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Н Новости

[Перевод] С новым годом: GPT в 500 строках на SQL

В минувшем году все только и говорили об ИИ и о том, как он может всё за вас сделать.

Мне нравится, когда кто-то или что-то работает за меня. Поэтому решил: попрошу-ка ChatGPT написать за меня новогодний пост:

"Эй, ChatGPT. А ты можешь реализовать большую языковую модель на SQL?"
"Нет, SQL не подходит для реализации больших языковых моделей. Язык SQL предназначен для выполнения запросов к данным, хранящимся в РСУБД и для управления этими запросами. Для реализации большой языковой модели требуются сложные алгоритмы, обширные датасеты, а зачастую – и фреймворки для глубокого обучения. SQL всеми этими возможностями не обладает."

Что ж, лишний раз убеждаешься, что, если хочешь что-то сделать хорошо – сделай это сам.

Давайте же воодушевимся этим оптимистическим планом и реализуем большую языковую модель на языке SQL.

Теория

Готовя этот пост, я вдохновлялся чудесной статьёй GPT in 60 Lines of NumPy, которую написал Джей Моди. В этой статье объяснено внутреннее устройство модели GPT, причём, это сделано гораздо лучше, чем могло бы получиться у меня. Поэтому для порядка вкратце напомню контекст.

Что представляет собой генеративная большая языковая модель с технической точки зрения?

Генеративная LLM – это функция. Она принимает на ввод текстовую последовательность символов (в терминологии ИИ она называется «промпт») и возвращает массив строк и чисел. Вот какова сигнатура этой функции:

llm(prompt: str) -> list[tuple[str, float]]

Это детерминированная функция. У неё под капотом выполняется серьёзная математика, но вся эта математика жёстко вшита в систему. Если вы будете многократно сообщать этой функции один и тот же ввод, то всякий раз будете получать от неё один и тот же вывод.

Тем, кому доводилось пользоваться ChatGPT и подобными продуктами, это может показаться удивительным, ведь система может давать разные ответы на один и тот же вопрос. Да, всё верно. Чуть ниже объясню, как это устроено.

Что за значения возвращает эта функция?

Нечто подобное:

	llm("I wish you a happy New")
 
0       (' Year', 0.967553)
1       (' Years', 0.018199688)
2       (' year', 0.003573329)
3       (' York', 0.003114716)
4       (' New', 0.0009022804)
…
50252   (' carbohyd', 2.3950911e-15)
50253   (' volunte', 2.2590102e-15)
50254   ('pmwiki', 1.369229e-15)
50255   (' proport', 1.1198108e-15)
50256   (' cumbers', 7.568147e-17)

Она возвращает массив кортежей. Каждый кортеж состоит из слова (скорее, строки) и числа. Число — это вероятность, с которой данное слово может оказаться промпте на следующей позиции. Модель «думает», что за фразой «I wish you a happy New…» («Поздравляю тебя с Новым…») с вероятностью 96,7% последует строка «Year» (…годом) – и так далее.

Слово «думает» выше поставлено в кавычках, так как, естественно, модель ни о чём не думает. Она механически возвращает массивы слов и чисел в соответствии с некоторой жёстко прописанной внутренней логикой.

Если эта система такая топорная и детерминированная, как же ей удаётся генерировать разные тексты?

Большие языковые модели используются в текстовых приложениях (чатботы, генераторы контента, кодинг-ассистенты, т.д.). Эти приложения раз за разом вызывают модель и выбирают подсказанное ею слово (с некоторой степенью произвольности). Последнее предложенное слово добавляется к промпту, и модель вызывается снова. Этот цикл продолжается до тех пор, пока не будет сгенерировано достаточное количество слов.

Накопленная таким образом последовательность слов выглядит как текст на естественном языке, с полноценной грамматикой, синтаксисом и даже мнимыми признаками интеллекта и логики. В данном отношении языковые модели подобны марковским цепям, работающим по такому же принципу.

На внутреннем уровне большая языковая модель устроена так, что каждое последующее предлагаемое слово естественным образом продолжало промпт, с учётом имеющейся грамматики, семантики и тональности. Оснастить функцию такой логикой стало возможно благодаря целой серии научных прорывов (и каторжной работе программистов). Удалось разработать целое семейство алгоритмов под названием GPT или «генеративные предобученные трансформеры».

Что такое "генеративный предобученный трансформер"

«Генеративный» означает, что алгоритм генерирует текст (рекурсивно достраивая продолжения к промпту как было показано выше).

«Трансформер» означает, что алгоритм использует конкретный тип нейронной сети. Сеть-трансформер была разработана компанией Google и описана в этой статье.

Термин «предобученный» требует небольшого исторического экскурса. Изначально считалось, что способность модели достраивать текст – это всего лишь предпосылка для получения более глубоких логических выводов в рамках специализированных задач (нужно улавливать логическую связь между фразами), классификации (например, угадать, сколько звёзд у отеля, проанализировав отзывы постояльцев), машинного перевода и т.д. Считалось, что две эти части алгоритма требуется обучать отдельно, и языковая часть позиционировалась как предобучение, подготовка к последующему обучению решать реальную задачу.

Как сформулировано в исходной статье по GPT:

Продемонстрировано, что возможно добиться больших успехов при решении таких задач путём генеративного предобучения языковой модели на разнородном корпусе неразмеченного текста с последующей тонкой настройкой различных параметров для различных слоёв сети (discriminative fine-tuning) в контексте каждой конкретной задачи.

Такие представления сохранялись до тех пор, пока не стало понятно, что для достаточно большой модели второй шаг зачастую излишен. Модель-трансформер, обученная исключительно генерации текстов, оказалась в состоянии без дополнительного обучения следовать человеческим инструкциям, содержащимся в этих текстах. Таким образом, не требовалось никакой дополнительной тонкой настройки.

Итак, с этими вопросами мы разобрались. Теперь давайте сосредоточимся на реализации.

Генерация

Вот что происходит, если мы пытаемся сгенерировать текст на основе промпта при помощи GPT2:

def generate(prompt: str) -> str:
  # Преобразует строку в список токенов.
  tokens = tokenize(prompt) # tokenize(prompt: str) -> list[int]
 
  while True:
 
    # Выполняет алгоритм.
    # Возвращает вероятностные значения для токенов: список из 50257 чисел с плавающей точкой, в сумме дающих 1.
    candidates = gpt2(tokens) # gpt2(tokens: list[int]) -> list[float]
 
    # Выбирает следующий токен из списка предложенных 
    next_token = select_next_token(candidates)
    # select_next_token(candidates: list[float]) -> int
 
    # Прикрепляет его к списку токенов
    tokens.append(next_token)
 
    # Решаем, хотим ли мы прекратить генерацию.
    # Здесь может быть счётчик токенов, задержка, стоп-слово или что-то ещё.
    if should_stop_generating():
      break
 
  # Преобразует список токенов в строку
  completion = detokenize(tokens) # detokenize(tokens: list[int]) -> str
  return completion

Давайте реализуем все эти элементы один за другим на языке SQL.

Токенизатор

Прежде, чем текст можно будет скормить нейронке, его требуется преобразовать в список чисел. Конечно, нас это не удивляет: именно такие задачи решаются при помощи текстовых кодировок вроде Unicode. Но обычный Unicode не слишком хорошо работает с нейронными сетями.

В сущности, нейронные сети построены на обширном перемножении матриц, и вся прогностическая сила нейронных сетей заключена в коэффициентах этих матриц. Некоторые из таких матриц содержат по строке на каждое из возможных значений в «алфавите», в других предусмотрено по строке на «символ».

В этом контексте смысл терминов «алфавит» и «символ» требуется пояснить. В Unicode длина «алфавита» составляет 149186 символов (именно столько отдельных точек Unicode существует на момент подготовки этой статьи), а в качестве «символа» может выступать, например: ﷽ (да, это одиночная точка Unicode, номер 65021, она соответствует целой фразе на арабском языке, особенно важной для мусульман). Отмечу, что эту фразу можно было бы записать и обычной арабской вязью. Таким образом, одному тексту может соответствовать несколько вариантов кодировки.

Давайте разберём эту ситуацию на примере слова "PostgreSQL". Если бы мы попытались закодировать её (преобразовать в массив чисел) при помощи Unicode, то у нас получилось бы 10 чисел, которые могли бы находиться в диапазоне от 1 до 149186. Таким образом, в нашей нейронной сети требовалось бы хранить матрицу из 149186 строк и совершить ряд вычислений над 10 строками из этой матрицы. Некоторые из этих строк (соответствующие буквам латиницы) использовались бы особенно часто, и в них было бы заключено много информации. Другие символы, например, смайлик какашки и таинственные символы из мёртвых языков едва ли вообще хоть раз использовались, но и на их хранение требуется место.

Естественно, мы хотим, чтобы оба эти числа, и длина «алфавита», и количество «символов» оставались как можно меньше. В идеале «символы» нашего алфавита должны быть распределены равномерно, а ещё мы по-прежнему хотим, чтобы наша кодировка не уступала по мощности Unicode.

Интуитивно понятно, что это можно сделать, присвоив уникальные номера тем последовательностям слов, которые часто встречаются в обрабатываемых нами текстах. В Unicode вышеупомянутая религиозная арабская фраза может быть закодирована либо как один кодовый символ, либо буква за буквой. Поскольку мы выкатываем нашу собственную кодировку, точно так же мы можем поступать с теми словами и фразами, которые важны в рамках нашей модели (например, они часто встречаются в текстах).

Например, можно было бы выделить конкретные числа для строк "Post", "greSQL" и "ing". Таким образом, оба слова "PostgreSQL" и "Posting" в нашем представлении будут иметь длину по 2. Конечно же, мы стремимся закреплять отдельные кодовые символы для более конкретных последовательностей и отдельных байт. Даже натыкаясь на тарабарщину или на иноязычный текст, такую информацию всё равно удастся закодировать, хотя, на это и потребуется больше времени.

В GPT2 используется вариант алгоритма под названием кодирование диадами (Byte Pair Encoding), предназначенный специально для этой цели. Токенизатор GPT2 использует словарь из 50257 кодовых точек (в терминологии ИИ — «токенов»), которые соответствуют различным последовательностям байт в UTF-8 (плюс отдельный токен, означающий «конец текста»).

