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DAPO: RL-алгоритм от ByteDance

📌 Переходите по ссылке: GitHub Pages, что бы получить доступ к более подробному обзору.

Аннотация

В данной работе представлена система DAPO (Decoupled Clip and Dynamic sAmpling Policy Optimization), представляющая собой открытую платформу для обучения больших языковых моделей (LLM) с использованием методов обучения с подкреплением (Reinforcement Learning, RL). Несмотря на значительные успехи современных LLM, таких как OpenAI o1 и DeepSeek R1, ключевые технические детали их RL-обучения остаются недоступными для научного сообщества, что существенно затрудняет воспроизводимость результатов и дальнейшие исследования. В ответ на эту проблему авторы предлагают инновационный алгоритм DAPO, который не только демонстрирует высокую эффективность, но и предоставляет полную открытость кода, данных и методологии.

Система DAPO достигла рекордного результата в 50 баллов на математическом конкурсе AIME 2024, превзойдя предыдущий рекорд модели DeepSeek-R1 (47 баллов). При этом DAPO добилась такого результата, сократив количество шагов обучения вдвое. В основе алгоритма лежат четыре ключевые технологии: стратегия Clip-Higher, динамическая выборка, оптимизация градиента на уровне токенов и интеллектуальный штраф длины. Эти методы направлены на решение основных проблем RL-обучения, таких как коллапс энтропии, шум вознаграждения и неэффективность обучения на длинных текстах.

Авторы подчеркивают, что масштабное обучение с подкреплением является критически важным для развития способности LLM к сложным рассуждениям. Однако, в отличие от предыдущих работ, где детали RL-обучения оставались скрытыми (например, в блогах OpenAI и технических отчетах DeepSeek R1), DAPO предоставляет полную прозрачность. В открытый доступ выложены не только исходные коды обучения, разработанные на базе фреймворка verl, но и тщательно подготовленные датасеты. Это способствует повышению воспроизводимости результатов и открывает новые возможности для исследований в области крупномасштабного RL-обучения LLM.

Таким образом, работа представляет собой значительный вклад в развитие открытых и воспроизводимых методов обучения больших языковых моделей, предлагая как теоретические инновации, так и практические инструменты для научного сообщества.

1. Введение

Появление моделей с расширенным временем тестирования и рассуждения (Test-time Compute), таких как O1 от OpenAI и R1 от DeepSeek, а так же совсем недавно Claude от Antropic, ознаменовало фундаментальный сдвиг парадигмы в области больших языковых моделей (LLM) на основе обучения с подкреплением (Reinforcement Learning, RL). Эти модели продемонстрировали беспрецедентные способности к комплексным рассуждениям, позволяющие им успешно решать сложные математические и программистские задачи уровня соревнований AIME и Codeforces.

Центральной технологией, обеспечивающей этот прорыв, выступает масштабное обучение с подкреплением (Reinforcement Learning, RL), которое стимулирует развитие сложных форм рассуждения, включая самопроверку, итеративное уточнение и рефлексию. Несмотря на впечатляющие результаты, конкретные алгоритмы и методологические подходы к масштабируемому RL-обучению остаются в значительной степени скрытыми в технических отчетах существующих моделей. Как отмечают авторы, "ключевые технические детали современных рассуждающих LLM скрыты (например, в блоге OpenAI о модели o1 и техническом отчете DeepSeek R1)", из-за чего исследовательское сообщество испытывает трудности с воспроизведением их результатов.

В ходе экспериментов авторы использовали Qwen2.5-32B в качестве предварительно обученной модели для применения обучения с подкреплением на основе обратной связи. При первоначальных запусках с использованием базового алгоритма GRPO (Generalized Reward-weighted Policy Optimization) модель достигла лишь 30 баллов на тесте AIME, что значительно уступает 47 баллам модели DeepSeek-RL. Углубленный анализ выявил, что наивная имплементация GRPO сталкивается с рядом критических проблем, среди которых:

Коллапс энтропии — тенденция модели к сужению разнообразия генерируемых ответов;
Шум вознаграждения — некорректное присвоение наград за частично правильные или слишком длинные ответы;
Нестабильность обучения — трудности при масштабировании процесса обучения на длинных цепочках рассуждений.

Аналогичные проблемы отмечались в более широком сообществе при попытках воспроизвести результаты DeepSeek, что указывает на возможное отсутствие ключевых деталей обучения в опубликованной статье о R1 — деталей, критически важных для разработки масштабируемых и воспроизводимых систем RL-обучения промышленного уровня.

