundColor #F8FAFC\nBorderColor #94A3B8\nFontColor #0F172A\nFontSize 12\nArrowColor #64748B\nArrowFontSize 11\n}",[5191,12768,12769],{},"title Порівняння градієнтного сигналу: Sigmoid vs ReLU (L = 4 шари)",[5191,12771,12772,12773,12775],{},"state \"Шар L (Вихід)\" as L4 #EFF6FF;line:2px;line:#2563EB {\nstate \"δ^",[5533,12774,8720],{}," = 1.0 (Базовий градієнт втрат)\" as d4 #FFFFFF;line:#3B82F6\n}",[5191,12777,12778,12779,12781,12782,12784,12785,12787],{},"state \"Проходження через Sigmoid (max σ' = 0.25)\" as SIG #FEF2F2;line:2px;line:#DC2626 {\nstate \"Шар 3: δ^",[5533,12780,7457],{}," ≈ 0.250\" as s3 #FFFFFF;line:#EF4444\nstate \"Шар 2: δ^",[5533,12783,6604],{}," ≈ 0.062\" as s2 #FFFFFF;line:#EF4444\nstate \"Шар 1: δ^",[5533,12786,5495],{}," ≈ 0.015\\n(Згасання: ваги майже не оновлюються)\" as s1 #FEE2E2;line:#B91C1C;text:#991B1B\ns3 -down-> s2 : \" * σ' ≤ 0.25\"\ns2 -down-> s1 : \" * σ' ≤ 0.25\"\n}",[5191,12789,12790,12791,12793,12794,12796,12797,12799],{},"state \"Проходження через ReLU (похідна = 1 при z > 0)\" as RELU #ECFDF5;line:2px;line:#059669 {\nstate \"Шар 3: δ^",[5533,12792,7457],{}," = 1.000\" as r3 #FFFFFF;line:#10B981\nstate \"Шар 2: δ^",[5533,12795,6604],{}," = 1.000\" as r2 #FFFFFF;line:#10B981\nstate \"Шар 1: δ^",[5533,12798,5495],{}," = 1.000\\n(Стабільний потік: швидке навчання)\" as r1 #D1FAE5;line:#047857;text:#065F46\nr3 -down-> r2 : \" * 1.0\"\nr2 -down-> r1 : \" * 1.0\"\n}",[5191,12801,12802],{},"L4 -down-> s3 : \" Backprop (Sigmoid)\"\nL4 -down-> r3 : \" Backprop (ReLU)\"\n@enduml",[6339,12804,12805,12810],{},[5191,12806,12807],{},[5198,12808,12809],{},"Чому ReLU ефективна для backprop:",[5191,12811,12812,12813,12816,12817,12820],{},"Похідна ReLU дуже проста: 1 або 0. Це означає, що градієнт ",[5198,12814,12815],{},"не згасає"," (на відміну від sigmoid, де похідна може бути дуже малою). Саме тому ReLU дозволила навчати ",[5198,12818,12819],{},"глибокі"," мережі (десятки та сотні шарів).",[5309,12822],{},[5351,12824,12826],{"id":12825},"спрощений-приклад-backpropagation-на-папері","Спрощений приклад backpropagation на папері",[5191,12828,12829],{},"Розглянемо мінімальну мережу: 1 вхід → 1 нейрон з sigmoid → 1 вихід.",[5191,12831,12832],{},[5198,12833,12834],{},"Дано:",[5249,12836,12837,12842,12848,12854],{},[5252,12838,8571,12839],{},[5369,12840],{"tex":12841,":inline":5372},"x = 0.5",[5252,12843,12844,12845],{},"Вага: ",[5369,12846],{"tex":12847,":inline":5372},"w = 0.8",[5252,12849,12850,12851],{},"Bias: ",[5369,12852],{"tex":12853,":inline":5372},"b = 0.2",[5252,12855,12856,12857],{},"Правильна відповідь: ",[5369,12858],{"tex":12859,":inline":5372},"y = 1",[5191,12861,12862],{},[5198,12863,12864],{},"Forward pass:",[5885,12866,12868],{"kernel":5887,"title":12867},"backprop_minimal.ipynb",[5890,12869,12871,13658],{"execution-count":12870},"7",[5523,12872,12874],{"className":5894,"code":12873,"language":5896,"meta":5528,"style":5528},"import numpy as np\n\n# Параметри\nx = 0.5\nw = 0.8\nb = 0.2\ny = 1.0\nlearning_rate = 0.5\n\n# Forward pass\nz = w * x + b\ny_pred = 1 \u002F (1 + np.exp(-z))  # sigmoid\n\n# Loss (Binary Cross-Entropy)\nloss = -(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred))\n\nprint(\"FORWARD PASS:\")\nprint(f\"z = w·x + b = {w}·{x} + {b} = {z:.4f}\")\nprint(f\"ŷ = σ(z) = {y_pred:.4f}\")\nprint(f\"Loss = -{y}·log({y_pred:.4f}) = {loss:.4f}\\n\")\n\n# Backward pass\ndL_dy_pred = -(y \u002F y_pred) + (1 - y) \u002F (1 - y_pred)  # Градієнт по виходу\ndy_pred_dz = y_pred * (1 - y_pred)  # Похідна sigmoid\ndL_dz = dL_dy_pred * dy_pred_dz  # Ланцюгове правило\n\n# Для sigmoid з BCE це спрощується до:\ndL_dz_simplified = y_pred - y\n\ndz_dw = x  # Похідна z по w\ndz_db = 1  # Похідна z по b\n\ndL_dw = dL_dz_simplified * dz_dw\ndL_db = dL_dz_simplified * dz_db\n\nprint(\"BACKWARD PASS:\")\nprint(f\"∂L\u002F∂ŷ = {dL_dy_pred:.4f}\")\nprint(f\"∂ŷ\u002F∂z = {dy_pred_dz:.4f}  (похідна sigmoid)\")\nprint(f\"∂L\u002F∂z = {dL_dz:.4f}  або спрощено: {dL_dz_simplified:.4f}\")\nprint(f\"∂L\u002F∂w = ∂L\u002F∂z · ∂z\u002F∂w = {dL_dz_simplified:.4f} · {x} = {dL_dw:.4f}\")\nprint(f\"∂L\u002F∂b = ∂L\u002F∂z · ∂z\u002F∂b = {dL_dz_simplified:.4f} · 1 = {dL_db:.4f}\\n\")\n\n# Оновлення параметрів\nw_new = w - learning_rate * dL_dw\nb_new = b - learning_rate * dL_db\n\nprint(\"ОНОВЛЕННЯ ПАРАМЕТРІВ:\")\nprint(f\"w := w - α·∂L\u002F∂w = {w} - {learning_rate}·{dL_dw:.4f} = {w_new:.4f}\")\nprint(f\"b := b - α·∂L\u002F∂b = {b} - {learning_rate}·{dL_db:.4f} = {b_new:.4f}\\n\")\n\n# Перевірка: forward pass з новими вагами\nz_new = w_new * x + b_new\ny_pred_new = 1 \u002F (1 + np.exp(-z_new))\nloss_new = -(y * np.log(y_pred_new) + (1 - y) * np.log(1 - y_pred_new))\n\nprint(\"ПЕРЕВІРКА (після оновлення):\")\nprint(f\"ŷ_new = {y_pred_new:.4f}  (було {y_pred:.4f})\")\nprint(f\"Loss_new = {loss_new:.4f}  (було {loss:.4f})\")\nprint(f\"Покращення: {loss - loss_new:.4f} ✓\" if loss_new \u003C loss else \"Погіршення ✗\")\n",[5530,12875,12876,12886,12890,12895,12902,12910,12918,12926,12933,12937,12942,12947,12964,12968,12973,12988,12992,13003,13051,13073,13115,13119,13124,13142,13154,13162,13166,13171,13176,13180,13188,13198,13202,13207,13212,13216,13227,13249,13272,13304,13343,13376,13380,13385,13390,13395,13399,13410,13458,13506,13510,13515,13520,13534,13548,13552,13563,13595,13625],{"__ignoreMap":5528},[5533,12877,12878,12880,12882,12884],{"class":5535,"line":5536},[5533,12879,5904],{"class":5903},[5533,12881,5908],{"class":5907},[5533,12883,5911],{"class":5903},[5533,12885,5914],{"class":5907},[5533,12887,12888],{"class":5535,"line":5542},[5533,12889,5563],{"emptyLinePlaceholder":5205},[5533,12891,12892],{"class":5535,"line":5548},[5533,12893,12894],{"class":5975},"# Параметри\n",[5533,12896,12897,12900],{"class":5535,"line":5554},[5533,12898,12899],{"class":5907},"x = ",[5533,12901,5995],{"class":5951},[5533,12903,12904,12907],{"class":5535,"line":5560},[5533,12905,12906],{"class":5907},"w = ",[5533,12908,12909],{"class":5951},"0.8\n",[5533,12911,12912,12915],{"class":5535,"line":5566},[5533,12913,12914],{"class":5907},"b = ",[5533,12916,12917],{"class":5951},"0.2\n",[5533,12919,12920,12923],{"class":5535,"line":5572},[5533,12921,12922],{"class":5907},"y = ",[5533,12924,12925],{"class":5951},"1.0\n",[5533,12927,12928,12931],{"class":5535,"line":5578},[5533,12929,12930],{"class":5907},"learning_rate = ",[5533,12932,5995],{"class":5951},[5533,12934,12935],{"class":5535,"line":5584},[5533,12936,5563],{"emptyLinePlaceholder":5205},[5533,12938,12939],{"class":5535,"line":5589},[5533,12940,12941],{"class":5975},"# Forward pass\n",[5533,12943,12944],{"class":5535,"line":5595},[5533,12945,12946],{"class":5907},"z = w * x + b\n",[5533,12948,12949,12952,12954,12956,12958,12961],{"class":5535,"line":5601},[5533,12950,12951],{"class":5907},"y_pred = ",[5533,12953,5495],{"class":5951},[5533,12955,7799],{"class":5907},[5533,12957,5495],{"class":5951},[5533,12959,12960],{"class":5907}," + np.exp(-z))  ",[5533,12962,12963],{"class":5975},"# sigmoid\n",[5533,12965,12966],{"class":5535,"line":5607},[5533,12967,5563],{"emptyLinePlaceholder":5205},[5533,12969,12970],{"class":5535,"line":5613},[5533,12971,12972],{"class":5975},"# Loss (Binary Cross-Entropy)\n",[5533,12974,12975,12978,12980,12983,12985],{"class":5535,"line":5619},[5533,12976,12977],{"class":5907},"loss = -(y * np.log(y_pred) + (",[5533,12979,5495],{"class":5951},[5533,12981,12982],{"class":5907}," - y) * np.log(",[5533,12984,5495],{"class":5951},[5533,12986,12987],{"class":5907}," - y_pred))\n",[5533,12989,12990],{"class":5535,"line":5625},[5533,12991,5563],{"emptyLinePlaceholder":5205},[5533,12993,12994,12996,12998,13001],{"class":5535,"line":5630},[5533,12995,6052],{"class":5927},[5533,12997,5931],{"class":5907},[5533,12999,13000],{"class":5942},"\"FORWARD