Этот словарь мы собрали путём статистического анализа, выполненного таким образом:

1. Начинаем с простой кодировки из 256 токенов: по токену за байт.

2. Берём большой корпус текстов (предпочтительно именно тот, на котором будет обучаться модель).

3. Кодируем его.

4. Вычисляем, какая пара токенов встречается чаще всего. Пусть это будет 0x20 0x74 (пробел, за которым следует строчная "t").

5. Присваиваем следующее доступное значение (257) этой паре байт.

6. Повторяем шаги 3-5, теперь обращая внимание на последовательности байт. Если последовательность байт можно закодировать сложным токеном, то используем сложный токен. При явных неоднозначностях (например, "abc" может в одном случае быть закодировано как "a" + "bc" или как "ab" + "c"), то пользуйтесь той, номер которой меньше (это означает, что она была добавлена раньше и, следовательно, встречается чаще). Это нужно делать рекурсивно, пока все последовательности, которые можно сложить в один токен, будут сложены в один токен.

7. Выполним такое «складывание» 50000 раз подряд.

Число 50000 выбрано разработчиками более или менее произвольно. В других моделях количество токенов также держится в подобном диапазоне (от 30k до 100k).

На каждой итерации данного алгоритма в словарь будет добавляться новый токен, получаемый конкатенацией двух предыдущих. В конечном итоге получим 50256 токенов. Добавляем токен с фиксированным номером, означающий «конец текста» - и всё готово.

В версии алгоритма BTE для GPT2 есть ещё один уровень кодировки: в словаре токенов эти токены отображаются на строки, а не на массивы байт. Отображение с байт на строковые символы определяется в этой функции. Тот словарь, который она производит, находится в таблице encoder.

Рассмотрим, как реализовать токенизатор на SQL.

Данный токенизатор – неотъемлемая часть GPT2, и словарь токенов можно скачать с сайта OpenAI, равно как и оставшуюся часть модели. Нам понадобится импортировать её в таблицу tokenizer. В самом конце этого поста вы найдёте ссылку на репозиторий с кодом. Этот код автоматизирует заполнение таблиц базы данных, необходимых для работы с моделью.

В рамках рекурсивного подхода CTE разбиваем слово на токены (начиная с единичных байт) и объединяем наилучшие смежные пары, пока больше материала для объединения не останется. Само объединение происходит по принципу вложенного рекурсивного CTE.

Для примера я выбрал слово «Mississippilessly». Каждая запись в наборе результатов соответствует наилучшей найденной к данному моменту паре, которую можно «сложить», а также прогресс в обработке запроса.

WITH    RECURSIVE
        bpe AS
        (
        SELECT  (n + 1)::BIGINT AS position, character, TRUE AS continue, 1 AS step,
                NULL::INT AS token, NULL::TEXT AS combined
        FROM    CONVERT_TO('Mississippilessly', 'UTF-8') AS bytes
        CROSS JOIN LATERAL
                GENERATE_SERIES(0, LENGTH(bytes) - 1) AS n
        JOIN    encoder
        ON      byte = GET_BYTE(bytes, n)
        UNION ALL
        (
        WITH    RECURSIVE
                base AS
                (
                SELECT  *
                FROM    bpe
                WHERE   continue
                ),
                bn AS
                (
                SELECT  ROW_NUMBER() OVER (ORDER BY position) AS position,
                        continue,
                        character,
                        character || LEAD(character) OVER (ORDER BY position) AS cluster
                FROM    base
                ),
                top_rank AS
                (
                SELECT  tokenizer.*
                FROM    bn
                CROSS JOIN LATERAL
                        (
                        SELECT  *
                        FROM    tokenizer
                        WHERE   tokenizer.cluster = bn.cluster
                        LIMIT   1
                        ) tokenizer
                ORDER BY
                        token
                LIMIT   1
                ),
                breaks AS
                (
                SELECT  0::BIGINT AS position, 1 AS length
                UNION ALL
                SELECT  bn.position,
                        CASE WHEN token IS NULL THEN 1 ELSE 2 END
                FROM    breaks
                JOIN    bn
                ON      bn.position = breaks.position + length
                LEFT JOIN
                        top_rank
                USING   (cluster)
                )
        SELECT  position, character, token IS NOT NULL,
                (SELECT step + 1 FROM base LIMIT 1), token, top_rank.cluster
        FROM    breaks
        LEFT JOIN
                top_rank
        ON      1 = 1
        CROSS JOIN LATERAL
                (
                SELECT  STRING_AGG(character, '' ORDER BY position) AS character
                FROM    bn
                WHERE   bn.position >= breaks.position
                        AND bn.position < breaks.position + length
                ) bn
        WHERE   position > 0
        )
        )
SELECT  step, MAX(token) AS token, MAX(combined) AS combined, ARRAY_AGG(character ORDER BY position)
FROM    bpe
WHERE   continue
GROUP BY
        step
ORDER BY
        step

На каждом шаге алгоритм BPE находит пару токенов, наиболее подходящую для слияния, и объединяет их (здесь в выводе вы видите такую слитую пару и ее ранг). При помощи такой процедуры размер пространства токенов можно сократить с 150k, присущих Unicode, до 50k, а количество токенов в данном конкретном слове с 17 до 5. В обоих случаях это отличное улучшение.

Когда приходится работать с множеством слов, токенизатор сначала разбивает текст на отдельные слова при помощи этого регулярного выражения и объединяет токены в каждом слове отдельно. К сожалению, при работе с PostgreSQL свойства символов Unicode не поддерживаются на уровне регулярных выражений, поэтому мне пришлось немного отладить систему (возможно, в процессе я угробил нормальную поддержку Unicode). Вот как результат выглядит в SQL:

WITH    input AS
        (
        SELECT  'PostgreSQL is great' AS prompt
        ),
        clusters AS
        (
        SELECT  part_position, bpe.*
        FROM    input
        CROSS JOIN LATERAL
                REGEXP_MATCHES(prompt, '''s|''t|''re|''ve|''m|''ll|''d| ?\w+| ?\d+| ?[^\s\w\d]+|\s+(?!\S)|\s+', 'g') WITH ORDINALITY AS rm (part, part_position)
        CROSS JOIN LATERAL
                (
                WITH    RECURSIVE
                        bpe AS
                        (
                        SELECT  (n + 1)::BIGINT AS position, character, TRUE AS continue
                        FROM    CONVERT_TO(part[1], 'UTF-8') AS bytes
                        CROSS JOIN LATERAL
                                GENERATE_SERIES(0, LENGTH(bytes) - 1) AS n
                        JOIN    encoder
                        ON      byte = GET_BYTE(bytes, n)
                        UNION ALL
                        (
                        WITH    RECURSIVE
                                base AS
                                (
                                SELECT  *
                                FROM    bpe
                                WHERE   continue
                                ),
                                bn AS
                                (
                                SELECT  ROW_NUMBER() OVER (ORDER BY position) AS position,
                                        continue,
                                        character,
                                        character || LEAD(character) OVER (ORDER BY position) AS cluster
                                FROM    base
                                ),
                                top_rank AS
                                (
                                SELECT  tokenizer.*
                                FROM    bn
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  *
                                        FROM    tokenizer
                                        WHERE   tokenizer.cluster = bn.cluster
                                        LIMIT   1
                                        ) tokenizer
                                ORDER BY
                                        token
                                LIMIT   1
                                ),
                                breaks AS
                                (
                                SELECT  0::BIGINT AS position, 1 AS length
                                UNION ALL
                                SELECT  bn.position,
                                        CASE WHEN token IS NULL THEN 1 ELSE 2 END
                                FROM    breaks
                                JOIN    bn
                                ON      bn.position = breaks.position + length
                                LEFT JOIN
                                        top_rank
                                USING   (cluster)
                                )
                        SELECT  position, character, token IS NOT NULL
                        FROM    breaks
                        LEFT JOIN
                                top_rank
                        ON      1 = 1
                        CROSS JOIN LATERAL
                                (
                                SELECT  STRING_AGG(character, '' ORDER BY position) AS character
                                FROM    bn
                                WHERE   bn.position >= breaks.position
                                        AND bn.position < breaks.position + length
                                ) bn
                        WHERE   position > 0
                        )
                        )
                SELECT  position, character AS cluster
                FROM    bpe
                WHERE   NOT continue
                ) bpe
        ),
        tokens AS
        (
        SELECT  token, cluster
        FROM    clusters
        JOIN    tokenizer
        USING   (cluster)
        )
SELECT  *
FROM    tokens

Странный символ Ġ соответствует пробелу.

Этот запрос токенизирует промпт и преобразует его в массив чисел. Вот промпт и готов к долгому пути сквозь слои модели.

Векторные представления

Токены - это представления единиц естественного языка (в целом, примерно 0,75 слова на токен), поэтому любая модель, претендующая на успешное автозавершение текстов, должна каким-то образом кодировать отношения между этими единицами. Даже в изоляции части речи обладают наборами ортогональных свойств.

Возьмём, к примеру, слово «subpoena» (повестка) – оказывается, в токенизаторе GPT2 на него отведён целый токен. С точки зрения английского языка – это существительное? Да, бесспорно. А глагол? Да, и глаголом может быть. А прилагательным? Уже не очень, но, в принципе, контекст придумать можно. Это канцелярит? Чёрт возьми, ещё какой. И так далее.

Все эти свойства ортогональны, то есть, не зависят друг от друга. Слово может быть официозным существительным, но не глаголом и не прилагательным. В английском возможны любые сочетания этих признаков.

Сущности с ортогональными свойствами лучше всего кодируются в виде векторных представлений. Пусть у нас будет не единственное свойство (например, номер), а много. При желании мы можем крутить ими как захотим. Например, фраза «В судебном решении, которое процитировал адвокат, фигурирует…» с высокой вероятностью продолжается каким-то существительным, которое, не менее вероятно, стилистически относится к канцеляриту. Нас совершенно не интересует, есть ли у этого слова маргинальная семантика «глагол», либо «прилагательное», либо «цветок».

В математике отображение сравнительно узких значений на более широкие пространства (например, ID токенов на векторы) называется векторным представлением. Именно этим мы здесь и занимаемся.