Для преодоления этого разрыва авторы предоставляют современную систему масштабного RL-обучения LLM с открытым исходным кодом, которая достигает 50 баллов на AIME 2024 на базе модели Qwen2.5-32B. Данный результат превосходит предыдущий рекорд DeepSeek-RL-Zero-Qwen-32B (47 баллов), при этом требуя лишь 50% объема тренировочных шагов (см. рисунок 1). В основе системы лежит предложенный авторами алгоритм Decoupled Clip and Dynamic sAmpling Policy Optimization (DAPO), включающий четыре ключевые инновации, которые принципиально улучшают эффективность RL-обучения в сценариях длинных цепочек рассуждений:

Рисунок 1. Результаты AIME 2024 модели DAPO на основе модели Qwen2.5-32B, превосходящие предыдущие результаты (SoTA) DeepSeek-R1-Zero-Qwen-32B, используя на 50% меньше шагов обучения.

Clip-Higher — стратегия, способствующая разнообразию генерации и позволяющая проводить адаптивную выборку, разделяя нижние и верхние границы клиппирования (ε-low и ε-high);
Dynamic Sampling — метод динамической выборки, повышающий эффективность и стабильность обучения путем исключения примеров с нулевым градиентом;
Token-Level Policy Gradient Loss — расчет градиента политики на уровне отдельных токенов, что критически важно для эффективного обучения на длинных последовательностях;
Overlong Reward Shaping — интеллектуальная система штрафов за превышение длины, снижающая шум вознаграждения и стабилизирующая процесс обучения.

Особую ценность работы составляет полная открытость всех аспектов системы: весь код реализации, построенный на фреймворке verl, вместе с тщательно подготовленным датасетом DAPO-Math-17K, доступны в открытом репозитории. Эта открытость контрастирует с предыдущими работами, которые, несмотря на впечатляющие результаты, не раскрывали критически важных деталей обучения.

В ходе экспериментов авторы также наблюдали интересное явление: модель не только усиливает существующие шаблоны рассуждения, но и постепенно развивает принципиально новые способности, в частности, поведение, связанное с самопроверкой и переосмыслением предыдущих шагов. Это открывает новые перспективы для понимания фундаментальных механизмов обучения LLM сложным формам рассуждения.

Далее мы шаг за шагом рассмотрим переход от PPO к GRPO, а затем к DAPO, чтобы увидеть, как был разработан этот новый алгоритм обучения с подкреплением.

2. Предпосылк

2.1 Проксимальная оптимизация политики (PPO)

Основная концепция

Проксимальная оптимизация политики (PPO) — это один из наиболее популярных и эффективных алгоритмов обучения с подкреплением, разработанный исследователями из OpenAI в 2017 году. PPO представляет собой усовершенствование предыдущих методов оптимизации политики, таких как TRPO (Trust Region Policy Optimization), но с более простой реализацией и сравнимой или лучшей производительностью.

Ключевые особенности PPO

Стабильность обучения: основная идея PPO заключается в ограничении изменений политики между итерациями, что предотвращает слишком резкие обновления, которые могут дестабилизировать процесс обучения;
Механизм отсечения: PPO использует функцию отсечения для ограничения коэффициента важности выборки, что гарантирует, что новая политика не будет сильно отклоняться от старой;
Эффективность выборки: по сравнению с другими алгоритмами, PPO более эффективно использует собранные данные, что позволяет достигать лучших результатов при меньшем количестве взаимодействий со средой.

Математическая формализация

Целевая функция PPO определяется следующим образом:

Proximal Policy Optimization

Advantage функция

Обобщим, что "под капотом" без математических деталей:

Политика (Policy): это как "инструкция" для программы, говорящая, какое действие нужно выбрать в каждой ситуации. В PPO политика представлена нейронной сетью.
Функция ценности (Value Function): это оценка того, насколько "хорошо" находиться в определенной ситуации. Она помогает программе понимать, к каким ситуациям стоит стремиться. Тоже обычно нейронная сеть.
Преимущество (Advantage): это разница между тем, насколько хорошо действие, которое программа выбрала, и насколько "в среднем" хорошо действовать в этой ситуации. Помогает понять, какие действия были действительно удачными.
Целевая функция PPO (формула (1)): это главная "цель" обучения. Программа пытается ее максимизировать, чтобы стать лучше. Самое важное в ней - это механизм "отсечения" (clip), который ограничивает изменения политики.
Оценка преимущества GAE (формула (2)): способ посчитать, насколько хороши были действия программы, учитывая не только немедленный результат, но и будущие последствия.
Временная разница (формула (3)): помогает функции ценности учиться, сравнивая предсказанную ценность ситуации с тем, что реально произошло.

Процесс работы PPO

Сбор опыта: агенты взаимодействуют со средой, следуя текущей политике π_old, и собирает траектории (последовательности состояний, действий, вознаграждений).
Оценка преимущества: для каждого временного шага в собранных траекториях рассчитывается оценка преимущества A_t (Advantage функция) с использованием формул (2) и (3).
Оптимизация политики: параметры политики θ обновляются путем оптимизации целевой функции (1) с использованием стохастического градиентного восхождения в течение нескольких эпох.
Обновление функции ценности: параметры функции ценности обновляются путем минимизации среднеквадратичной ошибки между предсказанными и фактическими ценностями состояний.
Итерация: шаги 1-4 повторяются до достижения желаемой производительности или заданного числа итераций.