PASS:\"",[5533,13002,6060],{"class":5907},[5533,13004,13005,13007,13009,13011,13014,13016,13018,13020,13023,13025,13027,13029,13032,13034,13036,13038,13041,13043,13045,13047,13049],{"class":5535,"line":5636},[5533,13006,6052],{"class":5927},[5533,13008,5931],{"class":5907},[5533,13010,6152],{"class":5923},[5533,13012,13013],{"class":5942},"\"z = w·x + b = ",[5533,13015,6158],{"class":5923},[5533,13017,12345],{"class":5907},[5533,13019,6164],{"class":5923},[5533,13021,13022],{"class":5942},"·",[5533,13024,6158],{"class":5923},[5533,13026,6853],{"class":5907},[5533,13028,6164],{"class":5923},[5533,13030,13031],{"class":5942}," + ",[5533,13033,6158],{"class":5923},[5533,13035,5416],{"class":5907},[5533,13037,6164],{"class":5923},[5533,13039,13040],{"class":5942}," = ",[5533,13042,6158],{"class":5923},[5533,13044,5453],{"class":5907},[5533,13046,11997],{"class":5923},[5533,13048,6155],{"class":5942},[5533,13050,6060],{"class":5907},[5533,13052,13053,13055,13057,13059,13062,13064,13067,13069,13071],{"class":5535,"line":5642},[5533,13054,6052],{"class":5927},[5533,13056,5931],{"class":5907},[5533,13058,6152],{"class":5923},[5533,13060,13061],{"class":5942},"\"ŷ = σ(z) = ",[5533,13063,6158],{"class":5923},[5533,13065,13066],{"class":5907},"y_pred",[5533,13068,11997],{"class":5923},[5533,13070,6155],{"class":5942},[5533,13072,6060],{"class":5907},[5533,13074,13075,13077,13079,13081,13084,13086,13088,13090,13093,13095,13097,13099,13102,13104,13107,13109,13111,13113],{"class":5535,"line":5648},[5533,13076,6052],{"class":5927},[5533,13078,5931],{"class":5907},[5533,13080,6152],{"class":5923},[5533,13082,13083],{"class":5942},"\"Loss = -",[5533,13085,6158],{"class":5923},[5533,13087,6862],{"class":5907},[5533,13089,6164],{"class":5923},[5533,13091,13092],{"class":5942},"·log(",[5533,13094,6158],{"class":5923},[5533,13096,13066],{"class":5907},[5533,13098,11997],{"class":5923},[5533,13100,13101],{"class":5942},") = ",[5533,13103,6158],{"class":5923},[5533,13105,13106],{"class":5907},"loss",[5533,13108,11997],{"class":5923},[5533,13110,6871],{"class":6870},[5533,13112,6155],{"class":5942},[5533,13114,6060],{"class":5907},[5533,13116,13117],{"class":5535,"line":5654},[5533,13118,5563],{"emptyLinePlaceholder":5205},[5533,13120,13121],{"class":5535,"line":5659},[5533,13122,13123],{"class":5975},"# Backward pass\n",[5533,13125,13126,13129,13131,13134,13136,13139],{"class":5535,"line":5664},[5533,13127,13128],{"class":5907},"dL_dy_pred = -(y \u002F y_pred) + (",[5533,13130,5495],{"class":5951},[5533,13132,13133],{"class":5907}," - y) \u002F (",[5533,13135,5495],{"class":5951},[5533,13137,13138],{"class":5907}," - y_pred)  ",[5533,13140,13141],{"class":5975},"# Градієнт по виходу\n",[5533,13143,13144,13147,13149,13151],{"class":5535,"line":5670},[5533,13145,13146],{"class":5907},"dy_pred_dz = y_pred * (",[5533,13148,5495],{"class":5951},[5533,13150,13138],{"class":5907},[5533,13152,13153],{"class":5975},"# Похідна sigmoid\n",[5533,13155,13156,13159],{"class":5535,"line":5676},[5533,13157,13158],{"class":5907},"dL_dz = dL_dy_pred * dy_pred_dz  ",[5533,13160,13161],{"class":5975},"# Ланцюгове правило\n",[5533,13163,13164],{"class":5535,"line":5681},[5533,13165,5563],{"emptyLinePlaceholder":5205},[5533,13167,13168],{"class":5535,"line":5686},[5533,13169,13170],{"class":5975},"# Для sigmoid з BCE це спрощується до:\n",[5533,13172,13173],{"class":5535,"line":5692},[5533,13174,13175],{"class":5907},"dL_dz_simplified = y_pred - y\n",[5533,13177,13178],{"class":5535,"line":5698},[5533,13179,5563],{"emptyLinePlaceholder":5205},[5533,13181,13182,13185],{"class":5535,"line":5704},[5533,13183,13184],{"class":5907},"dz_dw = x  ",[5533,13186,13187],{"class":5975},"# Похідна z по w\n",[5533,13189,13190,13193,13195],{"class":5535,"line":5710},[5533,13191,13192],{"class":5907},"dz_db = ",[5533,13194,5495],{"class":5951},[5533,13196,13197],{"class":5975},"  # Похідна z по b\n",[5533,13199,13200],{"class":5535,"line":5715},[5533,13201,5563],{"emptyLinePlaceholder":5205},[5533,13203,13204],{"class":5535,"line":5721},[5533,13205,13206],{"class":5907},"dL_dw = dL_dz_simplified * dz_dw\n",[5533,13208,13209],{"class":5535,"line":5726},[5533,13210,13211],{"class":5907},"dL_db = dL_dz_simplified * dz_db\n",[5533,13213,13214],{"class":5535,"line":5732},[5533,13215,5563],{"emptyLinePlaceholder":5205},[5533,13217,13218,13220,13222,13225],{"class":5535,"line":5738},[5533,13219,6052],{"class":5927},[5533,13221,5931],{"class":5907},[5533,13223,13224],{"class":5942},"\"BACKWARD PASS:\"",[5533,13226,6060],{"class":5907},[5533,13228,13229,13231,13233,13235,13238,13240,13243,13245,13247],{"class":5535,"line":5744},[5533,13230,6052],{"class":5927},[5533,13232,5931],{"class":5907},[5533,13234,6152],{"class":5923},[5533,13236,13237],{"class":5942},"\"∂L\u002F∂ŷ = ",[5533,13239,6158],{"class":5923},[5533,13241,13242],{"class":5907},"dL_dy_pred",[5533,13244,11997],{"class":5923},[5533,13246,6155],{"class":5942},[5533,13248,6060],{"class":5907},[5533,13250,13251,13253,13255,13257,13260,13262,13265,13267,13270],{"class":5535,"line":5750},[5533,13252,6052],{"class":5927},[5533,13254,5931],{"class":5907},[5533,13256,6152],{"class":5923},[5533,13258,13259],{"class":5942},"\"∂ŷ\u002F∂z = ",[5533,13261,6158],{"class":5923},[5533,13263,13264],{"class":5907},"dy_pred_dz",[5533,13266,11997],{"class":5923},[5533,13268,13269],{"class":5942},"  (похідна sigmoid)\"",[5533,13271,6060],{"class":5907},[5533,13273,13274,13276,13278,13280,13283,13285,13288,13290,13293,13295,13298,13300,13302],{"class":5535,"line":5755},[5533,13275,6052],{"class":5927},[5533,13277,5931],{"class":5907},[5533,13279,6152],{"class":5923},[5533,13281,13282],{"class":5942},"\"∂L\u002F∂z = ",[5533,13284,6158],{"class":5923},[5533,13286,13287],{"class":5907},"dL_dz",[5533,13289,11997],{"class":5923},[5533,13291,13292],{"class":5942},"  або спрощено: ",[5533,13294,6158],{"class":5923},[5533,13296,13297],{"class":5907},"dL_dz_simplified",[5533,13299,11997],{"class":5923},[5533,13301,6155],{"class":5942},[5533,13303,6060],{"class":5907},[5533,13305,13306,13308,13310,13312,13315,13317,13319,13321,13324,13326,13328,13330,13332,13334,13337,13339,13341],{"class":5535,"line":5761},[5533,13307,6052],{"class":5927},[5533,13309,5931],{"class":5907},[5533,13311,6152],{"class":5923},[5533,13313,13314],{"class":5942},"\"∂L\u002F∂w = ∂L\u002F∂z · ∂z\u002F∂w = ",[5533,13316,6158],{"class":5923},[5533,13318,13297],{"class":5907},[5533,13320,11997],{"class":5923},[5533,13322,13323],{"class":5942}," · ",[5533,13325,6158],{"class":5923},[5533,13327,6853],{"class":5907},[5533,13329,6164],{"class":5923},[5533,13331,13040],{"class":5942},[5533,13333,6158],{"class":5923},[5533,13335,13336],{"class":5907},"dL_dw",[5533,13338,11997],{"class":5923},[5533,13340,6155],{"class":5942},[5533,13342,6060],{"class":5907},[5533,13344,13345,13347,13349,13351,13354,13356,13358,13360,13363,13365,13368,13370,13372,13374],{"class":5535,"line":5767},[5533,13346,6052],{"class":5927},[5533,13348,5931],{"class":5907},[5533,13350,6152],{"class":5923},[5533,13352,13353],{"class":5942},"\"∂L\u002F∂b = ∂L\u002F∂z · ∂z\u002F∂b = ",[5533,13355,6158],{"class":5923},[5533,13357,13297],{"class":5907},[5533,13359,11997],{"class":5923},[5533,13361,13362],{"class":5942}," · 1 = ",[5533,13364,6158],{"class":5923},[5533,13366,13367],{"class":5907},"dL_db",[5533,13369,11997],{"class":5923},[5533,13371,6871],{"class":6870},[5533,13373,6155],{"class":5942},[5533,13375,6060],{"class":5907},[5533,13377,13378],{"class":5535,"line":5773},[5533,13379,5563],{"emptyLinePlaceholder":5205},[5533,13381,13382],{"class":5535,"line":5778},[5533,13383,13384],{"class":5975},"# Оновлення