Как решить, какие именно свойства окажутся представлены в этих векторах? А мы не будем. Мы просто предоставим достаточно векторного пространства для каждого токена и понадеемся, что модель на этапе обучения получит достаточно информации, чтобы заполнить все эти измерения осмысленным содержимым. В GPT2 под векторы отводится 768 измерений. Заранее (и, на самом деле, даже в ретроспективе) не известно, какое свойство слова будет закодировано, например, в измерении 247. Определённо, что-то закодировано там будет, но что именно – сказать сложно.

Какие свойства каждого из токенов мы внедрим в векторное пространство? Любые, которые помогут нам спрогнозировать, каков будет следующий токен.

ID токена? Естественно. Разные токены означают разные вещи.

Позиция токена в тексте? Да, пожалуйста. «Сине-фиолетовый» и «фиолетово-синий» — не одно и то же.

Взаимные отношения токенов? Естественно! Это, пожалуй, наиважнейшая часть задачи, и блок внимания (Attention) в архитектуре трансформера как раз впервые позволил решить эту часть задачи правильно.

Токены и позиции легко поддаются векторному представлению. Допустим, есть фраза «PostgreSQL is great», о которой заранее известно, что она отображается на четыре токена: [6307, 47701, 318, 1049].

Среди прочих параметров GPT2 есть две матрицы, называющиеся WTE (векторное представление лексических токенов) и WPE (векторное представление позиций слов). Как понятно из названия, в первом хранятся векторные представления токенов, а во втором – векторные представления их позиций. Конкретные значения, которыми окажутся заполнены эти представления, набираются в результате обучения модели, в данном случае GPT2. Насколько известно, в таблицах баз данных wte и wpe есть константы. Размер

WTE равен 50257×768, а размер WPE равен 1024×768. Второе означает, что в GPT2 можно использовать промпт, состоящий не более чем из 1024 токенов. Если записать в промпт больше токенов, мы просто не сможем вытянуть для токенов сверх 1024 их позиционные представления. Это архитектурный аспект (в терминологии ИИ – «гиперпараметр») модели, устанавливаемый на этапе её проектирования, и обучением его изменить невозможно. Когда говорят о «контекстном окне» большой языковой модели, имеют в виду именно это число.

Токен 6307 стоит у нас на месте 0, токен 47701 на месте 1, токен 318 на месте 2, а токен 1049 на месте 3. Для каждого из этих токенов и их позиций у нас по два вектора: один из WTE и один из WPE. Их требуется сложить. В результате получатся четыре вектора, которые послужат вводом для следующей части алгоритма: так работает нейронная сеть прямого распространения, в которой действует механизм внимания.

Для работы с SQL мы воспользуемся pgvector, это расширение PostgreSQL.

Небольшая оговорка: код для этого поста я пишу на обычном SQL, иногда вставляю чистые SQL-функции в качестве вспомогательных элементов. В рамках этого поста осуществить такое не составит труда, равно как определить векторные операции над массивами. Это делается за счёт небольшого снижения производительности (и уже было реализовано в версии 1 и работало, пусть и медленно). С распространением ИИ и ростом влияния векторных баз данных pgvector или эквивалентный механизм определённо укоренится в ядре PostgreSQL в течение двух-трёх релизов. Я просто решил оседлать волну, которая принесёт меня в будущее.

Вот как это делается в SQL:

WITH    embeddings AS
        (
        SELECT  place, values
        FROM    UNNEST(ARRAY[6307, 47701, 318, 1049]) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        )
SELECT  place, (values::REAL[])[0:5]
FROM    embeddings

(Чтобы вывод был короче, в этом запросе показаны только первые 5 измерений для каждого вектора).

Внимание

Та часть трансформерной архитектуры, благодаря которой она действительно феерит, называется «механизм внутреннего внимания» (self-attention). Он был впервые описан в 2017 году в статье «Attention is all you need» под авторством Васмани и др. Пожалуй, это наиизвестнейшая статья об искусственном интеллекте, и с тех пор её название превратилось в болванку (клише для именования других статей).

Итак, вероятно, к настоящему моменту у нас уже есть несколько векторов, в которых закодированы определённые синтаксические и семантические свойства слов, содержащихся в нашем промпте. Нам каким-то образом нужно донести эти свойства до последнего вектора. Сейчас будет небольшой спойлер: именно в последнем векторе будет храниться представление того слова, которым продолжится фраза.

Во фразе вида a «I looked at the violet and saw that it was not the usual …» (я взглянул на лиловое пятно и заметил, что это не обычный…), на месте многоточия должно быть что-то, увиденное вами (об этом свидетельствует слово «saw»), обладающее свойством «лиловости» и при этом «необычное» (сочетаем токены «не» и «обычный», тем самым меняя знак измерения «обычность» на противоположный). Можно привести такую реалистичную аналогию: человек читает книгу на иностранном языке, о котором имеет некоторое представление, но свободно им не владеет. В таком случае человеку придётся аккуратно сплетать каждое слово со следующим, и, если он не обратит внимания на ключевую часть фразы, то всю фразу поймёт неправильно.

Чтобы обеспечить такой перенос значения от одного токена к другому, требуется разрешить векторам всех токенов влиять друг на друга. Так, возвращаясь к английскому: если мы хотим наполнить слово «it» конкретной семантикой, то какая часть семантики должна поступить от предыдущих векторов в промпте, а какая – остаться от самого слова «it»?

В данной модели эта задача решается при помощи 12 наборов матриц, именуемых Q (запрос), K (ключ) и V (значение). В каждой из них по 64 столбца. Их мы получаем из векторных представлений через 768×2304-мерное линейное преобразование c_attn, веса и смещения которого хранятся в таблицах c_attn_w и c_attn_b.

Результатом c_attn является матрица со n_token строк и 2304 столбцами (3×12×64). Она состоит из 12 Q-матриц, 12 K-матриц и 12 V-матриц, упорядоченных горизонтально именно в таком порядке.

Каждый набор, состоящий из Q, K и V, называется «головой». С их помощью выполняется шаг под названием «многоголовое условное внутреннее внимание», на котором вычисляется функция внимания.

Она вычисляется по этой формуле:

где softmax – это функция нормализации весов. Она определяется так:

M - это матрица-константа, именуемая «условной маской». Она определяется так:

Функция Softmax обнуляет все отрицательные бесконечности.

Почему необходимо использовать маски?

В промпте из предыдущего примера было 4 токена, и модель первым делом вычисляла 4 векторных представления для 4 этих токенов. По мере дальнейшей работы модели над этими векторами будет выполнено много вычислений, но в основном они пойдут независимо и параллельно. Изменения в одном векторе не затронут другие векторы, как если бы иных векторов не существовало. Векторы влияют друг на друга только в пределах блока внутреннего внимания.

Как только модель справится с математикой, претенденты на роль следующего токена будут выбираться исключительно исходя из последнего векторного представления. Вся информация должна направляться именно к этому последнему вектору, а не прочь от него. Временные значения последнего вектора не должны влиять на временные значения предыдущих векторов, использовавшихся в ходе прямого распространения по данной модели.

Именно поэтому мы «маскируем» позднейшие векторы, чтобы они не влияли на более ранние через этот конкретный канал. В этом и заключается условность «многоголового условного внутреннего внимания».

Почему матрицы называются "запрос", "ключ" и "значение"?

Честно говоря, даже не уверен, что это хорошая аналогия. Но, тем не менее, попытаюсь объяснить, какова логика таких названий.

Как правило, в машинном обучении при вычислениях не должны использоваться циклы переменной длины или ветвление инструкций. Все задачи должны решаться компоновкой простых аналитических функций (сложение, умножение, возведение в степень, логарифмы и тригонометрия). Так обеспечивается обратное распространение для эффективной реализации которого требуются такие технологии, как автоматическое дифференцирование.

Математическая модель хранилища ключей и значений заключена в таком выражении:

Но это не гладкая дифференцируемая функция, и с обратным распространением она работать не будет. Чтобы формула работала, необходимо получить гладкую функцию, которая была бы близка к v, когда k близка к q, и близка к 0 в иных случаях.

Для этой цели отлично подходит Гауссово распределение («колоколообразная кривая») "bell curve"), отмасштабированная к v с ожиданием k и достаточно небольшим стандартным отклонением:

где σ - произвольный параметр, определяющий, насколько «остра» колоколообразная кривая.

Если взять в векторном пространстве с достаточно большим количеством измерений фиксированный вектор K и несколько векторов Q, которые случайным и равномерным образом отклоняются от K в каждом из измерений, то их скалярные произведения сложатся именно в колоколообразную кривую. Соответственно, в векторном пространстве «дифференцируемое хранилище ключей и значений» можно смоделировать при помощи выражения

того самого, которым мы пользовались в нашей функции внимания.

Опять же, эта аналогия немного натянута. Лучше не слишком зацикливаться на концептуальной составляющей внимания, то есть, на потоке операций, хеш-таблицах и пр. Можете считать, что они просто вдохновили меня на описанный математический фокус, который я догадался протестировать – и на практике он оказался весьма хорош.