Преимущества PPO

Простота реализации: PPO проще в реализации, чем TRPO и другие сложные алгоритмы обучения с подкреплением;
Высокая производительность: PPO показывает отличные результаты во многих задачах, от игр Atari до сложных задач робототехники;
Совместимость с нейронными сетями: PPO прекрасно работает с глубокими нейронными сетями и может использоваться для обучения сложных политик;
Хорошая масштабируемость: PPO можно эффективно распараллеливать для ускорения обучения.

Применение PPO

PPO широко используется в различных областях:

Игры: от простых игр до сложных стратегий и симуляторов;
Робототехника: обучение управлению роботами для выполнения сложных физических задач;
Системы рекомендаций: оптимизация стратегий рекомендаций в интерактивных системах;
Большие языковые модели: в последние годы PPO активно применяется для настройки языковых моделей через обучение с подкреплением на основе обратной связи от человека (RLHF).

Заключение

Проксимальная оптимизация политики (PPO) представляет собой мощный и гибкий алгоритм обучения с подкреплением, который благодаря своей простоте и эффективности стал стандартом де-факто в области глубокого обучения с подкреплением. Его применение простирается от игр и робототехники до обучения современных языковых моделей, демонстрируя универсальность и мощь данного подхода.

2.2 Оптимизация групповой относительной политики (GRPO)

Group Relative Policy Optimization (GRPO) — это алгоритм обучения с подкреплением, предназначенный для оптимизации LLM в задачах, требующих структурированного рассуждения, таких как математика и логика. Он был представлен в работах DeepSeekMath и DeepSeek-R1 как ответ на вызовы обучения моделей с миллиардами параметров. GRPO предлагает более эффективный подход по сравнению с традиционными методами, такими как Proximal Policy Optimization (PPO), за счет устранения ключевых узких мест, связанных с вычислением advantage-функций.

Новаторский подход GRPO к Advantage-функциям

Рисунок 4 | Сравнение PPO и GRPO.
GRPO отказывается от модели оценки (value model), вместо этого вычисляя базовый уровень (baseline) на основе групповых оценок, что значительно сокращает вычислительные ресурсы при обучении.

GRPO полностью устраняет необходимость в value-сети, используя групповую относительную нормализацию: для каждого промпта P генерируется группа из N ответов G={O1,O2,...,ON} с использованием политики π. Каждому ответу O_i присваивается награда Ri=R(Oi), отражающая его качество. Advantage-функция для i-го ответа O_i относительно группы G вычисляется по формуле:

Advantage функция

По сути, Advantage-функция в GRPO для каждого конкретного ответа рассчитывается как награда конкретного ответа минус среднее арифметическое наград всех ответов в группе.

Математическая формализация

Функция целевой оптимизации в GRPO:

Group Relative Policy Optimization

Обобщение: что "под капотом" GRPO без математических деталей:

Политика (Policy): как и в PPO, это нейронная сеть, которая определяет, какие действия (или какие токены для LLM) следует выбирать в каждом состоянии.
Групповая генерация ответов: в отличие от PPO, GRPO генерирует не один ответ на запрос, а сразу группу различных ответов (обычно 4-8) на один и тот же промпт.
Относительная нормализация вместо функции ценности: GRPO не использует отдельную функцию ценности (Value Function). Вместо этого качество каждого ответа оценивается относительно других ответов в группе – это ключевое отличие.
Преимущество (Advantage): рассчитывается как разница между наградой конкретного ответа и средней наградой всех ответов в группе. Это позволяет понять, какие ответы лучше среднего.
KL-дивергенция: жёстко интегрирована в функцию потерь, чтобы ограничить отклонение обновленной политики от исходной, обеспечивая стабильность обучения.
Экономия ресурсов: устранение value-сети снижает использование памяти на 40-60% и ускоряет обучение на ~35%.

Процесс работы GRPO

Генерация группы ответов: для каждого запроса модель генерирует группу из N различных ответов, используя текущую политику.
Оценка наград: каждый ответ получает награду от внешней функции награды (например, от модели-критика или по заданным правилам).
Расчет относительного преимущества: для каждого ответа вычисляется преимущество как разница между его наградой и средней наградой по группе: A_i=R_i−(R1+R2+...+R_N)/N
Оптимизация политики: Параметры модели обновляются так, чтобы увеличить вероятность генерации ответов с положительным преимуществом (лучше среднего) и уменьшить вероятность ответов с отрицательным преимуществом (хуже среднего).
Регуляризация с KL-дивергенцией: Обновление ограничивается, чтобы новая политика не слишком отличалась от предыдущей версии или от референсной модели.
Итерация: Шаги 1-5 повторяются до достижения желаемой производительности.