параметрів\n",[5533,13386,13387],{"class":5535,"line":5783},[5533,13388,13389],{"class":5907},"w_new = w - learning_rate * dL_dw\n",[5533,13391,13392],{"class":5535,"line":9498},[5533,13393,13394],{"class":5907},"b_new = b - learning_rate * dL_db\n",[5533,13396,13397],{"class":5535,"line":9532},[5533,13398,5563],{"emptyLinePlaceholder":5205},[5533,13400,13401,13403,13405,13408],{"class":5535,"line":9559},[5533,13402,6052],{"class":5927},[5533,13404,5931],{"class":5907},[5533,13406,13407],{"class":5942},"\"ОНОВЛЕННЯ ПАРАМЕТРІВ:\"",[5533,13409,6060],{"class":5907},[5533,13411,13412,13414,13416,13418,13421,13423,13425,13427,13430,13432,13435,13437,13439,13441,13443,13445,13447,13449,13452,13454,13456],{"class":5535,"line":9585},[5533,13413,6052],{"class":5927},[5533,13415,5931],{"class":5907},[5533,13417,6152],{"class":5923},[5533,13419,13420],{"class":5942},"\"w := w - α·∂L\u002F∂w = ",[5533,13422,6158],{"class":5923},[5533,13424,12345],{"class":5907},[5533,13426,6164],{"class":5923},[5533,13428,13429],{"class":5942}," - ",[5533,13431,6158],{"class":5923},[5533,13433,13434],{"class":5907},"learning_rate",[5533,13436,6164],{"class":5923},[5533,13438,13022],{"class":5942},[5533,13440,6158],{"class":5923},[5533,13442,13336],{"class":5907},[5533,13444,11997],{"class":5923},[5533,13446,13040],{"class":5942},[5533,13448,6158],{"class":5923},[5533,13450,13451],{"class":5907},"w_new",[5533,13453,11997],{"class":5923},[5533,13455,6155],{"class":5942},[5533,13457,6060],{"class":5907},[5533,13459,13460,13462,13464,13466,13469,13471,13473,13475,13477,13479,13481,13483,13485,13487,13489,13491,13493,13495,13498,13500,13502,13504],{"class":5535,"line":9590},[5533,13461,6052],{"class":5927},[5533,13463,5931],{"class":5907},[5533,13465,6152],{"class":5923},[5533,13467,13468],{"class":5942},"\"b := b - α·∂L\u002F∂b = ",[5533,13470,6158],{"class":5923},[5533,13472,5416],{"class":5907},[5533,13474,6164],{"class":5923},[5533,13476,13429],{"class":5942},[5533,13478,6158],{"class":5923},[5533,13480,13434],{"class":5907},[5533,13482,6164],{"class":5923},[5533,13484,13022],{"class":5942},[5533,13486,6158],{"class":5923},[5533,13488,13367],{"class":5907},[5533,13490,11997],{"class":5923},[5533,13492,13040],{"class":5942},[5533,13494,6158],{"class":5923},[5533,13496,13497],{"class":5907},"b_new",[5533,13499,11997],{"class":5923},[5533,13501,6871],{"class":6870},[5533,13503,6155],{"class":5942},[5533,13505,6060],{"class":5907},[5533,13507,13508],{"class":5535,"line":9596},[5533,13509,5563],{"emptyLinePlaceholder":5205},[5533,13511,13512],{"class":5535,"line":9627},[5533,13513,13514],{"class":5975},"# Перевірка: forward pass з новими вагами\n",[5533,13516,13517],{"class":5535,"line":9668},[5533,13518,13519],{"class":5907},"z_new = w_new * x + b_new\n",[5533,13521,13522,13525,13527,13529,13531],{"class":5535,"line":9709},[5533,13523,13524],{"class":5907},"y_pred_new = ",[5533,13526,5495],{"class":5951},[5533,13528,7799],{"class":5907},[5533,13530,5495],{"class":5951},[5533,13532,13533],{"class":5907}," + np.exp(-z_new))\n",[5533,13535,13536,13539,13541,13543,13545],{"class":5535,"line":9730},[5533,13537,13538],{"class":5907},"loss_new = -(y * np.log(y_pred_new) + (",[5533,13540,5495],{"class":5951},[5533,13542,12982],{"class":5907},[5533,13544,5495],{"class":5951},[5533,13546,13547],{"class":5907}," - y_pred_new))\n",[5533,13549,13550],{"class":5535,"line":9764},[5533,13551,5563],{"emptyLinePlaceholder":5205},[5533,13553,13554,13556,13558,13561],{"class":5535,"line":9789},[5533,13555,6052],{"class":5927},[5533,13557,5931],{"class":5907},[5533,13559,13560],{"class":5942},"\"ПЕРЕВІРКА (після оновлення):\"",[5533,13562,6060],{"class":5907},[5533,13564,13565,13567,13569,13571,13574,13576,13579,13581,13584,13586,13588,13590,13593],{"class":5535,"line":9815},[5533,13566,6052],{"class":5927},[5533,13568,5931],{"class":5907},[5533,13570,6152],{"class":5923},[5533,13572,13573],{"class":5942},"\"ŷ_new = ",[5533,13575,6158],{"class":5923},[5533,13577,13578],{"class":5907},"y_pred_new",[5533,13580,11997],{"class":5923},[5533,13582,13583],{"class":5942},"  (було ",[5533,13585,6158],{"class":5923},[5533,13587,13066],{"class":5907},[5533,13589,11997],{"class":5923},[5533,13591,13592],{"class":5942},")\"",[5533,13594,6060],{"class":5907},[5533,13596,13597,13599,13601,13603,13606,13608,13611,13613,13615,13617,13619,13621,13623],{"class":5535,"line":9820},[5533,13598,6052],{"class":5927},[5533,13600,5931],{"class":5907},[5533,13602,6152],{"class":5923},[5533,13604,13605],{"class":5942},"\"Loss_new = ",[5533,13607,6158],{"class":5923},[5533,13609,13610],{"class":5907},"loss_new",[5533,13612,11997],{"class":5923},[5533,13614,13583],{"class":5942},[5533,13616,6158],{"class":5923},[5533,13618,13106],{"class":5907},[5533,13620,11997],{"class":5923},[5533,13622,13592],{"class":5942},[5533,13624,6060],{"class":5907},[5533,13626,13627,13629,13631,13633,13636,13638,13641,13643,13646,13648,13651,13653,13656],{"class":5535,"line":9825},[5533,13628,6052],{"class":5927},[5533,13630,5931],{"class":5907},[5533,13632,6152],{"class":5923},[5533,13634,13635],{"class":5942},"\"Покращення: ",[5533,13637,6158],{"class":5923},[5533,13639,13640],{"class":5907},"loss - loss_new",[5533,13642,11997],{"class":5923},[5533,13644,13645],{"class":5942}," ✓\"",[5533,13647,5955],{"class":5903},[5533,13649,13650],{"class":5907}," loss_new \u003C loss ",[5533,13652,6139],{"class":5903},[5533,13654,13655],{"class":5942}," \"Погіршення ✗\"",[5533,13657,6060],{"class":5907},[6216,13659,13660],{"v-slot:output":5528},[5806,13661,13662,13678],{},[5809,13663,13664],{},[5812,13665,13666,13669,13672,13675],{},[5815,13667,13668],{"align":6241},"Етап розрахунку",[5815,13670,13671],{"align":6241},"Параметри та формули",[5815,13673,13674],{"align":5817},"Числове значення",[5815,13676,13677],{"align":6241},"Інтерпретація ефекту",[5826,13679,13680,13712,13761,13787],{},[5812,13681,13682,13687,13696,13709],{},[5831,13683,13684],{"align":6241},[5198,13685,13686],{},"Forward Pass",[5831,13688,13689,13690,13692,13693,13695],{"align":6241},"$z = 0.8 \\cdot 0.5 + 0.2$ ",[12093,13691],{}," $\\hat{y} = \\sigma(0.6000)$ ",[12093,13694],{}," $\\text{Loss} = -1 \\cdot \\ln(0.6457)$",[5831,13697,13698,13699,5479,13701,5479,13704,5479,13706],{"align":5817},"$0.6000$ ",[12093,13700],{},[5198,13702,13703],{},"0.6457",[12093,13705],{},[5198,13707,13708],{},"0.4378",[5831,13710,13711],{"align":6241},"Початкова помилка класифікації для $y=1$",[5812,13713,13714,13719,13734,13754],{},[5831,13715,13716],{"align":6241},[5198,13717,13718],{},"Backward Pass",[5831,13720,13721,13722,13724,13725,13727,13728,13730,13731,13733],{"align":6241},"$\\frac{\\partial L}{\\partial \\hat{y}} = -\\frac{1}{\\hat{y}}$ ",[12093,13723],{}," $\\frac{\\partial \\hat{y}}{\\partial z} = \\sigma(z)(1-\\sigma(z))$ ",[12093,13726],{}," $\\frac{\\partial L}{\\partial z} = \\hat{y} - y$ ",[12093,13729],{}," $\\frac{\\partial L}{\\partial w} = \\frac{\\partial L}{\\partial z} \\cdot x$ ",[12093,13732],{}," $\\frac{\\partial L}{\\partial b} = \\frac{\\partial L}{\\partial z} \\cdot 1$",[5831,13735,13736,13737,13739,13740,5479,13742,5479,13745,5479,13747,5479,13750,5479,13752],{"align":5817},"$-1.5486$ ",[12093,13738],{}," $0.2288$ ",[12093,13741],{},[5198,13743,13744],{},"-0.3543",[12093,13746],{},[5198,13748,13749],{},"-0.1772",[12093,13751],{},[5198,13753,13744],{},[5831,13755,13756,13757,13760],{"align":6241},"Негативний градієнт вказує на необхідність ",[5198,13758,13759],{},"збільшення"," ваги та зсуву",[5812,13762,13763,13768,13774,13784],{},[5831,13764,13765],{"align":6241},[5198,13766,13767],{},"Оновлення ($\\alpha=0.5$)",[5831,13769,13770,13771,13773],{"align":6241},"$w := 0.8 - 0.5 \\cdot (-0.1772)$ ",[12093,13772],{}," $b := 0.2 - 0.5 \\cdot (-0.3543)$",[5831,13775,13776,5479,13779,5479,13781],{"align":5817},[5198,13777,13778],{},"w = 0.8886",[12093,13780],{},[5198,13782,13783],{},"b = 0.3772",[5831,13785,13786],{"align":6241},"Вага та зміщення скориговані у бік класу 1",[5812,13788,13789,13794,13804,13814],{},[5831,13790,13791],{"align":6241},[5198,13792,13793],{},"Верифікація кроку",[5831,13795,13796,13797,13803],{"align":6241},"$\\hat{y}",[5493,13798,13799,13800,13802],{},"{\\text{new}} = \\sigma(0.8886 \\cdot 0.5 + 0.3772)$ ",[12093,13801],{}," $\\text{Loss}","{\\text{new}} = -\\ln(0.7220)$",[5831,13805,13806,5479,13809,5479,13811],{"align":5817},[5198,13807,13808],{},"0.7220",[12093,13810],{},[5198,13812,13813],{},"0.3260",[5831,13815,13816,13817,13820],{"align":6241},"✅ ",[5198,13818,13819],{},"Покращення Loss:"," $\\Delta = -0.1118$ за один крок!",[10174,13822,13823,13828,13835,13848],{},[5191,13824,13825],{},[5198,13826,13827],{},"Ключовий висновок:",[5191,13829,13830,13831,13834],{},"Після ",[5198,13832,13833],{},"одного кроку"," backpropagation:",[5249,13836,13837,13845],{},[5252,13838,13839,13840,13842,13843,6867],{},"Передбачення ",[5369,13841],{"tex":5471,":inline":5372}," покращилося: 0.6457 → 0.7220 (ближче до правильної відповіді ",[5369,13844],{"tex":12859,":inline":5372},[5252,13846,13847],{},"Втрати зменшилися: 0.4378 → 0.3260",[5191,13849,13850],{},"Якщо повторювати цей процес тисячі разів (епохи тренування), мережа поступово навчиться правильно класифікувати дані.",[5309,13852],{},[5186,13854,13856],{"id":13855},"оптимізатори-еволюція-градієнтного-спуску","Оптимізатори — еволюція градієнтного спуску",[5191,13858,13859],{},"Базовий градієнтний спуск має суттєві обмеження при навчанні нейронних мереж. Розглянемо еволюцію алгоритмів оптимізації від найпростішого до сучасних.",[5351,13861,13863],{"id":13862},"_1-vanilla-gradient-descent-batch-gd","1. Vanilla Gradient Descent (Batch GD)",[5191,13865,13866],{},[5198,13867,13868],{},"Формула оновлення:",[5369,13870],{"tex":13871},"\\theta := \\theta - \\alpha \\nabla\\_\\theta L(\\theta)",[5191,13873,13874,13877,13878,13881],{},[5198,13875,13876],{},"Принцип:"," обчислюємо градієнт по ",[5198,13879,13880],{},"всьому датасету",", потім робимо один крок.",[5191,13883,13884],{},[5198,13885,13886],{},"Проблеми:",[5241,13888,13889,13901],{},[5244,13890,13892,13893,13896,13897,13900],{"icon":4265,"title":13891},"⚠️ Повільність","Для датасету з 1 000 000 прикладів потрібно обробити ",[5198,13894,13895],{},"всі"," приклади, щоб зробити ",[5198,13898,13899],{},"один крок"," оновлення ваг. Навчання займає дні чи тижні.",[5244,13902,13905],{"icon":13903,"title":13904},"i-lucide-hard-drive","⚠️ Пам'ять","Неможливо завантажити великий датасет у пам'ять цілком (наприклад, ImageNet з мільйонами зображень).",[5309,13907],{},[5351,13909,13911],{"id":13910},"_2-stochastic-gradient-descent-sgd","2. Stochastic Gradient Descent (SGD)",[5191,13913,13914,13917,13918,13921],{},[5198,13915,13916],{},"Ідея:"," замість всього датасету використовуємо ",[5198,13919,13920],{},"один випадковий приклад"," для обчислення градієнта.",[5191,13923,13924],{},[5198,13925,8687],{},[5369,13927],{"tex":13928},"\\theta := \\theta - \\alpha \\nabla\\_\\theta L(\\theta; x^{(i)}, y^{(i)})",[5191,13930,13931],{},[5198,13932,10226],{},[5249,13934,13935,13938],{},[5252,13936,13937],{},"✅ Швидкі оновлення ваг (після кожного прикладу)",[5252,13939,13940],{},"✅ Може «вистрибнути» з локальних мінімумів завдяки шуму градієнта",[5191,13942,13943],{},[5198,13944,13886],{},[5249,13946,13947,13950],{},[5252,13948,13949],{},"⚠️ Дуже шумний градієнт — траєкторія навчання хаотична",[5252,13951,13952],{},"⚠️ Може не досягти точного мінімуму (буде коливатися навколо нього)",[5309,13954],{},[5351,13956,13958],{"id":13957},"_3-mini-batch-gradient-descent","3. Mini-Batch Gradient Descent",[5191,13960,13961,13877,13963,13966],{},[5198,13962,13916],{},[5198,13964,13965],{},"невеликій підмножині (batch)"," прикладів, зазвичай 32, 64, 128 або 256.",[5191,13968,13969],{},[5198,13970,8687],{},[5369,13972],{"tex":13973},"\\theta := \\theta - \\alpha \\frac{1}{m} \\sum*{i=1}^{m} \\nabla*\\theta L(\\theta; x^{(i)}, y^{(i)})",[5191,13975,12637,13976,13979],{},[5369,13977],{"tex":13978,":inline":5372},"m"," — розмір батча.",[5191,13981,13982],{},[5198,13983,10226],{},[5249,13985,13986,13989,13992],{},[5252,13987,13988],{},"✅ Баланс між швидкістю та стабільністю",[5252,13990,13991],{},"✅ Ефективне використання GPU (паралельна обробка батча)",[5252,13993,13994],{},"✅ Менш шумний градієнт, ніж у SGD",[7321,13996,13997],{},[5191,13998,13999,14002,14003,14006],{},[5198,14000,14001],{},"Зауваження:"," У сучасній літературі термін ",[5198,14004,14005],{},"«SGD»"," часто означає саме Mini-Batch GD, а не справжній стохастичний (по одному прикладу).",[5309,14008],{},[5351,14010,14012],{"id":14011},"_4-sgd-з-momentum","4. SGD з Momentum",[5191,14014,14015,14018],{},[5198,14016,14017],{},"Проблема vanilla SGD:"," у регіонах з різною кривизною функції втрат (наприклад, вузькі «яри») градієнт коливається між стінками, уповільнюючи рух до мінімуму.",[5191,14020,14021,14024],{},[5198,14022,14023],{},"Ідея Momentum:"," додати «інерцію» — враховувати попередній напрямок руху.",[5191,14026,14027],{},[5198,14028,14029],{},"Формули:",[5369,14031],{"tex":14032},"v*t = \\beta v*{t-1} + (1 - \\beta) \\nabla\\_\\theta L(\\theta)",[5369,14034],{"tex":14035},"\\theta := \\theta - \\alpha v_t",[5191,14037,12637,14038,14041,14042,14045],{},[5369,14039],{"tex":14040,":inline":5372},"v_t"," — швидкість (velocity), ",[5369,14043],{"tex":14044,":inline":5372},"\\beta"," — коефіцієнт momentum (зазвичай 0.9).",[5191,14047,14048],{},[5198,14049,10096],{},[7321,14051,14052],{},[5191,14053,14054,14055,14058],{},"Уявіть м'яч, що котиться вниз по схилу. Без momentum він зупиняється при кожній малій нерівності. З momentum він ",[5198,14056,14057],{},"набирає швидкість"," і пролітає крізь невеликі перешкоди, прямуючи до найнижчої точки.",[5191,14060,14061],{},[5224,14062],{"alt":14063,"className":14064,"src":14065},"Фізична аналогія методу Momentum: скочування кулі по рельєфу поверхні функції втрат та подолання ярів",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F11.png",[5329,14067,14069,14071,14073,14076,14079,14082,14085,14088],{"alt":14068},"Фізична аналогія спуску в яру: Vanilla SGD проти Momentum",[5191,14070,5334],{},[5191,14072,7374],{},[5191,14074,14075],{},"title Поведінка в ярах (Ravines) із сильною анізотропією кривизни",[5191,14077,14078],{},"state \"Точка на схилі яру\" as START #EFF6FF",[5191,14080,14081],{},"state \"Vanilla SGD (Без інерції)\" as SGD #FEF2F2 {\nstate \"Великий градієнт поперек яру\" as s_cross #FFFFFF\nstate \"Малий градієнт уздовж дна яру\" as s_along #FFFFFF\nstate \"Результат: хаотичні коливання між стінками,\\nповільне просування до мінімуму\" as s_res #FEE2E2\ns_cross -down-> s_res\ns_along -down-> s_res\n}",[5191,14083,14084],{},"state \"SGD + Momentum (З фізичною масою)\" as MOM #ECFDF5 {\nstate \"Коливання поперек компенсують одне одного (+\u002F-)\" as m_cross #FFFFFF\nstate \"Імпульс уздовж яру постійно акумулюється: v := β·v + (1-β)·∇\" as m_along #FFFFFF\nstate \"Результат: стрімке кочення вздовж яру\\nбез застрягання у дрібних ямках\" as m_res #D1FAE5\nm_cross -down-> m_res\nm_along -down-> m_res\n}",[5191,14086,14087],{},"START -down-> SGD\nSTART -down-> MOM",[5191,14089,5349],{},[5191,14091,14092],{},[5198,14093,10226],{},[5249,14095,14096,14099,14102],{},[5252,14097,14098],{},"✅ Швидша збіжність у напрямках зі слабкою кривизною",[5252,14100,14101],{},"✅ Зменшує коливання у напрямках із сильною кривизною",[5252,14103,14104],{},"✅ Може «перестрибнути» дрібні локальні мінімуми",[5309,14106],{},[5351,14108,14110],{"id":14109},"_5-adam-adaptive-moment-estimation","5. Adam (Adaptive Moment Estimation)",[5191,14112,14113,14116],{},[5198,14114,14115],{},"Adam"," — це найпопулярніший оптимізатор у сучасному глибокому навчанні. Він поєднує ідеї Momentum та адаптивного learning rate для кожного параметра окремо.",[5191,14118,14119],{},[5198,14120,13916],{},[5249,14122,14123,14130,14136],{},[5252,14124,14125,14126,14129],{},"Для кожної ваги зберігаємо ",[5198,14127,14128],{},"експоненційно згладжений градієнт"," (перший момент)",[5252,14131,14125,14132,14135],{},[5198,14133,14134],{},"експоненційно згладжений квадрат градієнта"," (другий момент)",[5252,14137,14138],{},"Автоматично адаптуємо learning rate: великий для параметрів із малими градієнтами, малий для параметрів із великими градієнтами",[5191,14140,14141],{},[5198,14142,14029],{},[5369,14144],{"tex":14145},"m*t = \\beta_1 m*{t-1} + (1 - \\beta*1) \\nabla*\\theta L(\\theta) \\quad \\text{(перший момент)}",[5369,14147],{"tex":14148},"v*t = \\beta_2 v*{t-1} + (1 - \\beta*2) (\\nabla*\\theta L(\\theta))^2 \\quad \\text{(другий момент)}",[5191,14150,14151],{},"Корекція зміщення (bias correction):",[5369,14153],{"tex":14154},"\\hat{m}\\_t = \\frac{m_t}{1 - \\beta_1^t}, \\quad \\hat{v}\\_t = \\frac{v_t}{1 - \\beta_2^t}",[5191,14156,14157],{},"Оновлення параметрів:",[5369,14159],{"tex":14160},"\\theta := \\theta - \\alpha \\frac{\\hat{m}\\_t}{\\sqrt{\\hat{v}\\_t} + \\epsilon}",[5191,14162,14163],{},[5198,14164,14165],{},"Типові гіперпараметри:",[5249,14167,14168,14174,14180,14186],{},[5252,14169,14170,14173],{},[5369,14171],{"tex":14172,":inline":5372},"\\alpha = 0.001"," (learning rate)",[5252,14175,14176,14179],{},[5369,14177],{"tex":14178,":inline":5372},"\\beta_1 = 0.9"," (експоненційне згасання для першого моменту)",[5252,14181,14182,14185],{},[5369,14183],{"tex":14184,":inline":5372},"\\beta_2 = 0.999"," (експоненційне згасання для другого моменту)",[5252,14187,14188,14191],{},[5369,14189],{"tex":14190,":inline":5372},"\\epsilon = 10^{-8}"," (для числової стабільності)",[5191,14193,14194],{},[5198,14195,10226],{},[5249,14197,14198,14204,14207,14210],{},[5252,14199,13816,14200,14203],{},[5198,14201,14202],{},"Адаптивний learning rate"," для кожного параметра",[5252,14205,14206],{},"✅ Добре працює «з коробки» без тонкого налаштування гіперпараметрів",[5252,14208,14209],{},"✅ Ефективний для розріджених градієнтів (NLP, рекомендаційні системи)",[5252,14211,14212],{},"✅ Швидка збіжність",[5191,14214,14215,5479,14217,14220],{},[5198,14216,10029],{},[5198,14218,14219],{},"за замовчуванням для більшості задач"," — якщо не маєте особливих причин, обирайте Adam.",[5309,14222],{},[5351,14224,14226],{"id":14225},"порівняльна-таблиця-оптимізаторів","Порівняльна таблиця оптимізаторів",[5806,14228,14229,14251],{},[5809,14230,14231],{},[5812,14232,14233,14236,14239,14242,14245,14248],{},[5815,14234,14235],{"align":6241},"Оптимізатор",[5815,14237,14238],{"align":6241},"Learning Rate",[5815,14240,14241],{"align":5817},"Швидкість збіжності",[5815,14243,14244],{"align":5817},"Стабільність",[5815,14246,14247],{"align":6241},"Налаштування",[5815,14249,14250],{"align":6241},"Рекомендації",[5826,14252,14253,14275,14295,14314,14334],{},[5812,14254,14255,14260,14263,14266,14269,14272],{},[5831,14256,14257],{"align":6241},[5198,14258,14259],{},"Batch GD",[5831,14261,14262],{"align":6241},"Фіксований",[5831,14264,14265],{"align":5817},"Повільна",[5831,14267,14268],{"align":5817},"Висока",[5831,14270,14271],{"align":6241},"α",[5831,14273,14274],{"align":6241},"❌ Не використовується на практиці",[5812,14276,14277,14282,14284,14287,14290,14292],{},[5831,14278,14279],{"align":6241},[5198,14280,14281],{},"SGD",[5831,14283,14262],{"align":6241},[5831,14285,14286],{"align":5817},"Середня",[5831,14288,14289],{"align":5817},"Низька",[5831,14291,14271],{"align":6241},[5831,14293,14294],{"align":6241},"Для простих задач, малих даних",[5812,14296,14297,14302,14304,14306,14308,14311],{},[5831,14298,14299],{"align":6241},[5198,14300,14301],{},"Mini-Batch SGD",[5831,14303,14262],{"align":6241},[5831,14305,14286],{"align":5817},[5831,14307,14286],{"align":5817},[5831,14309,14310],{"align":6241},"α, batch_size",[5831,14312,14313],{"align":6241},"Базовий вибір, якщо важлива передбачуваність",[5812,14315,14316,14321,14323,14326,14328,14331],{},[5831,14317,14318],{"align":6241},[5198,14319,14320],{},"SGD + Momentum",[5831,14322,14262],{"align":6241},[5831,14324,14325],{"align":5817},"Швидка",[5831,14327,14286],{"align":5817},[5831,14329,14330],{"align":6241},"α, β",[5831,14332,14333],{"align":6241},"Для глибоких мереж, комп'ютерного зору",[5812,14335,14336,14340,14343,14348,14350,14353],{},[5831,14337,14338],{"align":6241},[5198,14339,14115],{},[5831,14341,14342],{"align":6241},"Адаптивний",[5831,14344,14345],{"align":5817},[5198,14346,14347],{},"Дуже швидка",[5831,14349,14268],{"align":5817},[5831,14351,14352],{"align":6241},"α, β₁, β₂",[5831,14354,14355,14358],{"align":6241},[5198,14356,14357],{},"За замовчуванням"," для 90% задач",[5191,14360,14361],{},[5224,14362],{"alt":14363,"className":14364,"src":14365},"Порівняння траєкторій оптимізаторів (Batch GD, SGD, Momentum, Adam) на контурах функції втрат",[5208],"\u002Fimages\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp\u002F12.png",[5329,14367,14369,14371,14374,14377,14380,14387,14398],{"alt":14368},"Порівняльний аналіз алгоритмів оптимізації",[5191,14370,5334],{},[5191,14372,14373],{},"skinparam activity {\nBackgroundColor #F8FAFC\nBorderColor #94A3B8\nFontColor #0F172A\nFontSize 12\nArrowColor #64748B\nArrowFontSize 11\n}",[5191,14375,14376],{},"start\n:Поточний стан параметрів θ_t;",[5191,14378,14379],{},"partition \"Vanilla SGD\" {\n#FEF2F2:Обчислити ∇L на 1 прикладі;\n#FEE2E2:θ := θ - α * ∇L\\n(Високий шум, коливання);\n}",[5191,14381,14382,14383,14386],{},"partition \"SGD + Momentum\" {\n#EFF6FF:Обчислити ∇L на mini-batch;\n#DBEAFE:v_t = β",[5493,14384,14385],{},"v_ + (1-β)","∇L\\n(Акумуляція інерції руху);\n#BFDBFE:θ := θ - α * v_t\\n(Згладжування коливань у ярах);\n}",[5191,14388,14389,14390,14393,14394,14397],{},"partition \"Adam (State-of-the-Art)\" {\n#ECFDF5:Обчислити ∇L на mini-batch;\n#D1FAE5:m_t = β1",[5493,14391,14392],{},"m_ + (1-β1)","∇L  (1-й момент);\\nv_t = β2",[5493,14395,14396],{},"v_ + (1-β2)","(∇L)² (2-й момент);\n#A7F3D0:Корекція зсуву m̂_t, v̂_t;\n#6EE7B7:θ := θ - α * m̂_t \u002F (√v̂_t + ε)\\n(Індивідуальний адаптивний LR для кожної ваги);\n}",[5191,14399,14400],{},":Оновлений стан параметрів θ_{t+1};\nstop\n@enduml",[6339,14402,14403,14408],{},[5191,14404,14405],{},[5198,14406,14407],{},"Практичні рекомендації з вибору оптимізатора:",[7473,14409,14410,14416,14422,14425],{},[5252,14411,14412,14415],{},[5198,14413,14414],{},"Починайте з Adam"," (learning_rate = 0.001) — він працює добре для більшості задач",[5252,14417,14418,14419,14421],{},"Якщо Adam призводить до перенавчання, спробуйте ",[5198,14420,14320],{}," із меншим learning rate (0.01) та weight decay",[5252,14423,14424],{},"Для фінального тюнінгу (fine-tuning) моделі можна зменшити learning rate у 5–10 разів",[5252,14426,14427,14428,14431],{},"Використовуйте ",[5198,14429,14430],{},"learning rate scheduler"," (зменшення lr під час навчання) для покращення збіжності",[5309,14433],{},[5186,14435,14437],{"id":14436},"практичні-завдання","Практичні завдання",[14439,14440,14441,14472],"accordion",{},[14442,14443,14446,14452,14466],"accordion-item",{"icon":14444,"label":14445},"i-lucide-clipboard-list","📋 Завдання 1: Порахувати кількість параметрів MLP",[5191,14447,14448,14451],{},[5198,14449,14450],{},"Умова:"," Дано архітектуру нейронної мережі:",[5249,14453,14454,14457,14460,14463],{},[5252,14455,14456],{},"Вхід: 28×28 пікселів зображення (784 ознаки)",[5252,14458,14459],{},"Прихований