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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:

  1. Коллапс энтропии — тенденция модели к сужению разнообразия генерируемых ответов;

  2. Шум вознаграждения — некорректное присвоение наград за частично правильные или слишком длинные ответы;

  3. 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.
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

  1. Стабильность обучения: основная идея PPO заключается в ограничении изменений политики между итерациями, что предотвращает слишком резкие обновления, которые могут дестабилизировать процесс обучения;

  2. Механизм отсечения: PPO использует функцию отсечения для ограничения коэффициента важности выборки, что гарантирует, что новая политика не будет сильно отклоняться от старой;

  3. 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
Proximal Policy Optimization
Advantage функция
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

  1. Сбор опыта: агенты взаимодействуют со средой, следуя текущей политике π_old​, и собирает траектории (последовательности состояний, действий, вознаграждений).

  2. Оценка преимущества: для каждого временного шага в собранных траекториях рассчитывается оценка преимущества A_t (Advantage функция) с использованием формул (2) и (3).

  3. Оптимизация политики: параметры политики θ обновляются путем оптимизации целевой функции (1) с использованием стохастического градиентного восхождения в течение нескольких эпох.

  4. Обновление функции ценности: параметры функции ценности обновляются путем минимизации среднеквадратичной ошибки между предсказанными и фактическими ценностями состояний.

  5. Итерация: шаги 1-4 повторяются до достижения желаемой производительности или заданного числа итераций.

Преимущества PPO

  1. Простота реализации: PPO проще в реализации, чем TRPO и другие сложные алгоритмы обучения с подкреплением;

  2. Высокая производительность: PPO показывает отличные результаты во многих задачах, от игр Atari до сложных задач робототехники;

  3. Совместимость с нейронными сетями: PPO прекрасно работает с глубокими нейронными сетями и может использоваться для обучения сложных политик;

  4. Хорошая масштабируемость: PPO можно эффективно распараллеливать для ускорения обучения.

Применение PPO

PPO широко используется в различных областях:

  1. Игры: от простых игр до сложных стратегий и симуляторов;

  2. Робототехника: обучение управлению роботами для выполнения сложных физических задач;

  3. Системы рекомендаций: оптимизация стратегий рекомендаций в интерактивных системах;

  4. 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

Figure_19
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
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
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

  1. Генерация группы ответов: для каждого запроса модель генерирует группу из N различных ответов, используя текущую политику.

  2. Оценка наград: каждый ответ получает награду от внешней функции награды (например, от модели-критика или по заданным правилам).

  3. 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

  4. 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).

  5. Регуляризация с KL-дивергенцией: Обновление ограничивается, чтобы новая политика не слишком отличалась от предыдущей версии или от референсной модели.

  6. 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
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
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.
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.
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
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:

  1. Выполнение избыточной выборки подсказок;

  2. Фильтрация подсказок с точностью, равной 1 или 0;

  3. Сохранение только подсказок с допустимыми градиентами в пакете;

  4. 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
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.
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.
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
Token-Level Policy Gradient Loss

Ключевые отличия:

  1. Нормализация производится по общему количеству токенов во всех ответах;

  2. 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.
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
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
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.
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
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

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    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.10.25 18:07 crypto

    Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.

  • 15.10.25 21:52 harristhomas7376

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  • 15.10.25 21:52 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.10.25 20:17 tyleradams

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  • 17.10.25 20:20 lindseyvonn

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  • 17.10.25 20:22 richardcharles

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  • 17.10.25 20:23 stevekalfman

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  • 17.10.25 21:42 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.10.25 21:42 marcushenderson624

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  • 17.10.25 21:42 marcushenderson624

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  • 21.10.25 08:39 debby131

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  • 21.10.25 11:45 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 21.10.25 11:45 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 22.10.25 04:48 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 22.10.25 07:36 donnacollier

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  • 22.10.25 11:59 elizabethrush89

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  • 22.10.25 11:59 elizabethrush89

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  • 22.10.25 16:31 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 23.10.25 01:52 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 01:52 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 15:47 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 23.10.25 21:43 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.10.25 21:43 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:08 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 24.10.25 06:40 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:40 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 06:54 MATT PHILLIP

    I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $150,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.