Ключевые особенности GRPO подхода:

Групповая относительная нормализация: advantage-функция вычисляется относительно группы ответов, сгенерированных для одного и того же промпта, что обеспечивает относительную оценку качества;
Устранение value-сети: средняя награда по группе служит в качестве baseline, заменяя необходимость в отдельной value-сети для оценки ценности состояний или действий;
Обучение на основе сравнения: GRPO фокусируется на обучении политики, которая генерирует ответы, превосходящие в среднем другие ответы в группе, что делает его эффективным в задачах, где важна относительная оценка качества;
KL-дивергенция - жесткая интеграция в loss-функцию через относительные веса: KL-дивергенция вводится в функцию потерь для регуляризации, ограничивая величину изменения политики на каждом шаге обучения и предотвращая её резкие колебания, что способствует стабильности обучения.

Ограничения и замечания:

Эффективность GRPO подхода зависит от качества функции награды R(O). Необходимо корректно определить функцию награды, чтобы она адекватно отражала желаемые свойства ответов;
Размер группы N является гиперпараметром, который может влиять на стабильность и эффективность обучения. Выбор оптимального значения N может потребовать экспериментальной настройки;
GRPO, как и другие методы обучения с подкреплением, может быть чувствителен к выбору гиперпараметров оптимизации и архитектуры модели.

Практическая интерпретация для LLM

В GRPO advantage-функция становится инструментом ранжирования вариантов ответа:

Модель учится генерировать ответы, которые не просто "хороши", но значительно лучше среднего в своей группе.

Это стимулирует:

Поиск неочевидных, но эффективных цепочек рассуждений;
Избегание шаблонных ошибок, типичных для группы.

Эффект: модель фокусируется на качественных различиях между ответами, а не на абсолютных значениях наград, что критично для сложных задач с неоднозначными критериями успеха.

2.3 Устранение расхождения KL

Устранение расхождения KL в алгоритме DAPO для обучения моделей с длинными цепочками рассуждений.

В сценарии RLHF (обучение с подкреплением и обратной связью с человеком) штрафной член, основанный на расхождении Кульбака-Лейблера (KL), традиционно используется для регулирования отклонений между обновляемой онлайн-политикой и замороженной эталонной политикой. Его основная цель — обеспечить, чтобы в процессе обучения модель корректировала свое поведение, не отдаляясь слишком сильно от исходного распределения данных, что особенно важно для сохранения предсказуемости и стабильности.

Однако при обучении моделей, генерирующих длинные цепочки рассуждений (Chain-of-Thought, CoT), это ограничение теряет свою актуальность. В таких задачах распределение модели в процессе обучения может закономерно и значительно отклоняться от исходного из-за сложности и многошаговости выводов. Жесткое регулирование через KL-дивергенцию в данном случае становится избыточным, так как искусственно ограничивает способность модели к исследованию альтернативных стратегий генерации, необходимых для эффективного решения многоэтапных задач.

Алгоритм DAPO (Decoupled Adaptive Policy Optimization) предлагает устранить KL-штраф, чтобы смягчить это ограничение. Отказ от термина расхождения KL позволяет модели свободно адаптироваться в процессе обучения, не будучи привязанной к изначальному распределению эталонной политики. Это особенно важно для сценариев, где успешное выполнение задачи требует выхода за рамки шаблонных решений, например, при генерации сложных логических заключений или творческих текстов. Таким образом, DAPO фокусируется на балансе между исследованием новых стратегий и эффективной оптимизацией политики, что повышает гибкость модели в контексте длинных выводов без ущерба для качества генерации.

Данный подход подчеркивает, что в определенных сценариях RLHF строго контроля за отклонением от исходной политики можно избежать, чтобы раскрыть полный потенциал адаптивности модели в условиях сложных и неоднозначных задач.

First Checkpoint: DAPO устраняет штрафы за расхождение KL в RLHF для задач в стиле long-CoT, что позволяет повысить гибкость политики и улучшить возможности рассуждений.

2.4 Моделирование вознаграждения на основе правил

Традиционные модели вознаграждения часто сталкиваются с проблемой взлома вознаграждения (reward hacking), когда модель манипулирует сигналом вознаграждения для получения высоких оценок вместо того, чтобы действительно улучшить способности к рассуждению. DAPO напрямую использует в качестве вознаграждения окончательную точность проверяемой задачи, избегая при этом сложности модели вознаграждения. В частности, функция вознаграждения выглядит следующим образом:

Функция вознаграждения

Этот подход доказал свою эффективность в различных областях, включая автоматическое доказательство теорем, компьютерное программирование и математические соревнования.

ИМХО: в данном случае моделирование вознаграждения работает только для детерминированных задач, где ответ однозначен. Для задач с неопределенными ответами (например, ответ LLM на вопрос, где в качестве ответа используется эвристика, а не строгое доказательство) это не сработает.

Second Checkpoint: DAPO заменяет сложные модели вознаграждения на прямое использование итоговой точности задачи, что устраняет проблему взлома вознаграждения (reward hacking) и упрощает обучение.