Проиллюстрирую этот шаг:

WITH    embeddings AS
        (
        SELECT  place, values
        FROM    UNNEST(ARRAY[6307, 47701, 318, 1049]) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        ),
        c_attn_w AS
        (
        SELECT  *
        FROM    c_attn_w
        WHERE   block = 0
        ),
        c_attn_b AS
        (
        SELECT  *
        FROM    c_attn_b
        WHERE   block = 0
        ),
        ln_1_g AS
        (
        SELECT  *
        FROM    ln_1_g
        WHERE   block = 0
        ),
        ln_1_b AS
        (
        SELECT  *
        FROM    ln_1_b
        WHERE   block = 0
        ),
        mha_norm AS
        (
        SELECT  place, mm.values + c_attn_b.values AS values
        FROM    (
                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                FROM    (
                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                        FROM    (
                                SELECT  place, norm.values
                                FROM    embeddings
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  AVG(value) AS mean,
                                                VAR_POP(value) AS variance
                                        FROM    UNNEST(values::REAL[]) value
                                        ) agg
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                        ) norm
                                ) agg
                        CROSS JOIN
                                ln_1_b
                        CROSS JOIN
                                ln_1_g
                        ) layer_norm
                CROSS JOIN
                        c_attn_w
                GROUP BY
                        place
                ) mm
        CROSS JOIN
                c_attn_b
        ),
        head AS
        (
        SELECT  place,
                (values::REAL[])[1:64]::VECTOR(64) AS q,
                (values::REAL[])[1 + 768:64 + 768]::VECTOR(64) AS k,
                (values::REAL[])[1 + 1536:64 + 1536]::VECTOR(64) AS v
        FROM    mha_norm
        ),
        sm_input AS
        (
        SELECT  h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
        FROM    head h1
        CROSS JOIN
                head h2
        ),
        sm_diff AS
        (
        SELECT  x, y, value - MAX(value) OVER (PARTITION BY x) AS diff
        FROM    sm_input
        ),
        sm_exp AS
        (
        SELECT  x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
        FROM    sm_diff
        ),
        softmax AS
        (
        SELECT  x, y AS place, e / SUM(e) OVER (PARTITION BY x) AS value
        FROM    sm_exp
        ),
        attention AS
        (
        SELECT  place, (ARRAY_AGG(value ORDER BY ordinality))[:3] AS values
        FROM    (
                SELECT  x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * head.v) AS values
                FROM    softmax
                JOIN    head
                USING   (place)
                GROUP BY
                        x
                ) q
        CROSS JOIN LATERAL
                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
        GROUP BY
                place
        )
SELECT  place,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((q::REAL[])[:3]) AS n) AS q,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((k::REAL[])[:3]) AS n) AS k,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((v::REAL[])[:3]) AS n) AS v,
        matrix,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((values::REAL[])[:3]) AS n) AS attention
FROM    head
JOIN    attention
USING   (place)
JOIN    (
        SELECT  x AS place, STRING_AGG(CASE WHEN value > 0 THEN TO_CHAR(value, '0.00') ELSE '    0' END, ' ' ORDER BY place) AS matrix
        FROM    softmax
        GROUP BY
                x
        ) softmax_grouped
USING   (place)

Вот что мы сделали:

1. Прежде, чем вычислять функцию внимания, мы нормализовали векторы при помощи линейного преобразования R’ = RГ₁ + B₁. Матрица Г₁ и вектор B₁называются, соответственно, «масштабирование» и «сдвиг». Это параметры, изученные моделью, которые хранятся в таблицах ln_1_g и ln_1_b

2. Мы показываем только первую голову первого слоя, используемого в этом алгоритме. После того, как умножим векторы на изученные коэффициенты из c_attn_w и c_attn_b («вес» и «смещение»), порежем полученные в результате 2304-мерные векторы. Возьмём 64-мерные векторы, начинающиеся в позициях 0, 768 и 1536. Они соответствуют векторам Q, K и V первой головы.

3. EXP в PostgreSQL плохо работает с очень малыми числами, и именно поэтому мы прибегаем к нулю, если EXP получает аргумент менее -745,13.

4. Для каждого вектора мы показываем только первые три элемента. Марицу внимания показываем полностью.

Итак, значение первого вектора копируется в вывод как есть (так мы поступаем с первым значением на каждом слое алгоритма). Это означает, что, когда модель уже обучена, результирующее векторное представление первого токена будет определяться только значением первого токена. В принципе, на этапе рекурсивного вывода, пока токены только добавляются в промпт, по сравнению с предыдущей итерацией изменится лишь самое последнее векторное представление в выводе. Именно поэтому применяется условная маска.

Заглянем немного вперёд: блок внимания – это единственное место во всём алгоритме, где токены могут влиять друг на друга на этапе прямого прохода. Поскольку на данном этапе мы не позволяем позднейшим токенам влиять на более раннее (и отключили такую возможность), все вычисления, проделанные над более ранними токенами, можно повторно использовать на разных итерациях прямого прохода по модели.

Напомню, модель при работе добавляет токены в промпт. Если исходный (токенизированный) промпт – это «Post greSQL Ġis Ġgreat», а следующий, например, будет «Post greSQL Ġis Ġgreat Ġfor», то все результаты вычислений, проделанных над первыми четырьмя токенами, можно будет повторно использовать и в новом промпте. Они никогда не изменятся, независимо от того, что ещё будет прикреплено к этому промпту.

В статье Джея Муди, которую я привёл для примера, этот аспект не задействуется (равно как и в моей статье – для простоты), но в оригинальной реализации GPT2 он задействован.

Закончив работу со всеми головами, получаем 12 матриц. Каждая из них будет по 64 столбца в ширину и по n_tokens строк в высоту. Чтобы вновь отобразить её на размерность векторных представлений (768), нам просто нужно составить эти матрицы горизонтально.

Последний этап обработки многоголового внимания связан с проецированием значений путём линейного преобразования в том же самом измерении. Соответствующие веса и смещения хранятся в таблицах c_proj_w и c_proj_b.

Ниже приведён полный код, описывающий реализацию многоголового внимания в первом слое:

WITH    embeddings AS
        (
        SELECT  place, values
        FROM    UNNEST(ARRAY[6307, 47701, 318, 1049]) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        ),
        c_proj_w AS
        (
        SELECT  *
        FROM    c_proj_w
        WHERE   block = 0
        ),
        c_proj_b AS
        (
        SELECT  *
        FROM    c_proj_b
        WHERE   block = 0
        ),
        mlp_c_fc_w AS
        (
        SELECT  *
        FROM    mlp_c_fc_w
        WHERE   block = 0
        ),
        mlp_c_fc_b AS
        (
        SELECT  *
        FROM    mlp_c_fc_b
        WHERE   block = 0
        ),
        mlp_c_proj_w AS
        (
        SELECT  *
        FROM    mlp_c_proj_w
        WHERE   block = 0
        ),
        mlp_c_proj_b AS
        (
        SELECT  *
        FROM    mlp_c_proj_b
        WHERE   block = 0
        ),
        c_attn_w AS
        (
        SELECT  *
        FROM    c_attn_w
        WHERE   block = 0
        ),
        c_attn_b AS
        (
        SELECT  *
        FROM    c_attn_b
        WHERE   block = 0
        ),
        ln_1_g AS
        (
        SELECT  *
        FROM    ln_1_g
        WHERE   block = 0
        ),
        ln_1_b AS
        (
        SELECT  *
        FROM    ln_1_b
        WHERE   block = 0
        ),
        mha_norm AS
        (
        SELECT  place, mm.values + c_attn_b.values AS values
        FROM    (
                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                FROM    (
                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                        FROM    (
                                SELECT  place, norm.values
                                FROM    embeddings
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  AVG(value) AS mean,
                                                VAR_POP(value) AS variance
                                        FROM    UNNEST(values::REAL[]) value
                                        ) agg
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                        ) norm
                                ) agg
                        CROSS JOIN
                                ln_1_b
                        CROSS JOIN
                                ln_1_g
                        ) layer_norm
                CROSS JOIN
                        c_attn_w
                GROUP BY
                        place
                ) mm
        CROSS JOIN
                c_attn_b
        ),
        heads AS
        (
        SELECT  place, head,
                (values::REAL[])[(head * 64 + 1):(head * 64 + 64)]::VECTOR(64) AS q,
                (values::REAL[])[(head * 64 + 1 + 768):(head * 64 + 64 + 768)]::VECTOR(64) AS k,
                (values::REAL[])[(head * 64 + 1 + 1536):(head * 64 + 64 + 1536)]::VECTOR(64) AS v
        FROM    mha_norm
        CROSS JOIN
                GENERATE_SERIES(0, 11) head
        ),
        sm_input AS
        (
        SELECT  head, h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
        FROM    heads h1
        JOIN    heads h2
        USING   (head)
        ),
        sm_diff AS
        (
        SELECT  head, x, y, value - MAX(value) OVER (PARTITION BY head, x) AS diff
        FROM    sm_input
        ),
        sm_exp AS
        (
        SELECT  head, x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
        FROM    sm_diff
        ),
        softmax AS
        (
        SELECT  head, x, y AS place, e / SUM(e) OVER (PARTITION BY head, x) AS value
        FROM    sm_exp
        ),
        attention AS
        (
        SELECT  place, ARRAY_AGG(value ORDER BY head * 64 + ordinality)::VECTOR(768) AS values
        FROM    (
                SELECT  head, x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * heads.v) AS values
                FROM    softmax
                JOIN    heads
                USING   (head, place)
                GROUP BY
                        head, x
                ) q
        CROSS JOIN LATERAL
                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
        GROUP BY
                place
        ),
        mha AS
        (
        SELECT  place, w.values + c_proj_b.values AS values
        FROM    (
                SELECT  attention.place, ARRAY_AGG(INNER_PRODUCT(attention.values, c_proj_w.values) ORDER BY c_proj_w.place)::VECTOR(768) AS values
                FROM    attention
                CROSS JOIN
                        c_proj_w
                GROUP BY
                        attention.place
                ) w
        CROSS JOIN
                c_proj_b
        )
SELECT  place,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((values::REAL[])[:10]) AS n) AS q
FROM    mha

Прежде чем результаты многоголового внимания будут переданы на следующий шаг, к ним нужно добавить оригинальные входные данные. Этот фокус был описан ещё в исходной статье по трансформерам. Предполагается, что он должен помочь с затухающими и взрывными градиентами.

Это распространённая проблема при обучении: иногда градиенты параметров оказываются слишком малы или слишком велики. Если менять их при очередной итерации обучения, это также очень слабо влияет на функцию потерь (поэтому модель сходится очень медленно). Бывает и обратный эффект: даже минимальное изменение отбрасывает функцию потерь слишком далеко от локального минимума, тем самым обесценивая всю работу по обучению.

Прямое распространение

Именно в этом и заключается работа глубоких нейронных сетей. Большая часть параметров модели на самом деле используется именно на этом этапе.