шар 1: 128 нейронів, ReLU",[5252,14461,14462],{},"Прихований шар 2: 64 нейрони, ReLU",[5252,14464,14465],{},"Вихід: 10 нейронів, Softmax (класифікація 10 цифр)",[5191,14467,14468,14471],{},[5198,14469,14470],{},"Запитання:"," Скільки всього параметрів (ваг + bias) має ця мережа?",[14442,14473,14475,14480,14485,14502,14507,14522,14527,14542,14547,14550],{"icon":10129,"label":14474},"✅ Розв'язок Завдання 1",[5191,14476,14477],{},[5198,14478,14479],{},"Розрахунок:",[5191,14481,14482],{},[5198,14483,14484],{},"Шар 1 (784 → 128):",[5249,14486,14487,14493,14496],{},[5252,14488,14489,14490],{},"Ваги: ",[5369,14491],{"tex":14492,":inline":5372},"784 \\times 128 = 100\\,352",[5252,14494,14495],{},"Bias: 128",[5252,14497,14498,14501],{},[5198,14499,14500],{},"Разом:"," 100,480 параметрів",[5191,14503,14504],{},[5198,14505,14506],{},"Шар 2 (128 → 64):",[5249,14508,14509,14514,14517],{},[5252,14510,14489,14511],{},[5369,14512],{"tex":14513,":inline":5372},"128 \\times 64 = 8\\,192",[5252,14515,14516],{},"Bias: 64",[5252,14518,14519,14521],{},[5198,14520,14500],{}," 8,256 параметрів",[5191,14523,14524],{},[5198,14525,14526],{},"Вихідний шар (64 → 10):",[5249,14528,14529,14534,14537],{},[5252,14530,14489,14531],{},[5369,14532],{"tex":14533,":inline":5372},"64 \\times 10 = 640",[5252,14535,14536],{},"Bias: 10",[5252,14538,14539,14541],{},[5198,14540,14500],{}," 650 параметрів",[5191,14543,14544],{},[5198,14545,14546],{},"Загальна кількість параметрів:",[5369,14548],{"tex":14549},"100\\,480 + 8\\,256 + 650 = 109\\,386 \\text{ параметрів}",[6339,14551,14552,14557,14562],{},[5191,14553,14554],{},[5198,14555,14556],{},"Загальна формула для повнозв'язного шару (Fully Connected Layer):",[5191,14558,10905,14559,5462],{},[5369,14560],{"tex":14561,":inline":5372},"n*{\\text{in}} \\to n*{\\text{out}}",[5369,14563],{"tex":14564},"\\text{Параметри} = n*{\\text{in}} \\times n*{\\text{out}} + n\\_{\\text{out}}",[14439,14566,14567,14608,15066],{},[14442,14568,14570,14579,14596,14599],{"icon":14444,"label":14569},"📋 Завдання 2: Реалізувати прямий прохід на NumPy",[5191,14571,14572,14574,14575,14578],{},[5198,14573,14450],{}," Реалізуйте функцію ",[5530,14576,14577],{},"forward_pass",", яка приймає:",[5249,14580,14581,14590,14593],{},[5252,14582,14583,14584,14586,14587,6867],{},"Вхідний вектор ",[5369,14585],{"tex":6853,":inline":5372}," (наприклад, ",[5530,14588,14589],{},"[0.5, 0.3, 0.8]",[5252,14591,14592],{},"Список ваг та bias для кожного шару",[5252,14594,14595],{},"Список функцій активації",[5191,14597,14598],{},"Функція має повертати остаточний вихід мережі.",[5191,14600,14601,14604,14605,14607],{},[5198,14602,14603],{},"Підказка:"," використайте цикл ",[5530,14606,6086],{}," для проходження по шарах.",[14442,14609,14611],{"icon":10129,"label":14610},"✅ Розв'язок Завдання 2",[5885,14612,14614],{"kernel":5887,"title":14613},"forward_pass_solution.ipynb",[5890,14615,14616],{"execution-count":6750},[5523,14617,14619],{"className":5894,"code":14618,"language":5896,"meta":5528,"style":5528},"import numpy as np\n\ndef relu(z):\n    return np.maximum(0, z)\n\ndef sigmoid(z):\n    return 1 \u002F (1 + np.exp(-z))\n\ndef forward_pass(x, layers, activations):\n    \"\"\"\n    Прямий прохід по нейронній мережі\n\n    Parameters:\n    - x: вхідний вектор (shape: n_features)\n    - layers: список (W, b) для кожного шару\n    - activations: список функцій активації для кожного шару\n\n    Returns:\n    - Вихід мережі (shape: n_output)\n    \"\"\"\n    a = x.reshape(-1, 1)  # Перетворюємо на вектор-стовпець\n\n    for (W, b), activation in zip(layers, activations):\n        z = W @ a + b\n        a = activation(z)\n\n    return a.flatten()  # Повертаємо як 1D масив\n\n# Приклад використання\nnp.random.seed(42)\n\n# Архітектура: 3 → 4 (ReLU) → 2 (ReLU) → 1 (Sigmoid)\nlayers = [\n    (np.random.randn(4, 3) * 0.1, np.zeros((4, 1))),  # Шар 1\n    (np.random.randn(2, 4) * 0.1, np.zeros((2, 1))),  # Шар 2\n    (np.random.randn(1, 2) * 0.1, np.zeros((1, 1)))   # Вихідний шар\n]\n\nactivations = [relu, relu, sigmoid]\n\n# Вхід\nx = np.array([0.5, 0.3, 0.8])\n\n# Прямий прохід\noutput = forward_pass(x, layers, activations)\n\nprint(f\"Вхід: {x}\")\nprint(f\"Вихід мережі: {output[0]:.4f}\")\nprint(f\"Інтерпретація: ймовірність класу 1 = {output[0]:.2%}\")\n",[5530,14620,14621,14631,14635,14647,14657,14661,14673,14685,14689,14712,14717,14722,14726,14731,14736,14741,14746,14750,14755,14760,14764,14781,14785,14800,14805,14810,14814,14824,14828,14833,14841,14845,14850,14855,14884,14910,14937,14941,14945,14950,14954,14959,14976,14980,14985,14990,14994,15015,15041],{"__ignoreMap":5528},[5533,14622,14623,14625,14627,14629],{"class":5535,"line":5536},[5533,14624,5904],{"class":5903},[5533,14626,5908],{"class":5907},[5533,14628,5911],{"class":5903},[5533,14630,5914],{"class":5907},[5533,14632,14633],{"class":5535,"line":5542},[5533,14634,5563],{"emptyLinePlaceholder":5205},[5533,14636,14637,14639,14641,14643,14645],{"class":5535,"line":5548},[5533,14638,5924],{"class":5923},[5533,14640,8814],{"class":5927},[5533,14642,5931],{"class":5907},[5533,14644,5453],{"class":5934},[5533,14646,5937],{"class":5907},[5533,14648,14649,14651,14653,14655],{"class":5535,"line":5554},[5533,14650,5948],{"class":5903},[5533,14652,8827],{"class":5907},[5533,14654,5833],{"class":5951},[5533,14656,8832],{"class":5907},[5533,14658,14659],{"class":5535,"line":5560},[5533,14660,5563],{"emptyLinePlaceholder":5205},[5533,14662,14663,14665,14667,14669,14671],{"class":5535,"line":5566},[5533,14664,5924],{"class":5923},[5533,14666,7779],{"class":5927},[5533,14668,5931],{"class":5907},[5533,14670,5453],{"class":5934},[5533,14672,5937],{"class":5907},[5533,14674,14675,14677,14679,14681,14683],{"class":5535,"line":5572},[5533,14676,5948],{"class":5903},[5533,14678,5952],{"class":5951},[5533,14680,7799],{"class":5907},[5533,14682,5495],{"class":5951},[5533,14684,7804],{"class":5907},[5533,14686,14687],{"class":5535,"line":5578},[5533,14688,5563],{"emptyLinePlaceholder":5205},[5533,14690,14691,14693,14696,14698,14700,14702,14705,14707,14710],{"class":5535,"line":5584},[5533,14692,5924],{"class":5923},[5533,14694,14695],{"class":5927}," forward_pass",[5533,14697,5931],{"class":5907},[5533,14699,6853],{"class":5934},[5533,14701,5987],{"class":5907},[5533,14703,14704],{"class":5934},"layers",[5533,14706,5987],{"class":5907},[5533,14708,14709],{"class":5934},"activations",[5533,14711,5937],{"class":5907},[5533,14713,14714],{"class":5535,"line":5589},[5533,14715,14716],{"class":5942},"    \"\"\"\n",[5533,14718,14719],{"class":5535,"line":5595},[5533,14720,14721],{"class":5942},"    Прямий прохід по нейронній мережі\n",[5533,14723,14724],{"class":5535,"line":5601},[5533,14725,5563],{"emptyLinePlaceholder":5205},[5533,14727,14728],{"class":5535,"line":5607},[5533,14729,14730],{"class":5942},"    Parameters:\n",[5533,14732,14733],{"class":5535,"line":5613},[5533,14734,14735],{"class":5942},"    - x: вхідний вектор (shape: n_features)\n",[5533,14737,14738],{"class":5535,"line":5619},[5533,14739,14740],{"class":5942},"    - layers: список (W, b) для кожного шару\n",[5533,14742,14743],{"class":5535,"line":5625},[5533,14744,14745],{"class":5942},"    - activations: список функцій активації для кожного шару\n",[5533,14747,14748],{"class":5535,"line":5630},[5533,14749,5563],{"emptyLinePlaceholder":5205},[5533,14751,14752],{"class":5535,"line":5636},[5533,14753,14754],{"class":5942},"    Returns:\n",[5533,14756,14757],{"class":5535,"line":5642},[5533,14758,14759],{"class":5942},"    - Вихід мережі (shape: n_output)\n",[5533,14761,14762],{"class":5535,"line":5648},[5533,14763,14716],{"class":5942},[5533,14765,14766,14769,14771,14773,14775,14778],{"class":5535,"line":5654},[5533,14767,14768],{"class":5907},"    