3. Алгоритм DAPO

Исследователи предложили алгоритмы Decouple Clip и Dynamic Sampling Strategy Optimization (DAPO). DAPO делает выборку группы выходных данных для каждого вопроса q, связанного с ответом a, и оптимизирует политику через следующую целевую функцию:

Dynamic Sampling Strategy Optimization

Ниже попробуем разобрать ключевые технологии, связанные с DAPO.

📌 3.1 Clip-Higher: повышение лимита

В алгоритмах обучения с подкреплением (RL), таких как Proximal Policy Optimization (PPO) и Generalized Proximal Policy Optimization (GRPO), часто наблюдается явление коллапса энтропии, когда энтропия политики быстро уменьшается по мере обучения. Это приводит к тому, что генерируемые ответы становятся практически идентичными, что свидетельствует об ограниченном исследовании пространства возможных действий и преждевременной детерминированности стратегии. В данной работе предлагается стратегия Clip-Higher — модификация стандартного механизма отсечения в PPO, направленная на решение этой проблемы путем улучшения возможностей исследования для токенов с низкой вероятностью.

Проблема коллапса энтропии

В ходе первоначальных экспериментов с использованием стандартных реализаций PPO и GRPO было обнаружено, что энтропия политики быстро снижается по мере обучения, что можно наблюдать на рисунке 2b. Выборочные ответы для некоторых групп часто оказываются практически идентичными, что указывает на ограниченное исследование пространства возможных действий и раннюю детерминированность стратегии, потенциально препятствующую процессу расширения.

В основе этой проблемы лежит механизм отсечения коэффициента важности выборки, введенный в алгоритме PPO-Clip для ограничения области доверия и повышения стабильности обучения с подкреплением. Хотя этот механизм обеспечивает стабильность обучения, он также может ограничивать исследование пространства политики, особенно для токенов с низкой вероятностью.

Рисунок 2: Точность на тестовом наборе AIME и энтропия вероятностей, сгенерированных акторной моделью в процессе обучения с подкреплением (RL), до и после применения стратегии Clip-Higher.

Асимметрия ограничения коэффициента важности

Стандартный механизм отсечения в PPO использует единый параметр ε (обычно установленный на 0.2) для ограничения изменения вероятностей как в большую, так и в меньшую сторону. Однако это создает асимметрию в возможностях изменения вероятностей для различных токенов.

Рассмотрим пример с двумя действиями, имеющими вероятности π_data(o_i∣q)=0,01 и 0,9 соответственно в исходном распределении. При стандартном ограничении коэффициента важности с ε = 0.2, максимально возможные обновленные вероятности составят π(o_i∣q)=0,012 и 1,08 соответственно. Это означает, что для токенов с высокой исходной вероятностью (например, 0.9) существует меньше ограничений на рост их вероятности, тогда как для токенов с низкой исходной вероятностью (например, 0.01) возможности значительного увеличения вероятности сильно ограничены.

Эмпирические наблюдения также подтверждают, что максимальная вероятность обрезки токена обычно составляет π(o_i∣q)<0,2, как показано на рисунке 3а. Это подтверждает теоретический анализ, согласно которому верхний порог отсечения ограничивает рост вероятности токенов с низкой исходной вероятностью, тем самым потенциально ограничивая разнообразие системы.

Рисунок 3: Энтропия распределения вероятностей акторной модели и динамика изменения длины ответов.

Cтратегия Clip-Higher

Для решения вышеописанной проблемы предлагается стратегия Clip-Higher, основанная на разделении нижнего и верхнего диапазонов отсечения на ε_low и ε_high соответственно. Математически это выражается следующей формулой:

Clip-Higher

В отличие от стандартного подхода PPO, где ε_low = ε_high = 0.2, стратегия Clip-Higher использует различные значения для этих параметров: ε_low остается равным 0.2, а ε_high увеличивается до 0.28. Это увеличение верхнего порога отсечения оставляет больше пространства для роста вероятности токенов с низкой исходной вероятностью, тем самым стимулируя исследование "токенов с длинным хвостом".

Экспериментальные результаты

Как показано на графиках выше, предложенная корректировка механизма отсечения эффективно улучшает энтропию стратегии и способствует созданию более разнообразных выборок. Исследователи сознательно решили сохранить ε_low относительно небольшим (0.2), поскольку увеличение этого параметра может привести к чрезмерному снижению вероятности некоторых токенов, что в конечном итоге может вызвать коллапс пространства выборки.

Third Checkpoint: Стратегия Clip-Higher борется с коллапсом энтропии в PPO/GRPO, вводя асимметричные пороги отсечения (ε_low < ε_high). Увеличение верхнего порога (ε_high) стимулирует исследование токенов с низкой вероятностью, повышая разнообразие генерируемых ответов.