Здесь мы имеем дело с многослойным перцептроном, у которого три слоя (768, 3072, 768), а в качестве функции активации используем линейную единицу гауссовской ошибки (GELU):

Как показывает практика, эта функция даёт очень хорошие результаты при работе с глубокими нейронными сетями. Её можно аналитически аппроксимировать вот так:

Изученные параметры линейного преобразования для связей в слое называются c_fc (768 → 3072) и c_proj (3072 → 768). Значения с первого слоя сначала нормализуются при помощи коэффициентов, содержащихся в изученном параметре ln_2. По завершении этапа прямого распространения его ввод вновь добавляется к выводу. Этот элемент также входит в самый первый вариант дизайна трансформеров. Весь этап прямого распространения выглядит так:

А вот как это делается на SQL:

WITH    embeddings AS
        (
        SELECT  place, values
        FROM    UNNEST(ARRAY[6307, 47701, 318, 1049]) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        ),
        c_proj_w AS
        (
        SELECT  *
        FROM    c_proj_w
        WHERE   block = 0
        ),
        c_proj_b AS
        (
        SELECT  *
        FROM    c_proj_b
        WHERE   block = 0
        ),
        mlp_c_fc_w AS
        (
        SELECT  *
        FROM    mlp_c_fc_w
        WHERE   block = 0
        ),
        mlp_c_fc_b AS
        (
        SELECT  *
        FROM    mlp_c_fc_b
        WHERE   block = 0
        ),
        mlp_c_proj_w AS
        (
        SELECT  *
        FROM    mlp_c_proj_w
        WHERE   block = 0
        ),
        mlp_c_proj_b AS
        (
        SELECT  *
        FROM    mlp_c_proj_b
        WHERE   block = 0
        ),
        c_attn_w AS
        (
        SELECT  *
        FROM    c_attn_w
        WHERE   block = 0
        ),
        c_attn_b AS
        (
        SELECT  *
        FROM    c_attn_b
        WHERE   block = 0
        ),
        ln_1_g AS
        (
        SELECT  *
        FROM    ln_1_g
        WHERE   block = 0
        ),
        ln_1_b AS
        (
        SELECT  *
        FROM    ln_1_b
        WHERE   block = 0
        ),
        ln_2_b AS
        (
        SELECT  *
        FROM    ln_2_b
        WHERE   block = 0
        ),
        ln_2_g AS
        (
        SELECT  *
        FROM    ln_2_g
        WHERE   block = 0
        ),
        mha_norm AS
        (
        SELECT  place, mm.values + c_attn_b.values AS values
        FROM    (
                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                FROM    (
                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                        FROM    (
                                SELECT  place, norm.values
                                FROM    embeddings
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  AVG(value) AS mean,
                                                VAR_POP(value) AS variance
                                        FROM    UNNEST(values::REAL[]) value
                                        ) agg
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                        ) norm
                                ) agg
                        CROSS JOIN
                                ln_1_b
                        CROSS JOIN
                                ln_1_g
                        ) layer_norm
                CROSS JOIN
                        c_attn_w
                GROUP BY
                        place
                ) mm
        CROSS JOIN
                c_attn_b
        ),
        heads AS
        (
        SELECT  place, head,
                (values::REAL[])[(head * 64 + 1):(head * 64 + 64)]::VECTOR(64) AS q,
                (values::REAL[])[(head * 64 + 1 + 768):(head * 64 + 64 + 768)]::VECTOR(64) AS k,
                (values::REAL[])[(head * 64 + 1 + 1536):(head * 64 + 64 + 1536)]::VECTOR(64) AS v
        FROM    mha_norm
        CROSS JOIN
                GENERATE_SERIES(0, 11) head
        ),
        sm_input AS
        (
        SELECT  head, h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
        FROM    heads h1
        JOIN    heads h2
        USING   (head)
        ),
        sm_diff AS
        (
        SELECT  head, x, y, value - MAX(value) OVER (PARTITION BY head, x) AS diff
        FROM    sm_input
        ),
        sm_exp AS
        (
        SELECT  head, x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
        FROM    sm_diff
        ),
        softmax AS
        (
        SELECT  head, x, y AS place, e / SUM(e) OVER (PARTITION BY head, x) AS value
        FROM    sm_exp
        ),
        attention AS
        (
        SELECT  place, ARRAY_AGG(value ORDER BY head * 64 + ordinality)::VECTOR(768) AS values
        FROM    (
                SELECT  head, x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * heads.v) AS values
                FROM    softmax
                JOIN    heads
                USING   (head, place)
                GROUP BY
                        head, x
                ) q
        CROSS JOIN LATERAL
                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
        GROUP BY
                place
        ),
        mha AS
        (
        SELECT  place, w.values + c_proj_b.values + embeddings.values AS values
        FROM    (
                SELECT  attention.place, ARRAY_AGG(INNER_PRODUCT(attention.values, c_proj_w.values) ORDER BY c_proj_w.place)::VECTOR(768) AS values
                FROM    attention
                CROSS JOIN
                        c_proj_w
                GROUP BY
                        attention.place
                ) w
        CROSS JOIN
                c_proj_b
        JOIN    embeddings
        USING   (place)
        ),
        ffn_norm AS
        (
        SELECT  place, agg.values * ln_2_g.values + ln_2_b.values AS values
        FROM    (
                SELECT  place, norm.values
                FROM    mha
                CROSS JOIN LATERAL
                        (
                        SELECT  AVG(value) AS mean,
                                VAR_POP(value) AS variance
                        FROM    UNNEST(values::REAL[]) value
                        ) agg
                CROSS JOIN LATERAL
                        (
                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                        ) norm
                ) agg
        CROSS JOIN
                ln_2_b
        CROSS JOIN
                ln_2_g
        ),
        ffn_a AS
        (
        SELECT  gelu.place, gelu.values
        FROM    (
                SELECT  place, w.values + mlp_c_fc_b.values AS values
                FROM    (
                        SELECT  ffn_norm.place, ARRAY_AGG(INNER_PRODUCT(ffn_norm.values, mlp_c_fc_w.values) ORDER BY mlp_c_fc_w.place)::VECTOR(3072) AS values
                        FROM    ffn_norm
                        CROSS JOIN
                                mlp_c_fc_w
                        GROUP BY
                                ffn_norm.place
                        ) w
                CROSS JOIN
                        mlp_c_fc_b
                ) v
        CROSS JOIN LATERAL
                (
                SELECT  place, ARRAY_AGG(0.5 * value * (1 + TANH(0.797884560802 * (value + 0.044715 * value*value*value))) ORDER BY ordinality)::VECTOR(3072) AS values
                FROM    UNNEST(values::REAL[]) WITH ORDINALITY n (value, ordinality)
                GROUP BY
                        place
                ) gelu
        ),
        ffn AS
        (
        SELECT  place, w.values + mlp_c_proj_b.values + mha.values AS values
        FROM    (
                SELECT  ffn_a.place, ARRAY_AGG(INNER_PRODUCT(ffn_a.values, mlp_c_proj_w.values) ORDER BY mlp_c_proj_w.place)::VECTOR(768) AS values
                FROM    ffn_a
                CROSS JOIN
                        mlp_c_proj_w
                GROUP BY
                        ffn_a.place
                ) w
        CROSS JOIN
                mlp_c_proj_b
        JOIN    mha
        USING   (place)
        )
SELECT  place,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((values::REAL[])[:10]) AS n) AS q
FROM    ffn

Именно этот вывод получаем из первого блока GPT2.

Блоки

Операции, рассмотренные на предыдущих этапах, повторяются в каждом из слоёв (именуемых «блоками»). Блоки выстраиваются в виде конвейера, так, что вывод из предыдущего блока сразу подаётся на ввод следующему. У каждого из блоков – свой набор изученных параметров.

В SQL потребуется соединить блоки при помощи рекурсивного CTE.

Как только финальный блок выдаст значения, результат потребуется нормализовать при помощи изученного параметра ln_f.

Вот как в итоге будет выглядеть модель:

А вот как результат выглядит на SQL:

WITH    RECURSIVE
        initial AS
        (
        SELECT  ARRAY[6307, 47701, 318, 1049] AS input
        ),
        hparams AS
        (
        SELECT  12 AS n_block
        ),
        embeddings AS
        (
        SELECT  place, values
        FROM    initial
        CROSS JOIN
                hparams
        CROSS JOIN LATERAL
                UNNEST(input) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        ),
        transform AS
        (
        SELECT  0 AS block, place, values
        FROM    embeddings
        UNION ALL
        (
        WITH    previous AS
                (
                SELECT  *
                FROM    transform
                )
        SELECT  block + 1 AS block, transformed_layer.*
        FROM    hparams
        CROSS JOIN LATERAL
                (
                SELECT  block
                FROM    previous
                WHERE   block < 12
                LIMIT   1
                ) q
        CROSS JOIN LATERAL
                (
                WITH    ln_2_b AS
                        (
                        SELECT  *
                        FROM    ln_2_b
                        WHERE   block = q.block
                        ),
                        ln_2_g AS
                        (
                        SELECT  *
                        FROM    ln_2_g
                        WHERE   block = q.block
                        ),
                        c_proj_w AS
                        (
                        SELECT  *
                        FROM    c_proj_w
                        WHERE   block = q.block
                        ),
                        c_proj_b AS
                        (
                        SELECT  *
                        FROM    c_proj_b
                        WHERE   block = q.block
                        ),
                        mlp_c_fc_w AS
                        (
                        SELECT  *
                        FROM    mlp_c_fc_w
                        WHERE   block = q.block
                        ),
                        mlp_c_fc_b AS
                        (
                        SELECT  *
                        FROM    mlp_c_fc_b
                        WHERE   block = q.block
                        ),
                        mlp_c_proj_w AS
                        (
                        SELECT  *
                        FROM    mlp_c_proj_w
                        WHERE   block = q.block
                        ),
                        mlp_c_proj_b AS
                        (
                        SELECT  *
                        FROM    mlp_c_proj_b
                        WHERE   block = q.block
                        ),
                        c_attn_w AS
                        (
                        SELECT  *
                        FROM    c_attn_w
                        WHERE   block = q.block
                        ),
                        c_attn_b AS
                        (
                        SELECT  *
                        FROM    c_attn_b
                        WHERE   block = q.block
                        ),
                        ln_1_g AS
                        (
                        SELECT  *
                        FROM    ln_1_g
                        WHERE   block = q.block
                        ),
                        ln_1_b AS
                        (
                        SELECT  *
                        FROM    ln_1_b
                        WHERE   block = q.block
                        ),
                        mha_norm AS
                        (
                        SELECT  place, mm.values + c_attn_b.values AS values
                        FROM    (
                                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                                FROM    (
                                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                                        FROM    (
                                                SELECT  place, norm.values
                                                FROM    previous
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  AVG(value) AS mean,
                                                                VAR_POP(value) AS variance
                                                        FROM    UNNEST(values::REAL[]) value
                                                        ) agg
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                                        ) norm
                                                ) agg
                                        CROSS JOIN
                                                ln_1_b
                                        CROSS JOIN
                                                ln_1_g
                                        ) layer_norm
                                CROSS JOIN
                                        c_attn_w
                                GROUP BY
                                        place
                                ) mm
                        CROSS JOIN
                                c_attn_b
                        ),
                        heads AS
                        (
                        SELECT  place, head,
                                (values::REAL[])[(head * 64 + 1):(head * 64 + 64)]::VECTOR(64) AS q,
                                (values::REAL[])[(head * 64 + 1 + 768):(head * 64 + 64 + 768)]::VECTOR(64) AS k,
                                (values::REAL[])[(head * 64 + 1 + 1536):(head * 64 + 64 + 1536)]::VECTOR(64) AS v
                        FROM    mha_norm
                        CROSS JOIN
                                GENERATE_SERIES(0, 11) head
                        ),
                        sm_input AS
                        (
                        SELECT  head, h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
                        FROM    heads h1
                        JOIN    heads h2
                        USING   (head)
                        ),
                        sm_diff AS
                        (
                        SELECT  head, x, y, value - MAX(value) OVER (PARTITION BY head, x) AS diff
                        FROM    sm_input
                        ),
                        sm_exp AS
                        (
                        SELECT  head, x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
                        FROM    sm_diff
                        ),
                        softmax AS
                        (
                        SELECT  head, x, y AS place, e / SUM(e) OVER (PARTITION BY head, x) AS value
                        FROM    sm_exp
                        ),
                        attention AS
                        (
                        SELECT  place, ARRAY_AGG(value ORDER BY head * 64 + ordinality)::VECTOR(768) AS values
                        FROM    (
                                SELECT  head, x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * heads.v) AS values
                                FROM    softmax
                                JOIN    heads
                                USING   (head, place)
                                GROUP BY
                                        head, x
                                ) q
                        CROSS JOIN LATERAL
                                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
                        GROUP BY
                                place
                        ),
                        mha AS
                        (
                        SELECT  place, w.values + c_proj_b.values + previous.values AS values
                        FROM    (
                                SELECT  attention.place, ARRAY_AGG(INNER_PRODUCT(attention.values, c_proj_w.values) ORDER BY c_proj_w.place)::VECTOR(768) AS values
                                FROM    attention
                                CROSS JOIN
                                        c_proj_w
                                GROUP BY
                                        attention.place
                                ) w
                        CROSS JOIN
                                c_proj_b
                        JOIN    previous
                        USING   (place)
                        ),
                        ffn_norm AS
                        (
                        SELECT  place, agg.values * ln_2_g.values + ln_2_b.values AS values
                        FROM    (
                                SELECT  place, norm.values
                                FROM    mha
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  AVG(value) AS mean,
                                                VAR_POP(value) AS variance
                                        FROM    UNNEST(values::REAL[]) value
                                        ) agg
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                        ) norm
                                ) agg
                        CROSS JOIN
                                ln_2_b
                        CROSS JOIN
                                ln_2_g
                        ),
                        ffn_a AS
                        (
                        SELECT  gelu.place, gelu.values
                        FROM    (
                                SELECT  place, w.values + mlp_c_fc_b.values AS values
                                FROM    (
                                        SELECT  ffn_norm.place, ARRAY_AGG(INNER_PRODUCT(ffn_norm.values, mlp_c_fc_w.values) ORDER BY mlp_c_fc_w.place)::VECTOR(3072) AS values
                                        FROM    ffn_norm
                                        CROSS JOIN
                                                mlp_c_fc_w
                                        GROUP BY
                                                ffn_norm.place
                                        ) w
                                CROSS JOIN
                                        mlp_c_fc_b
                                ) v
                        CROSS JOIN LATERAL
                                (
                                SELECT  place, ARRAY_AGG(0.5 * value * (1 + TANH(0.797884560802 * (value + 0.044715 * value*value*value))) ORDER BY ordinality)::VECTOR(3072) AS values
                                FROM    UNNEST(values::REAL[]) WITH ORDINALITY n (value, ordinality)
                                GROUP BY
                                        place
                                ) gelu
                        ),
                        ffn AS
                        (
                        SELECT  place, w.values + mlp_c_proj_b.values + mha.values AS values
                        FROM    (
                                SELECT  ffn_a.place, ARRAY_AGG(INNER_PRODUCT(ffn_a.values, mlp_c_proj_w.values) ORDER BY mlp_c_proj_w.place)::VECTOR(768) AS values
                                FROM    ffn_a
                                CROSS JOIN
                                        mlp_c_proj_w
                                GROUP BY
                                        ffn_a.place
                                ) w
                        CROSS JOIN
                                mlp_c_proj_b
                        JOIN    mha
                        USING   (place)
                        )
                SELECT  *
                FROM    ffn
                ) transformed_layer
        )
        ),
        block_output AS
        (
        SELECT  *
        FROM    hparams
        JOIN    transform
        ON      transform.block = n_block
        ),
        ln_f AS
        (
        SELECT  place, norm.values * ln_f_g.values + ln_f_b.values AS values
        FROM    block_output
        CROSS JOIN LATERAL
                (
                SELECT  AVG(value) AS mean,
                        VAR_POP(value) AS variance
                FROM    UNNEST(values::REAL[]) AS n(value)
                ) agg
        CROSS JOIN LATERAL
                (
                SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n (value, ordinality)
                ) norm
        CROSS JOIN
                ln_f_b
        CROSS JOIN
                ln_f_g
        )
SELECT  place,
        (SELECT STRING_AGG(TO_CHAR(n, 'S0.000'), ' ') || ' …' FROM UNNEST((values::REAL[])[:10]) AS n) AS q
FROM    ln_f

Это вывод модели.

Четвёртый вектор – это и есть фактическое представление следующего токена, предсказанного моделью. Нам просто нужно отобразить его обратно на токены.

Токены

У нас уже есть векторное представление (768-мерное), в котором, согласно модели, заключены семантика и грамматика наиболее вероятного продолжения промпта. Теперь нам нужно отобразить его обратно на токен.

Одна из первых операций, совершаемых моделью – это отображение токенов на их векторные представления. Эта операция делается при помощи матрицы wpe размером 50257×768. Той же самой матрицей нам потребуется воспользоваться, чтобы отобразить векторное представление обратно на токен.

Проблема в том, что строго обратное отображение выполнить невозможно: (вероятно) векторное представление не будет совпадать ни с одной из строк в матрице. Поэтому нам придётся найти токен, который «ближе всего» к векторному представлению.

Поскольку (как мы надеемся), в измерениях векторных представлений заключены некоторые семантические и грамматические аспекты токена, необходимо сопоставить их как можно точнее. Один из способов консолидировать «степень близости» каждого из измерений – вычислить скалярное произведение двух векторных представлений. Чем выше будет это значение, тем ближе токен к прогнозу.

Для этого умножим векторное представление на матрицу wte. В результате получим матрицу из одного столбца и 50257 строк. Каждое значение в этом результате будет произведением спрогнозированного вектора и векторного представления токена. Чем выше это число, тем вероятнее, что токен станет продолжением промпта.

Чтобы выбрать следующий токен, нужно просто преобразовать значения сходства в значения вероятности. Для этого нам пригодится старая добрая функция softmax (та самая, при помощи которой мы уже нормализовали веса внимания).

Почему стоит использовать softmax для работы с вероятностями?

Softmax – это удобное свойство аксиомы выбора Льюса. Оно таково: относительная вероятность двух вариантов не зависит от наличия прочих вероятностных вариантов. Если вариант A влвое вероятнее варианта B, то это соотношение не зависит от наличия или отсутствия других вариантов (хотя, конечно, абсолютные значения при этом могут измениться).

Вектор скалярных произведений («логит» в терминологии ИИ) содержит произвольные значения, которые могут не укладываться в какую-либо шкалу. Если балл A выше, чем балл B, то известно, что A вероятнее – а больше ничего не известно. Можно подкорректировать входные значения softmax так, как нам угодно, главное, соблюдать их порядок (более крупные значения остаются более крупными).

Распространённый подход, позволяющий этого добиться – нормализация значений путём вычитания наибольшего значения из каждого значения в множестве (так что наибольшее значение становится равным 0, а все остальные – отрицательным числам). Затем берём фиксированное количество наивысших значений (скажем, топ-5 или топ-10). Наконец, перед передачей всех значений softmax умножаем их на константу.

Количество наивысших значений, с которым мы работаем, обычно называется top_n, а множитель-константа (вернее, обратное ему число) называется «температурой» (Т). Чем выше температура, тем более гладкое распределение вероятностей у нас получится, и тем выше вероятность, что на место продолжения будет выбран не первый попавшийся токен.

Формула для расчёта вероятностей токенов

где scores — это множество из наивысших top_n баллов.

Почему этот показатель называется "температурой"

Функция softmax также называется распределение Больцмана. Она широко используется в физике. Среди прочего, на ней основана барометрическая формула, по которой рассчитывается изменение плотности воздуха в зависимости от высоты.

Как известно, тёплый воздух поднимается вверх и распределяется на сравнительно большой высоте. В горячем воздухе сравнительно высока вероятность, что молекула ль частых столкновений с другими молекулами заберётся на такую высоту, куда в ином случае бы не попала. В отличие от ситуации с более холодными температурами, плотность воздуха увеличивается на больших высотах и падает на уровне моря.

Сравните, как воздух движется при разных температурах:

\Иллюстрация Доминика Форда, Bouncing Balls and the Boltzmann Distribution

Аналогично, в рассматриваемом нами примере, чем больше «температура», тем выше вероятность, что будет выбран не самый очевидный токен (разумеется, за счёт наиболее очевидных). Логический вывод становится менее предсказуемым и более «творческим».