  • 24.10.25 18:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.10.25 18:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.10.25 00:49 tyleradams

    *HOW TO GET BACK YOUR STOLEN BITCOIN FROM SCAMMERS* ⭐️⭐️⭐️⭐️⭐️ Hello everyone, I can see a lot of things going wrong these last few days of investing online and getting scammed. I was in your shoes when I invested in a bogus binary option and was duped out of $87,000 in BTC, but thanks to the assistance of NVIDIA TECH HACKERS. They helped me get back my BTC. I didn’t trust the Hackers at first, but they were recommended to me by a friend whom I greatly respect. I received my refund in two days. I must recommend NVIDIA TECH HACKERS they are fantastic. 📧 [email protected]

  • 25.10.25 00:50 stevekalfman

    If you ever need hacking services, look no further. I found myself in a difficult situation after losing almost $510,000 USD in bitcoin. I was distraught and had no hope of survival because i lost my life savings to this scam, I had no chance of recovering my investment. Until i came across an article on google about ([email protected]). A real-life recovery expert, everything changed completely after contacting him and explaining my ordeal to him and he quickly stepped in and assisted me in recovering 95% of my lost funds. They guarantee their clients and i got the highest level of happiness their services are highly recommended. so I’m putting this here for anyone who require their services too" Email: [email protected]

  • 25.10.25 05:05 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 25.10.25 10:13 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 25.10.25 10:13 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.10.25 01:03 Christopherbelle

    A terrible financial shock hit me hard. I lost $860,000 in a fake crypto scheme. Things looked good until I tried to cash out my earnings. Suddenly, my account vanished into thin air. I told the police many times, but help never showed up. Despair washed over me; I felt totally beaten. Then, I found Sylvester Bryant Intelligence. Right away, they were skilled and honest about the whole thing. They looked deep into my situation. They tracked where the stolen funds went. They fought hard for me every step of the way. To my great surprise, they got my money back. I thought that was impossible. I owe them so much for their hard work and truthfulness. Sylvester Bryant Intelligence restored my peace. If scams took your crypto, contact them now. Contact Info: Yt7cracker@gmail . com WhatsApp: ‪+1 512 577 7957. or +44 7428 662701.

  • 26.10.25 18:09 victoriabenny463

    A few months ago, I fell for what looked like a legitimate online trading platform. The website was sleek, the support team was responsive, and they even showed me fake profit charts that seemed to grow daily. I started small, and after a few test withdrawals worked, I invested more eventually depositing 2 Bitcoin in hopes of long-term returns. But one morning, when I tried to withdraw, everything changed. The platform suddenly locked my account, claiming there were additional fees to release my funds. The support chat stopped responding, and the website started giving error messages. That’s when I realized I’d been scammed. I was devastated. Two Bitcoins wasn’t pocket change, it was my savings. I filed reports online, but everyone told me it was impossible to recover crypto once it’s sent. Then, through a discussion forum, I came across Dexdert Net Recovery, a team specializing in tracing and recovering stolen digital assets. Skeptical but desperate, I reached out. Their response was immediate and professional. They asked for transaction IDs, wallet addresses, screenshots of my correspondence with the fake platform, and any proof of payment I had. Within days, their analysts traced the stolen Bitcoin through multiple wallets using blockchain forensics, They updated me step-by-step, Working with their recovery experts and blockchain partners, Dexdert Net Recovery successfully froze the funds and verified ownership of my wallet. After 2 days of persistence and verification, I finally saw my 2 Bitcoin restored back into my own wallet. I couldn’t believe it. What stood out most wasn’t just that they recovered my funds, but how transparent and supportive the Dexdert team was throughout the process. They educated me on crypto safety, how to spot fake trading sites, and how to secure my digital assets in the future. Dexdert Net Recovery truly lives up to its name. They gave me back not just my Bitcoin, but my peace of mind. Reach Out Information Below Via: Email: ([email protected]) Telegram: (https://t.me/Dexdertprorecovery) WhatsApp: (+1 (859) 609‑4156)

  • 27.10.25 11:15 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 27.10.25 11:15 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 27.10.25 17:08 raymondgonzales