📌 3.2 Dynamic Sampling: повышение эффективности градиентного обучения

Проблема снижения градиента

Существующие алгоритмы обучения с подкреплением (RL) часто страдают от проблемы снижения градиента, которая возникает, когда точность некоторых подсказок достигает значения 1. Например, в алгоритме GRPO, если все выходные данные для конкретной подсказки верны и получают одинаковое вознаграждение 1, результирующее преимущество группы становится равным нулю. Это ведет к обновлению политики без градиентов, что существенно снижает эффективность выборки.

Эмпирические наблюдения показывают (Figure3.b - график чуть выще был), что количество образцов с точностью, равной 1, продолжает увеличиваться в процессе обучения. В результате количество действительных сигналов в каждой партии уменьшается, что приводит к:

Увеличению дисперсии градиента;
Ослаблению градиентного сигнала для обучения модели.

Решение: метод динамической выборки

Для решения этой проблемы предлагается метод динамической выборки. Основная идея заключается в следующем:

Выполнение избыточной выборки подсказок;
Фильтрация подсказок с точностью, равной 1 или 0;
Сохранение только подсказок с допустимыми градиентами в пакете;
Поддержание постоянного количества подсказок в обучающем пакете.

Процесс выборки продолжается до тех пор, пока пакет не будет полностью заполнен примерами, точность которых строго находится в диапазоне (0,1).

Математическая формализация

Опять же, наша целевая функция DAPO, тут нас интересует ограничение, выделенное красным:

Dynamic Sampling

Это ограничение гарантирует, что в пакете содержатся только подсказки с точностью в диапазоне между 0 и 1. В случае динамической выборки эксперимент может достичь той же производительности быстрее. Наблюдение показано на рисунке 6.

Рисунок 6: Ход обучения до и после применения динамического сэмплирования в базовой конфигурации.

Метод динамической выборки представляет собой эффективное решение проблемы снижения градиента в алгоритмах обучения с подкреплением. Путем целенаправленной фильтрации подсказок с крайними значениями точности (0 или 1) и сосредоточения вычислительных ресурсов на подсказках с промежуточной точностью, данный метод позволяет существенно повысить эффективность обучения и ускорить достижение конвергенции модели.

Fourth Checkpoint: Dynamic Sampling. Метод динамической выборки решает проблему снижения градиента в RL-алгоритмах, исключая подсказки с точностью 0 или 1. Фильтрация примеров с промежуточной точностью (0 < acc < 1) позволяет сохранять значимые градиенты в пакете, уменьшает их дисперсию и усиливает сигнал для обучения. Поддержание постоянного размера пакета с «полезными» примерами ускоряет конвергенцию модели.

📌 3.3 Token-Level Policy Gradient Loss: действие по перебалансировке

Исходный алгоритм GRPO использует расчет потерь на уровне выборки, который включает в себя сначала усреднение потерь по токенам в каждой выборке, а затем агрегирование потерь по всем выборкам. При таком подходе каждому образцу присваивается одинаковый вес при окончательном расчете потерь. Однако авторы обнаружили, что этот подход к сокращению потерь создает ряд проблем в сценариях RL с длинной цепочкой мысли.

Поскольку при расчете потерь всем образцам присваивается одинаковый вес, токены в более длинных ответах (содержащих больше токенов) могут вносить непропорционально меньший вклад в общие потери, что может привести к двум нежелательным эффектам. Во-первых, для высококачественных длинных выборок этот эффект может помешать модели изучить закономерности, связанные с рассуждениями. Во-вторых, слишком длинные образцы часто демонстрируют некачественные паттерны, такие как бессмысленная тарабарщина и повторяющиеся слова. Таким образом, расчет потерь на уровне выборки не может эффективно устранить эти плохие закономерности в длинных выборках, что приводит к нездоровому увеличению энтропии и длины отклика, как показано на рисунках 4а и 4б.

Рисунок 4: Энтропия распределения вероятностей акторной модели и изменение длины ответов в процессе обучения.

Авторы вводят градиентную потерю политики на уровне токенов в сценарий долгосрочной цепочки мышления (RL) для решения вышеуказанных ограничений:

Token-Level Policy Gradient Loss

Ключевые отличия:

Нормализация производится по общему количеству токенов во всех ответах;
Токены агрегируются напрямую, без предварительного усреднения по выборкам.

Fifth Checkpoint: Token-level Policy Gradient Loss. Стандартный расчет потерь GRPO на уровне сэмпла ослабляет градиенты от токенов в длинных ответах long-CoT, ухудшая обучение и подавление ошибок. Предложенный расчет потерь на уровне токенов решает эту проблему путем прямой агрегации и нормализации по всем токенам батча, обеспечивая каждому токену пропорциональный вклад в градиент.

📌 3.4 Overlong Reward Shaping: супердлинное формирование вознаграждения

При обучении с подкреплением обычно устанавливается фиксированная максимальная длина генерации и соответствующим образом обрезаются очень длинные образцы. Авторы обнаружили, что неправильное формирование вознаграждения для усеченных выборок может привести к появлению шума вознаграждения и существенно нарушить процесс обучения.