Давайте выразим всё это на SQL. У нас был промпт «PostgreSQL is great». Вот первые 5 токенов, которые, в соответствии с этой моделью, являются наиболее вероятными продолжениями этой фразы. Показаны их вероятности при разной температуре:

WITH    RECURSIVE
        initial AS
        (
        SELECT  ARRAY[6307, 47701, 318, 1049] AS input
        ),
        hparams AS
        (
        SELECT  12 AS n_block,
                5 AS top_n,
                ARRAY_LENGTH(input, 1) AS n_seq
        FROM    initial
        ),
        embeddings AS
        (
        SELECT  place, values
        FROM    initial
        CROSS JOIN
                hparams
        CROSS JOIN LATERAL
                UNNEST(input) WITH ORDINALITY AS tokens (token, ordinality)
        CROSS JOIN LATERAL
                (
                SELECT  ordinality - 1 AS place
                ) o
        CROSS JOIN LATERAL
                (
                SELECT  wte.values + wpe.values AS values
                FROM    wte
                CROSS JOIN
                        wpe
                WHERE   wte.token = tokens.token
                        AND wpe.place = o.place
                ) embedding
        ),
        transform AS
        (
        SELECT  0 AS block, place, values
        FROM    embeddings
        UNION ALL
        (
        WITH    previous AS
                (
                SELECT  *
                FROM    transform
                )
        SELECT  block + 1 AS block, transformed_layer.*
        FROM    hparams
        CROSS JOIN LATERAL
                (
                SELECT  block
                FROM    previous
                WHERE   block < 12
                LIMIT   1
                ) q
        CROSS JOIN LATERAL
                (
                WITH    ln_2_b AS
                        (
                        SELECT  *
                        FROM    ln_2_b
                        WHERE   block = q.block
                        ),
                        ln_2_g AS
                        (
                        SELECT  *
                        FROM    ln_2_g
                        WHERE   block = q.block
                        ),
                        c_proj_w AS
                        (
                        SELECT  *
                        FROM    c_proj_w
                        WHERE   block = q.block
                        ),
                        c_proj_b AS
                        (
                        SELECT  *
                        FROM    c_proj_b
                        WHERE   block = q.block
                        ),
                        mlp_c_fc_w AS
                        (
                        SELECT  *
                        FROM    mlp_c_fc_w
                        WHERE   block = q.block
                        ),
                        mlp_c_fc_b AS
                        (
                        SELECT  *
                        FROM    mlp_c_fc_b
                        WHERE   block = q.block
                        ),
                        mlp_c_proj_w AS
                        (
                        SELECT  *
                        FROM    mlp_c_proj_w
                        WHERE   block = q.block
                        ),
                        mlp_c_proj_b AS
                        (
                        SELECT  *
                        FROM    mlp_c_proj_b
                        WHERE   block = q.block
                        ),
                        c_attn_w AS
                        (
                        SELECT  *
                        FROM    c_attn_w
                        WHERE   block = q.block
                        ),
                        c_attn_b AS
                        (
                        SELECT  *
                        FROM    c_attn_b
                        WHERE   block = q.block
                        ),
                        ln_1_g AS
                        (
                        SELECT  *
                        FROM    ln_1_g
                        WHERE   block = q.block
                        ),
                        ln_1_b AS
                        (
                        SELECT  *
                        FROM    ln_1_b
                        WHERE   block = q.block
                        ),
                        mha_norm AS
                        (
                        SELECT  place, mm.values + c_attn_b.values AS values
                        FROM    (
                                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                                FROM    (
                                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                                        FROM    (
                                                SELECT  place, norm.values
                                                FROM    previous
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  AVG(value) AS mean,
                                                                VAR_POP(value) AS variance
                                                        FROM    UNNEST(values::REAL[]) value
                                                        ) agg
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                                        ) norm
                                                ) agg
                                        CROSS JOIN
                                                ln_1_b
                                        CROSS JOIN
                                                ln_1_g
                                        ) layer_norm
                                CROSS JOIN
                                        c_attn_w
                                GROUP BY
                                        place
                                ) mm
                        CROSS JOIN
                                c_attn_b
                        ),
                        heads AS
                        (
                        SELECT  place, head,
                                (values::REAL[])[(head * 64 + 1):(head * 64 + 64)]::VECTOR(64) AS q,
                                (values::REAL[])[(head * 64 + 1 + 768):(head * 64 + 64 + 768)]::VECTOR(64) AS k,
                                (values::REAL[])[(head * 64 + 1 + 1536):(head * 64 + 64 + 1536)]::VECTOR(64) AS v
                        FROM    mha_norm
                        CROSS JOIN
                                GENERATE_SERIES(0, 11) head
                        ),
                        sm_input AS
                        (
                        SELECT  head, h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
                        FROM    heads h1
                        JOIN    heads h2
                        USING   (head)
                        ),
                        sm_diff AS
                        (
                        SELECT  head, x, y, value - MAX(value) OVER (PARTITION BY head, x) AS diff
                        FROM    sm_input
                        ),
                        sm_exp AS
                        (
                        SELECT  head, x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
                        FROM    sm_diff
                        ),
                        softmax AS
                        (
                        SELECT  head, x, y AS place, e / SUM(e) OVER (PARTITION BY head, x) AS value
                        FROM    sm_exp
                        ),
                        attention AS
                        (
                        SELECT  place, ARRAY_AGG(value ORDER BY head * 64 + ordinality)::VECTOR(768) AS values
                        FROM    (
                                SELECT  head, x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * heads.v) AS values
                                FROM    softmax
                                JOIN    heads
                                USING   (head, place)
                                GROUP BY
                                        head, x
                                ) q
                        CROSS JOIN LATERAL
                                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
                        GROUP BY
                                place
                        ),
                        mha AS
                        (
                        SELECT  place, w.values + c_proj_b.values + previous.values AS values
                        FROM    (
                                SELECT  attention.place, ARRAY_AGG(INNER_PRODUCT(attention.values, c_proj_w.values) ORDER BY c_proj_w.place)::VECTOR(768) AS values
                                FROM    attention
                                CROSS JOIN
                                        c_proj_w
                                GROUP BY
                                        attention.place
                                ) w
                        CROSS JOIN
                                c_proj_b
                        JOIN    previous
                        USING   (place)
                        ),
                        ffn_norm AS
                        (
                        SELECT  place, agg.values * ln_2_g.values + ln_2_b.values AS values
                        FROM    (
                                SELECT  place, norm.values
                                FROM    mha
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  AVG(value) AS mean,
                                                VAR_POP(value) AS variance
                                        FROM    UNNEST(values::REAL[]) value
                                        ) agg
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                        ) norm
                                ) agg
                        CROSS JOIN
                                ln_2_b
                        CROSS JOIN
                                ln_2_g
                        ),
                        ffn_a AS
                        (
                        SELECT  gelu.place, gelu.values
                        FROM    (
                                SELECT  place, w.values + mlp_c_fc_b.values AS values
                                FROM    (
                                        SELECT  ffn_norm.place, ARRAY_AGG(INNER_PRODUCT(ffn_norm.values, mlp_c_fc_w.values) ORDER BY mlp_c_fc_w.place)::VECTOR(3072) AS values
                                        FROM    ffn_norm
                                        CROSS JOIN
                                                mlp_c_fc_w
                                        GROUP BY
                                                ffn_norm.place
                                        ) w
                                CROSS JOIN
                                        mlp_c_fc_b
                                ) v
                        CROSS JOIN LATERAL
                                (
                                SELECT  place, ARRAY_AGG(0.5 * value * (1 + TANH(0.797884560802 * (value + 0.044715 * value*value*value))) ORDER BY ordinality)::VECTOR(3072) AS values
                                FROM    UNNEST(values::REAL[]) WITH ORDINALITY n (value, ordinality)
                                GROUP BY
                                        place
                                ) gelu
                        ),
                        ffn AS
                        (
                        SELECT  place, w.values + mlp_c_proj_b.values + mha.values AS values
                        FROM    (
                                SELECT  ffn_a.place, ARRAY_AGG(INNER_PRODUCT(ffn_a.values, mlp_c_proj_w.values) ORDER BY mlp_c_proj_w.place)::VECTOR(768) AS values
                                FROM    ffn_a
                                CROSS JOIN
                                        mlp_c_proj_w
                                GROUP BY
                                        ffn_a.place
                                ) w
                        CROSS JOIN
                                mlp_c_proj_b
                        JOIN    mha
                        USING   (place)
                        )
                SELECT  *
                FROM    ffn
                ) transformed_layer
        )
        ),
        block_output AS
        (
        SELECT  *
        FROM    hparams
        JOIN    transform
        ON      transform.block = n_block
        ),
        ln_f AS
        (
        SELECT  place, norm.values * ln_f_g.values + ln_f_b.values AS values
        FROM    block_output
        CROSS JOIN LATERAL
                (
                SELECT  AVG(value) AS mean,
                        VAR_POP(value) AS variance
                FROM    UNNEST(values::REAL[]) AS n(value)
                ) agg
        CROSS JOIN LATERAL
                (
                SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n (value, ordinality)
                ) norm
        CROSS JOIN
                ln_f_b
        CROSS JOIN
                ln_f_g
        ),
        logits AS
        (
        SELECT  logits.*
        FROM    hparams
        CROSS JOIN LATERAL
                (
                SELECT  token, INNER_PRODUCT(ln_f.values, wte.values) AS value
                FROM    ln_f
                CROSS JOIN
                        wte
                WHERE   ln_f.place = n_seq - 1
                ORDER BY
                        value DESC
                LIMIT   (top_n)
                ) logits
        ),
        temperatures (temperature) AS
        (
        VALUES
        (0.5),
        (1),
        (2)
        ),
        tokens AS
        (
        SELECT  token, value, softmax, temperature
        FROM    temperatures
        CROSS JOIN LATERAL
                (
                SELECT  *, (e / SUM(e) OVER ()) AS softmax
                FROM    (
                        SELECT  *,
                                (value - MAX(value) OVER ()) / temperature AS diff
                        FROM    logits
                        ) exp_x
                CROSS JOIN LATERAL
                        (
                        SELECT  CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
                        ) exp
                ) q
        )
SELECT  token,
        cluster,
        TO_CHAR(t1.value, 'S00.000') AS score,
        TO_CHAR(t1.softmax, '0.00') AS "temperature = 0.5",
        TO_CHAR(t2.softmax, '0.00') AS "temperature = 1",
        TO_CHAR(t3.softmax, '0.00') AS "temperature = 2"
FROM    (
        SELECT  *
        FROM    tokens
        WHERE   temperature = 0.5
        ) t1
JOIN    (
        SELECT  *
        FROM    tokens
        WHERE   temperature = 1
        ) t2
USING   (token)
JOIN    (
        SELECT  *
        FROM    tokens
        WHERE   temperature = 2
        ) t3
USING   (token)
JOIN    tokenizer
USING   (token)

Логический вывод

Вот мы и готовы перейти к реальному логическому выводу: запустить модель, выбрать токен в соответствии с полученной вероятностью, добавить токен к промпту и повторять этот процесс до тех пор, пока не будет сгенерировано достаточное количество токенов.