    Three Cheers for Wizard Hilton Cyber Tech, Bitcoin Savior Extraordinaire In the ever-evolving world of cryptocurrency, where volatility and uncertainty reign supreme, one individual has emerged as a beacon of hope and innovation - Wizard Hilton Cyber Tech, the self-proclaimed "Bitcoin Savior Extraordinaire." This enigmatic figure, with his uncanny ability to navigate the complexities of the digital asset landscape, has captivated the attention of crypto enthusiasts and skeptics alike. Wizard Hilton Cyber Tech journey began as a humble programmer, tinkering with the underlying blockchain technology that powers Bitcoin. But it was his visionary approach and unwavering commitment to the cryptocurrency's potential that propelled him into the limelight. Through a series of strategic investments, groundbreaking algorithmic trading strategies, and a knack for anticipating market shifts, Wizard Hilton Cyber Tech has managed to consistently outperform even the savviest of Wall Street traders. Wizard Hilton Cyber Tech ability to turn even the most tumultuous of Bitcoin price swings into opportunities for substantial gains has earned him the moniker "Wizard," a testament to his unparalleled mastery of the digital currency realm. But Wizard Hilton Cyber Tech impact extends far beyond personal wealth accumulation - Wizard Hilton Cyber Tech has tirelessly advocated for the widespread adoption of Bitcoin, working tirelessly to educate the public, lobby policymakers, and collaborate with industry leaders to overcome the barriers that have long hindered the cryptocurrency's mainstream acceptance. With infectious enthusiasm and boundless energy, Wizard Hilton Cyber Tech has become a true champion of the Bitcoin cause, inspiring a new generation of crypto enthusiasts to embrace the transformative power of this revolutionary technology. As the digital currency landscape continues to evolve, Wizard Hilton Cyber Tech name will undoubtedly be etched in the annals of cryptocurrency history as a visionary, a trailblazer, and, above all, the Bitcoin Savior Extraordinaire. To get your stolen bitcoin back, reach out to Wizard Hilton Cyber Tech via: Email : wizardhiltoncybertech ( @ ) gmail (. ) com WhatsApp number  +18737715701 Good Day.

  • 27.10.25 17:20 fatimanorth

    The Federal Trade Commission said that more than $1 billion had been lost to cryptocurrency scams in 2023. Victims frequently lose everything, including hope, trust, and wealth. When your hard-earned money disappears into digital shadows, you feel trapped. Nowadays, cryptocurrency frauds are very common. You can get help from recovery specialist Marie at [email protected] and via WhatsApp at +1 7127594675.

  • 28.10.25 00:55 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 28.10.25 00:55 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 29.10.25 03:43 Christopherbelle

    A sudden money crisis struck me. I dropped $82,000 to a phony crypto scam. All seemed fine until I went to pull out my gains. Then, i was unable to get back my hard earned money. I reported it to the police several times. No aid came my way. Deep sadness hit me; I felt crushed. That's when I learned about Sylvester Bryant Intelligence. They acted quick and fair from the start. They checked my case closely. They followed the path of my lost cash. They pushed strong for me at each turn. In shock, they brought my funds back. I had figured it could not happen. I thank them for their effort and honesty. Sylvester Bryant Intelligence gave me calm again. If a scam stole your crypto, reach out to them today. Contact Info: Yt7cracker@gmail . com WhatsApp: +1 512 577 7957 or +44 7428 662701.

  • 29.10.25 10:56 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 29.10.25 10:56 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 30.10.25 09:49 Christopherbelle

    I suffered a huge money blow when $80,000 slipped away in a bogus crypto plot. It all looked great at first. Then I went to pull out my gains, and poof—my account was gone. I kept telling the cops about it, but they did zip. I felt shattered and lost. That's when I stumbled on Sylvester Bryant Intelligence. Things turned around fast. Right away, they showed clear steps, sharp know-how, and real drive to fix it. They tracked my missing cash step by step and pushed hard till they got it back. I swear, I figured it was a lost cause. Their straight-up work and trust brought back my calm. If a scam stole your crypto, reach out to them now. yt7cracker@gmail . com | WhatsApp: +1 512 577 7957 or +44 7428 662701

  • 30.10.25 12:03 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

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