По умолчанию назначается штрафное вознаграждение за усеченные образцы. Такой подход может внести шум в процесс обучения, поскольку разумный процесс вывода может быть наказан просто за то, что он слишком длинный. Этот штраф может запутать модель относительно эффективности ее процесса рассуждения.

Чтобы изучить влияние этого шума вознаграждения, исследователи сначала применили очень длинную стратегию фильтрации, чтобы замаскировать потерю усеченных выборок. Было обнаружено, что такой подход значительно стабилизировал обучение и улучшил результаты, как показано на рисунке 5.

Рисунок 5: Точность акторной модели на тестовом наборе AIME и энтропия её генерационных вероятностей до и после применения стратегии Overlong Reward Shaping.

Кроме того, исследователи предложили мягкий штраф за превышение длины (Формула 13) — механизм штрафа, учитывающий длину, для усеченных выборок. В частности, определяется штрафной интервал, когда длина ответа превышает предопределенное максимальное значение. В пределах этого интервала, чем длиннее ответ, тем больше штраф. Этот штраф добавляется к изначальной награде за правильность, основанной на правилах, сигнализируя модели о необходимости избегать слишком длинных ответов.

Условия штрафа

Sixth Checkpoint: Overlong Reward Shaping. Традиционное бинарное пенальти за превышение длины ответа вносит шум в обучение, наказывая даже частично корректные длинные решения. Предложенный подход Overlong Reward Shaping заменяет жесткий штраф на постепенную линейную функцию в интервале 16-20К токенов, снижая уровень шума и позволяя модели эффективно учиться на длинных последовательностях без резкого отбрасывания данных.

4 Эксперименты

4.1 Подробности обучения

Исследователи сосредоточили свое внимание на математических задачах для оценки разработанного алгоритма, который может быть легко адаптирован для других задач с четкими и точными сигналами вознаграждения. Для обучения был использован фреймворк verl с GRPO в качестве базового горитма. Преимущество оценивалось с помощью нормализации группового вознаграждения.

В работе были применены следующие гиперпараметры: оптимизатор AdamW с постоянной скоростью обучения 1e-6 и линейным разогревом в 20 шагов. Размер пакета подсказок составил 512, с выбором 16 ответов на каждую подсказку. Для сверхдлинного формирования вознаграждения была установлена ожидаемая максимальная длина в 16 384 токенов с дополнительным мягким штрафным буфером в 4906 токенов. Параметры обрезки c_low и c_high были установлены на уровне 0,2 и 0,28 соответственно.

4.2 Основные результаты

В экспериментах на AIME 2024 метод DAPO успешно обучил базовую модель Qwen-32B, превратив её в мощную модель вывода, превзойдя результаты DeepSeek с использованием метода R1 на Qwen2.5-32B. Было показано значительное улучшение производительности AIME 2024: точность увеличилась с почти 0% до 50% при использовании только 50% шагов обучения, необходимых для DeepSeek-R1-Zero-Qwen-32B.

Исследователи проанализировали вклад каждой методики обучения в их подход. Улучшения демонстрируют эффективность этих методик в обучении с подкреплением. В условиях наивной настройки GRPO обучение на основе базовой модели Qwen.2-5-32B достигло только 30% точности.

AIME Step-by-step

4.3 Динамика тренировки

Процесс обучения DAPO продемонстрировал сложность RL в больших языковых моделях. Исследователи обеспечили стабильность обучения, отслеживая ключевые показатели. Эксперименты показали, что DAPO не только улучшает способность модели к рассуждению, но и усиливает её исследовательские способности.

Рисунок 7: Кривые метрик, включающие длину ответа, оценку вознаграждения, энтропию генерации и среднюю вероятность модели DAPO, которые отражают динамику обучения с подкреплением (RL) и служат ключевыми индикаторами для выявления потенциальных проблем.

4.4 Анализ случая

В ходе обучения с подкреплением модель DAPO продемонстрировала динамически развивающуюся модель рассуждений. По мере обучения модель не только укрепляла существующие шаблоны рассуждений, но и постепенно формировала новые модели поведения.

Таблица 2: Проявление рефлексивного поведения при обучении с подкреплением

5. Заключение

Запуск системы DAPO стал, на мой взгляд, небольшим, но всё же прорывом в области крупномасштабного обучения языковых моделей с подкреплением. Благодаря открытому исходному коду алгоритмов, кода и наборов данных, система предоставила ценные ресурсы для будущих исследований.

Четыре основные технологии DAPO — Clip-Higher, Dynamic Sampling, Token-Level Policy Gradient Loss и Overlong Reward Shaping — предлагают новые решения для обучения с подкреплением. Выпуск DAPO с открытым исходным кодом позволил мировому исследовательскому сообществу лучше понимать и применять методы обучения с подкреплением для крупномасштабных языковых моделей.