a = x.reshape(-",[5533,14770,5495],{"class":5951},[5533,14772,5987],{"class":5907},[5533,14774,5495],{"class":5951},[5533,14776,14777],{"class":5907},")  ",[5533,14779,14780],{"class":5975},"# Перетворюємо на вектор-стовпець\n",[5533,14782,14783],{"class":5535,"line":5659},[5533,14784,5563],{"emptyLinePlaceholder":5205},[5533,14786,14787,14790,14793,14795,14797],{"class":5535,"line":5664},[5533,14788,14789],{"class":5903},"    for",[5533,14791,14792],{"class":5907}," (W, b), activation ",[5533,14794,6092],{"class":5903},[5533,14796,10459],{"class":5927},[5533,14798,14799],{"class":5907},"(layers, activations):\n",[5533,14801,14802],{"class":5535,"line":5670},[5533,14803,14804],{"class":5907},"        z = W @ a + b\n",[5533,14806,14807],{"class":5535,"line":5676},[5533,14808,14809],{"class":5907},"        a = activation(z)\n",[5533,14811,14812],{"class":5535,"line":5681},[5533,14813,5563],{"emptyLinePlaceholder":5205},[5533,14815,14816,14818,14821],{"class":5535,"line":5686},[5533,14817,5948],{"class":5903},[5533,14819,14820],{"class":5907}," a.flatten()  ",[5533,14822,14823],{"class":5975},"# Повертаємо як 1D масив\n",[5533,14825,14826],{"class":5535,"line":5692},[5533,14827,5563],{"emptyLinePlaceholder":5205},[5533,14829,14830],{"class":5535,"line":5698},[5533,14831,14832],{"class":5975},"# Приклад використання\n",[5533,14834,14835,14837,14839],{"class":5535,"line":5704},[5533,14836,11537],{"class":5907},[5533,14838,11540],{"class":5951},[5533,14840,6060],{"class":5907},[5533,14842,14843],{"class":5535,"line":5710},[5533,14844,5563],{"emptyLinePlaceholder":5205},[5533,14846,14847],{"class":5535,"line":5715},[5533,14848,14849],{"class":5975},"# Архітектура: 3 → 4 (ReLU) → 2 (ReLU) → 1 (Sigmoid)\n",[5533,14851,14852],{"class":5535,"line":5721},[5533,14853,14854],{"class":5907},"layers = [\n",[5533,14856,14857,14860,14862,14864,14866,14868,14870,14873,14875,14877,14879,14882],{"class":5535,"line":5726},[5533,14858,14859],{"class":5907},"    (np.random.randn(",[5533,14861,8720],{"class":5951},[5533,14863,5987],{"class":5907},[5533,14865,7457],{"class":5951},[5533,14867,11565],{"class":5907},[5533,14869,10381],{"class":5951},[5533,14871,14872],{"class":5907},", np.zeros((",[5533,14874,8720],{"class":5951},[5533,14876,5987],{"class":5907},[5533,14878,5495],{"class":5951},[5533,14880,14881],{"class":5907},"))),  ",[5533,14883,11729],{"class":5975},[5533,14885,14886,14888,14890,14892,14894,14896,14898,14900,14902,14904,14906,14908],{"class":5535,"line":5732},[5533,14887,14859],{"class":5907},[5533,14889,6604],{"class":5951},[5533,14891,5987],{"class":5907},[5533,14893,8720],{"class":5951},[5533,14895,11565],{"class":5907},[5533,14897,10381],{"class":5951},[5533,14899,14872],{"class":5907},[5533,14901,6604],{"class":5951},[5533,14903,5987],{"class":5907},[5533,14905,5495],{"class":5951},[5533,14907,14881],{"class":5907},[5533,14909,11829],{"class":5975},[5533,14911,14912,14914,14916,14918,14920,14922,14924,14926,14928,14930,14932,14935],{"class":5535,"line":5738},[5533,14913,14859],{"class":5907},[5533,14915,5495],{"class":5951},[5533,14917,5987],{"class":5907},[5533,14919,6604],{"class":5951},[5533,14921,11565],{"class":5907},[5533,14923,10381],{"class":5951},[5533,14925,14872],{"class":5907},[5533,14927,5495],{"class":5951},[5533,14929,5987],{"class":5907},[5533,14931,5495],{"class":5951},[5533,14933,14934],{"class":5907},")))   ",[5533,14936,11929],{"class":5975},[5533,14938,14939],{"class":5535,"line":5744},[5533,14940,6663],{"class":5907},[5533,14942,14943],{"class":5535,"line":5750},[5533,14944,5563],{"emptyLinePlaceholder":5205},[5533,14946,14947],{"class":5535,"line":5755},[5533,14948,14949],{"class":5907},"activations = [relu, relu, sigmoid]\n",[5533,14951,14952],{"class":5535,"line":5761},[5533,14953,5563],{"emptyLinePlaceholder":5205},[5533,14955,14956],{"class":5535,"line":5767},[5533,14957,14958],{"class":5975},"# Вхід\n",[5533,14960,14961,14964,14966,14968,14970,14972,14974],{"class":5535,"line":5773},[5533,14962,14963],{"class":5907},"x = np.array([",[5533,14965,6923],{"class":5951},[5533,14967,5987],{"class":5907},[5533,14969,6997],{"class":5951},[5533,14971,5987],{"class":5907},[5533,14973,11679],{"class":5951},[5533,14975,7856],{"class":5907},[5533,14977,14978],{"class":5535,"line":5778},[5533,14979,5563],{"emptyLinePlaceholder":5205},[5533,14981,14982],{"class":5535,"line":5783},[5533,14983,14984],{"class":5975},"# Прямий прохід\n",[5533,14986,14987],{"class":5535,"line":9498},[5533,14988,14989],{"class":5907},"output = forward_pass(x, layers, activations)\n",[5533,14991,14992],{"class":5535,"line":9532},[5533,14993,5563],{"emptyLinePlaceholder":5205},[5533,14995,14996,14998,15000,15002,15005,15007,15009,15011,15013],{"class":5535,"line":9559},[5533,14997,6052],{"class":5927},[5533,14999,5931],{"class":5907},[5533,15001,6152],{"class":5923},[5533,15003,15004],{"class":5942},"\"Вхід: ",[5533,15006,6158],{"class":5923},[5533,15008,6853],{"class":5907},[5533,15010,6164],{"class":5923},[5533,15012,6155],{"class":5942},[5533,15014,6060],{"class":5907},[5533,15016,15017,15019,15021,15023,15026,15028,15031,15033,15035,15037,15039],{"class":5535,"line":9585},[5533,15018,6052],{"class":5927},[5533,15020,5931],{"class":5907},[5533,15022,6152],{"class":5923},[5533,15024,15025],{"class":5942},"\"Вихід мережі: ",[5533,15027,6158],{"class":5923},[5533,15029,15030],{"class":5907},"output[",[5533,15032,5833],{"class":5951},[5533,15034,8144],{"class":5907},[5533,15036,11997],{"class":5923},[5533,15038,6155],{"class":5942},[5533,15040,6060],{"class":5907},[5533,15042,15043,15045,15047,15049,15052,15054,15056,15058,15060,15062,15064],{"class":5535,"line":9590},[5533,15044,6052],{"class":5927},[5533,15046,5931],{"class":5907},[5533,15048,6152],{"class":5923},[5533,15050,15051],{"class":5942},"\"Інтерпретація: ймовірність класу 1 = ",[5533,15053,6158],{"class":5923},[5533,15055,15030],{"class":5907},[5533,15057,5833],{"class":5951},[5533,15059,8144],{"class":5907},[5533,15061,12055],{"class":5923},[5533,15063,6155],{"class":5942},[5533,15065,6060],{"class":5907},[6216,15067,15068,15090,15093,15095],{"v-slot:output":5528},[5241,15069,15070,15078,15082],{},[5244,15071,15074,15077],{"icon":15072,"title":15073},"i-lucide-arrow-right-circle","📥 Вхідний вектор ознак",[5530,15075,15076],{},"x = [0.5, 0.3, 0.8]"," ($3$ числові ознаки)",[5244,15079,15081],{"icon":92,"title":15080},"⚡ Вихід нейронної мережі","$\\hat{y} = \\mathbf{0.4998}$ (вихід після Sigmoid)",[5244,15083,15085,15086,15089],{"icon":10129,"title":15084},"🎯 Класифікаційне рішення","Ймовірність класу 1: ",[5198,15087,15088],{},"49.98%"," (знаходиться на межі невизначеності)",[5191,15091,15092],{},"::",[5191,15094,15092],{},[5191,15096,15097],{},":::",[14439,15099,15100,15106],{},[14442,15101,15103,15105],{"icon":14444,"label":15102},"📋 Завдання 3: Пояснити, чому XOR не лінійно роздільний",[5198,15104,14470],{}," Поясніть своїми словами (без коду), чому одношаровий персептрон не може розв'язати задачу XOR. Які класи треба розділити? Чому жодна пряма лінія не може цього зробити?",[14442,15107,15109,15113,15116,15130,15137,15152,15165],{"icon":10129,"label":15108},"✅ Розв'язок Завдання 3",[5191,15110,15111],{},[5198,15112,5876],{},[5191,15114,15115],{},"У задачі XOR потрібно розділити:",[5249,15117,15118,15124],{},[5252,15119,15120,15123],{},[5198,15121,15122],{},"Клас 0"," (червоні точки): (0, 0) та (1, 1)",[5252,15125,15126,15129],{},[5198,15127,15128],{},"Клас 1"," (сині точки): (0, 1) та (1, 0)",[5191,15131,15132,15133,15136],{},"Якщо ми намалюємо ці точки на площині, побачимо, що вони розташовані ",[5198,15134,15135],{},"по діагоналі"," — червоні точки в протилежних кутах, сині — у двох інших