Наконец, позвольте мне добавить некоторые ограничения, которые пришли мне в голову:

С точки зрения итоговой производительности 50%-ная точность AIME все еще отстает от 72,6% DeepSeek-R1-Distill-Qwen-32B;
Эффективность этого метода была проверена только на одном обучающем наборе, одном тестовом наборе и одной модели, и его обобщение сомнительно;
С другой стороны, даже если DAPO обладает средней степенью обобщения, мы можем представить четыре приема, описанные в этой статье, как набор инструментов, из которого мы можем брать различные инструменты для конкретных сценариев, а не использовать весь DAPO как черный ящик. Фактически, из четырех приемов три предназначены для формирования вознаграждения, которое используется для поощрения исследовательской деятельности, лучшей обработки длинных ответов и лучшей обработки штрафа за длину, а оставшийся — для повышения эффективности выборки. Видно, что между ними нет зависимости, и любое подмножество рационально

🔥Не пропустите важные обновления и углубленные материалы!🔥

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30 мар. 2025 г.

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30.07.26 00:04 Ahmed

A really cool analysis, thank you. I was especially struck by how strictly the order is defined: data processing and formatting come first, with color only at the very end. This really saves you from the typical mistake of "first a pretty palette, then we figure out what the chart is for." And the palette validator with OKLCH + colorblindness check is absolutely fantastic; you almost never see that in regular tools. By the way, while reading about rank-trajectory and the logarithmic scale, I immediately remembered how convenient it is to analyze dynamics on charts in ExpertOption—I've been trading there for quite some time now. When the data is well visualized, decisions are noticeably easier and more relaxed. I also liked the point about "no more than eight colors" and the dual-axis ban. Strict restrictions sometimes actually produce better results than complete freedom. I'll try this approach myself.
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04.08.26 11:05 Kisnoles

Excellent analysis, thank you. I was particularly struck by how rigidly the skill sets the order: data processing and form come first, with color coming last. This really cures the habit of "first a pretty palette, then we'll figure it out." A palette validator using OKLCH + color blindness + WCAG is something most chart generators lack. And regarding the boundaries of competence, it's very clear. Where there's a self-checking loop (color), you delegate freely. Where there's a heuristic (form, data interpretation), you remain the final filter. This is a universal principle, not just for /dataviz. By the way, when you look at trading dashboards (including those of decent platforms like ExpertOption), it's immediately clear who thought about readability and who just threw in rainbow lines. Tools like this skill could greatly improve the quality of analytics. Thanks again for the detailed analysis – saved.
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23.08.26 20:02 leslieyee

Excellent analysis by /dataviz! I was particularly struck by how strictly the order is defined: "data meaning first, color last" and how the validator actually adjusts the palette according to OKLCH, color blindness, and WCAG standards. These rules greatly improve the quality of charts. By the way, a similar approach to clean and legible charts is highly valued in trading—for example, on the ExpertOption platform, the interface and price visualization are designed to ensure information is read instantly and without unnecessary noise.
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
04.09.26 21:51 Kovengray

Recovering your lost investment funds as the case might be, is not what you can do alone, you’d require the service of a trained recovery specialist. A recovery specialist is a person or a group of people who are well equipped to work around the brokerage network. They have vast knowledge about the whole network and have the right software and private keys to follow any transaction. I was ripped off trading online to an investment broker, good thing I got every penny back through the help of Gavin ray he’s a genius Contact : Gavinray78 at gmail com or WhatsApp +1 352 322 2096 It is also important to be patient and really calm during the process.
05.09.26 21:38 [email protected]

I invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place ‎Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 23:22 Fraddy Pual

Hearing that these individuals are focusing on other people makes me very sad. I had a similar situation with them and lost a lot of money, but after learning about (Cruxcipherteam @ proton DoT me), whataqq:+168160-15021, telegram: @Cruxcipherteam I was able to get my money back. It's critical that we all be watchful and keep reporting these occurrences.
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
15.09.26 03:35 elioduncan

I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.10.26 21:26 [email protected]

I Invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 17:44 Darrell1717

I fell victim of a scam I invested to total of 5thousand into. I know it could be risky but after I trusted this man I was dating online he lured me into investing with him. I know hard I worked of my money so I wanted every way possible to get it back. I really appreciate Blockrecoveryexpert for successfully recovered my funds form this scammer. This is all I can say. You can reachout if you ever need help contact blockrecoveryexpert (at) gmail (dot)com
11.10.26 03:04 Patricia014

Most recovery companies will take your money again. I personally think they’re the same set of people running all of them. It’s a sad, unending cycle, and so many people fall for cloned websites. The only recovery agent I know is Agent Rottgen Raphael. I’ve visited their physical company address, and they’ll tell you if they can handle your case instead of taking upfront payment when they know they can’t help. I highly appreciate their support in recovering my money from the scammers’ wallet within 24 hours. RottgenRaphael@Gmail. com
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
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