кутах.",[5191,15138,15139,15142,15143,15146,15147,15149,15150,5799],{},[5198,15140,15141],{},"Пряма лінія"," може розділити простір лише на ",[5198,15144,15145],{},"два півпростори",". Щоб правильно класифікувати XOR, потрібна ",[5198,15148,7149],{}," (наприклад, коло) або ",[5198,15151,7153],{},[5191,15153,15154,15155,15157,15158,15161,15162,15164],{},"Одношаровий персептрон — це ",[5198,15156,6593],{},", він може провести лише одну лінію. Тому для XOR ",[5198,15159,15160],{},"математично неможливо"," знайти такі ваги ",[5369,15163],{"tex":5870,":inline":5372},", що персептрон правильно класифікує всі 4 точки.",[5191,15166,15167,15170],{},[5198,15168,15169],{},"Рішення:"," додати приховані шари → MLP зможе створити нелінійні межі розділення.",[5309,15172],{},[5186,15174,15176],{"id":15175},"резюме-модуля","Резюме модуля",[5241,15178,15179,15186,15193,15204,15212,15220],{},[5244,15180,15182,15183,15185],{"icon":4795,"title":15181},"🧠 Персептрон","Найпростіша нейронна мережа: зважена сума входів → функція активації → вихід. Може розв'язувати ",[5198,15184,7142],{}," задачі (AND, OR, але не XOR).",[5244,15187,15189,15190,15192],{"icon":658,"title":15188},"🔗 Багатошаровий персептрон (MLP)","Додавання ",[5198,15191,10088],{}," дозволяє створювати нелінійні межі розділення. MLP може апроксимувати будь-яку неперервну функцію (теорема про універсальну апроксимацію).",[5244,15194,15196,15197,15199,15200,15203],{"icon":92,"title":15195},"⚡ Функції активації","Без нелінійних активацій мережа редукується до лінійної моделі. ",[5198,15198,10785],{}," — стандартний вибір для прихованих шарів. ",[5198,15201,15202],{},"Sigmoid\u002FSoftmax"," — для виходу.",[5244,15205,15208,15209,5799],{"icon":15206,"title":15207},"i-lucide-arrow-right","➡️ Forward Propagation","Послідовне обчислення виходів кожного шару від входу до виходу. Формула шару: ",[5369,15210],{"tex":15211,":inline":5372},"a^{[l]} = \\sigma(W^{[l]} a^{[l-1]} + b^{[l]})",[5244,15213,15216,15217,15219],{"icon":15214,"title":15215},"i-lucide-arrow-left","⬅️ Backpropagation","Алгоритм обчислення градієнтів функції втрат по всіх параметрах. Використовує ",[5198,15218,12353],{}," диференціювання. Помилка поширюється від виходу до входу.",[5244,15221,15223,15225,15226,15229,15230,15232,15233,5799],{"icon":5246,"title":15222},"🎯 Оптимізатори",[5198,15224,14281],{}," — базовий, ",[5198,15227,15228],{},"Momentum"," — з інерцією, ",[5198,15231,14115],{}," — адаптивний learning rate (найпопулярніший). За замовчуванням обирайте ",[5198,15234,14115],{},[5309,15236],{},[5186,15238,15240],{"id":15239},"ключові-терміни-та-визначення","Ключові терміни та визначення",[5806,15242,15243,15253],{},[5809,15244,15245],{},[5812,15246,15247,15250],{},[5815,15248,15249],{"align":6241},"Термін",[5815,15251,15252],{"align":6241},"Визначення",[5826,15254,15255,15265,15275,15285,15295,15306,15318,15327,15336,15346,15356,15366,15376,15386],{},[5812,15256,15257,15262],{},[5831,15258,15259],{"align":6241},[5198,15260,15261],{},"Персептрон (Perceptron)",[5831,15263,15264],{"align":6241},"Одношарова нейронна мережа, що обчислює зважену суму входів та застосовує функцію активації",[5812,15266,15267,15272],{},[5831,15268,15269],{"align":6241},[5198,15270,15271],{},"MLP (Multi-Layer Perceptron)",[5831,15273,15274],{"align":6241},"Багатошарова нейронна мережа з прихованими шарами",[5812,15276,15277,15282],{},[5831,15278,15279],{"align":6241},[5198,15280,15281],{},"Лінійна роздільність",[5831,15283,15284],{"align":6241},"Властивість датасету, коли класи можна розділити гіперплощиною (лінією, площиною)",[5812,15286,15287,15292],{},[5831,15288,15289],{"align":6241},[5198,15290,15291],{},"Функція активації",[5831,15293,15294],{"align":6241},"Нелінійна функція, що перетворює зважену суму нейрона",[5812,15296,15297,15301],{},[5831,15298,15299],{"align":6241},[5198,15300,10785],{},[5831,15302,15303,15305],{"align":6241},[5369,15304],{"tex":10790,":inline":5372}," — найпопулярніша функція активації для прихованих шарів",[5812,15307,15308,15312],{},[5831,15309,15310],{"align":6241},[5198,15311,10735],{},[5831,15313,15314,15317],{"align":6241},[5369,15315],{"tex":15316,":inline":5372},"1\u002F(1+e^{-z})"," — для бінарної класифікації на виході",[5812,15319,15320,15324],{},[5831,15321,15322],{"align":6241},[5198,15323,10835],{},[5831,15325,15326],{"align":6241},"Перетворює вектор у розподіл ймовірностей — для багатокласової класифікації",[5812,15328,15329,15333],{},[5831,15330,15331],{"align":6241},[5198,15332,10897],{},[5831,15334,15335],{"align":6241},"Обчислення виходу мережі шляхом послідовного проходження даних через шари",[5812,15337,15338,15343],{},[5831,15339,15340],{"align":6241},[5198,15341,15342],{},"Backpropagation",[5831,15344,15345],{"align":6241},"Алгоритм обчислення градієнтів за допомогою ланцюгового правила",[5812,15347,15348,15353],{},[5831,15349,15350],{"align":6241},[5198,15351,15352],{},"Градієнт (Gradient)",[5831,15354,15355],{"align":6241},"Вектор часткових похідних функції втрат по всіх параметрах",[5812,15357,15358,15363],{},[5831,15359,15360],{"align":6241},[5198,15361,15362],{},"Learning Rate (α)",[5831,15364,15365],{"align":6241},"Розмір кроку при оновленні ваг",[5812,15367,15368,15373],{},[5831,15369,15370],{"align":6241},[5198,15371,15372],{},"Оптимізатор (Optimizer)",[5831,15374,15375],{"align":6241},"Алгоритм оновлення параметрів (SGD, Momentum, Adam)",[5812,15377,15378,15383],{},[5831,15379,15380],{"align":6241},[5198,15381,15382],{},"Epoch (Епоха)",[5831,15384,15385],{"align":6241},"Один повний прохід по всьому тренувальному датасету",[5812,15387,15388,15393],{},[5831,15389,15390],{"align":6241},[5198,15391,15392],{},"Batch (Батч)",[5831,15394,15395],{"align":6241},"Підмножина прикладів для одного кроку оновлення ваг",[5309,15397],{},[5186,15399,15401],{"id":15400},"що-далі","Що далі?",[5191,15403,15404,15405,15408],{},"У наступній статті ми познайомимося з ",[5198,15406,15407],{},"бібліотекою PyTorch"," — найпопулярнішим фреймворком для побудови нейронних мереж. Ви навчитеся:",[5249,15410,15411,15414,15420,15423],{},[5252,15412,15413],{},"Працювати з тензорами та графами обчислень",[5252,15415,15416,15417],{},"Визначати моделі за допомогою ",[5530,15418,15419],{},"nn.Module",[5252,15421,15422],{},"Використовувати вбудовані оптимізатори та функції втрат",[5252,15424,15425],{},"Навчати свою першу нейронну мережу на реальному датасеті",[6339,15427,15428,15433],{},[5191,15429,15430],{},[5198,15431,15432],{},"Для закріплення матеріалу:",[7473,15434,15435,15446,15449],{},[5252,15436,15437,15438,15445],{},"Перегляньте відео ",[15439,15440,15444],"a",{"href":15441,"rel":15442},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=aircAruvnKk",[15443],"nofollow","«But what is a neural network?»"," від 3Blue1Brown (візуалізація backpropagation)",[5252,15447,15448],{},"Прочитайте оригінальну статтю «Learning representations by back-propagating errors» (Rumelhart et al., 1986)",[5252,15450,15451],{},"Реалізуйте MLP на чистому NumPy для датасету Iris (без використання бібліотек ML)",[15453,15454,15455],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: 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Функції активації, прямий та зворотний прохід, оптимізатори.","md",null,{},{"title":3892,"description":15511},"B4ztdeeyjyOWBcE2lep_154NC7vA3n26kfd0GgckZHE",[15518,15520],{"title":3883,"path":3884,"stem":3885,"description":15519,"children":-1},"Confusion Matrix, Accuracy, Precision, Recall, F1-Score, ROC-AUC — як правильно оцінювати моделі класифікації та уникати типових помилок",{"title":3901,"path":3902,"stem":3903,"description":15521,"children":-1},"Основи роботи з тензорами, операції, broadcasting, граф обчислень та механізм autograd для автоматичного обчислення градієнтів.",1791987124655]