Как было показано выше, сама большая языковая модель является детерминированной. Это просто последовательные перемножения матриц и другие математические операции, производимые над заранее определёнными константами. Пока промпт и такие гиперпараметры как температура и топ-N остаются неизменными, вывод также остаётся неизменным.

Единственный недетерминированный процесс в данном случае – это выбор токена. В нём заложена (переменная) степень случайности. Вот почему чатботы, основанные на GPT, могут давать разные ответы на один и тот же промпт.

Воспользуемся в качестве промпта фразой «Happy New Year! I wish» и прикажем модели сгенерировать 10 новых токенов для этого промпта. Температуру установим в 2, а top_n в 5.

У меня на компьютере на этот запрос уходит 2 минуты и 44 секунды. Вот такой вывод получается:

SELECT SETSEED(0.20231231);
 
WITH    RECURSIVE
        input AS
        (
        SELECT  'Happy New Year! I wish you' AS prompt,
                10 AS threshold,
                2 AS temperature,
                1 AS top_n
        ),
        clusters AS
        (
        SELECT  part_position, bpe.*
        FROM    input
        CROSS JOIN LATERAL
                REGEXP_MATCHES(prompt, '''s|''t|''re|''ve|''m|''ll|''d| ?\w+| ?\d+| ?[^\s\w\d]+|\s+(?!\S)|\s+', 'g') WITH ORDINALITY AS rm (part, part_position)
        CROSS JOIN LATERAL
                (
                WITH    RECURSIVE
                        bpe AS
                        (
                        SELECT  (n + 1)::BIGINT AS position, character, TRUE AS continue
                        FROM    CONVERT_TO(part[1], 'UTF-8') AS bytes
                        CROSS JOIN LATERAL
                                GENERATE_SERIES(0, LENGTH(bytes) - 1) AS n
                        JOIN    encoder
                        ON      byte = GET_BYTE(bytes, n)
                        UNION ALL
                        (
                        WITH    RECURSIVE
                                base AS
                                (
                                SELECT  *
                                FROM    bpe
                                WHERE   continue
                                ),
                                bn AS
                                (
                                SELECT  ROW_NUMBER() OVER (ORDER BY position) AS position,
                                        continue,
                                        character,
                                        character || LEAD(character) OVER (ORDER BY position) AS cluster
                                FROM    base
                                ),
                                top_rank AS
                                (
                                SELECT  tokenizer.*
                                FROM    bn
                                CROSS JOIN LATERAL
                                        (
                                        SELECT  *
                                        FROM    tokenizer
                                        WHERE   tokenizer.cluster = bn.cluster
                                        LIMIT   1
                                        ) tokenizer
                                ORDER BY
                                        token
                                LIMIT   1
                                ),
                                breaks AS
                                (
                                SELECT  0::BIGINT AS position, 1 AS length
                                UNION ALL
                                SELECT  bn.position,
                                        CASE WHEN token IS NULL THEN 1 ELSE 2 END
                                FROM    breaks
                                JOIN    bn
                                ON      bn.position = breaks.position + length
                                LEFT JOIN
                                        top_rank
                                USING   (cluster)
                                )
                        SELECT  position, character, token IS NOT NULL
                        FROM    breaks
                        LEFT JOIN
                                top_rank
                        ON      1 = 1
                        CROSS JOIN LATERAL
                                (
                                SELECT  STRING_AGG(character, '' ORDER BY position) AS character
                                FROM    bn
                                WHERE   bn.position >= breaks.position
                                        AND bn.position < breaks.position + length
                                ) bn
                        WHERE   position > 0
                        )
                        )
                SELECT  position, character AS cluster
                FROM    bpe
                WHERE   NOT continue
                ) bpe
        ),
        tokens AS
        (
        SELECT  ARRAY_AGG(token ORDER BY part_position, position) AS input
        FROM    clusters
        JOIN    tokenizer
        USING   (cluster)
        ),
        gpt AS
        (
        SELECT  input, ARRAY_LENGTH(input, 1) AS original_length
        FROM    tokens
        UNION ALL
        SELECT  input || next_token.token, original_length
        FROM    gpt
        CROSS JOIN
                input
        CROSS JOIN LATERAL
                (
                WITH    RECURSIVE
                        hparams AS
                        (
                        SELECT  ARRAY_LENGTH(input, 1) AS n_seq,
                                12 AS n_block
                        ),
                        embeddings AS
                        (
                        SELECT  place, values
                        FROM    hparams
                        CROSS JOIN LATERAL
                                UNNEST(input) WITH ORDINALITY AS tokens (token, ordinality)
                        CROSS JOIN LATERAL
                                (
                                SELECT  ordinality - 1 AS place
                                ) o
                        CROSS JOIN LATERAL
                                (
                                SELECT  wte.values + wpe.values AS values
                                FROM    wte
                                CROSS JOIN
                                        wpe
                                WHERE   wte.token = tokens.token
                                        AND wpe.place = o.place
                                ) embedding
                        ),
                        transform AS
                        (
                        SELECT  0 AS block, place, values
                        FROM    embeddings
                        UNION ALL
                        (
                        WITH    previous AS
                                (
                                SELECT  *
                                FROM    transform
                                )
                        SELECT  block + 1 AS block, transformed_layer.*
                        FROM    hparams
                        CROSS JOIN LATERAL
                                (
                                SELECT  block
                                FROM    previous
                                WHERE   block < 12
                                LIMIT   1
                                ) q
                        CROSS JOIN LATERAL
                                (
                                WITH    ln_2_b AS
                                        (
                                        SELECT  *
                                        FROM    ln_2_b
                                        WHERE   block = q.block
                                        ),
                                        ln_2_g AS
                                        (
                                        SELECT  *
                                        FROM    ln_2_g
                                        WHERE   block = q.block
                                        ),
                                        c_proj_w AS
                                        (
                                        SELECT  *
                                        FROM    c_proj_w
                                        WHERE   block = q.block
                                        ),
                                        c_proj_b AS
                                        (
                                        SELECT  *
                                        FROM    c_proj_b
                                        WHERE   block = q.block
                                        ),
                                        mlp_c_fc_w AS
                                        (
                                        SELECT  *
                                        FROM    mlp_c_fc_w
                                        WHERE   block = q.block
                                        ),
                                        mlp_c_fc_b AS
                                        (
                                        SELECT  *
                                        FROM    mlp_c_fc_b
                                        WHERE   block = q.block
                                        ),
                                        mlp_c_proj_w AS
                                        (
                                        SELECT  *
                                        FROM    mlp_c_proj_w
                                        WHERE   block = q.block
                                        ),
                                        mlp_c_proj_b AS
                                        (
                                        SELECT  *
                                        FROM    mlp_c_proj_b
                                        WHERE   block = q.block
                                        ),
                                        c_attn_w AS
                                        (
                                        SELECT  *
                                        FROM    c_attn_w
                                        WHERE   block = q.block
                                        ),
                                        c_attn_b AS
                                        (
                                        SELECT  *
                                        FROM    c_attn_b
                                        WHERE   block = q.block
                                        ),
                                        ln_1_g AS
                                        (
                                        SELECT  *
                                        FROM    ln_1_g
                                        WHERE   block = q.block
                                        ),
                                        ln_1_b AS
                                        (
                                        SELECT  *
                                        FROM    ln_1_b
                                        WHERE   block = q.block
                                        ),
                                        mha_norm AS
                                        (
                                        SELECT  place, mm.values + c_attn_b.values AS values
                                        FROM    (
                                                SELECT  place, ARRAY_AGG(INNER_PRODUCT(c_attn_w.values, layer_norm.values) ORDER BY y)::VECTOR(2304) AS values
                                                FROM    (
                                                        SELECT  place, agg.values * ln_1_g.values + ln_1_b.values AS values
                                                        FROM    (
                                                                SELECT  place, norm.values
                                                                FROM    previous
                                                                CROSS JOIN LATERAL
                                                                        (
                                                                        SELECT  AVG(value) AS mean,
                                                                                VAR_POP(value) AS variance
                                                                        FROM    UNNEST(values::REAL[]) value
                                                                        ) agg
                                                                CROSS JOIN LATERAL
                                                                        (
                                                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                                                        ) norm
                                                                ) agg
                                                        CROSS JOIN
                                                                ln_1_b
                                                        CROSS JOIN
                                                                ln_1_g
                                                        ) layer_norm
                                                CROSS JOIN
                                                        c_attn_w
                                                GROUP BY
                                                        place
                                                ) mm
                                        CROSS JOIN
                                                c_attn_b
                                        ),
                                        heads AS
                                        (
                                        SELECT  place, head,
                                                (values::REAL[])[(head * 64 + 1):(head * 64 + 64)]::VECTOR(64) AS q,
                                                (values::REAL[])[(head * 64 + 1 + 768):(head * 64 + 64 + 768)]::VECTOR(64) AS k,
                                                (values::REAL[])[(head * 64 + 1 + 1536):(head * 64 + 64 + 1536)]::VECTOR(64) AS v
                                        FROM    mha_norm
                                        CROSS JOIN
                                                GENERATE_SERIES(0, 11) head
                                        ),
                                        sm_input AS
                                        (
                                        SELECT  head, h1.place AS x, h2.place AS y, INNER_PRODUCT(h1.q, h2.k) / 8 + CASE WHEN h2.place > h1.place THEN -1E10 ELSE 0 END AS value
                                        FROM    heads h1
                                        JOIN    heads h2
                                        USING   (head)
                                        ),
                                        sm_diff AS
                                        (
                                        SELECT  head, x, y, value - MAX(value) OVER (PARTITION BY head, x) AS diff
                                        FROM    sm_input
                                        ),
                                        sm_exp AS
                                        (
                                        SELECT  head, x, y, CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
                                        FROM    sm_diff
                                        ),
                                        softmax AS
                                        (
                                        SELECT  head, x, y AS place, e / SUM(e) OVER (PARTITION BY head, x) AS value
                                        FROM    sm_exp
                                        ),
                                        attention AS
                                        (
                                        SELECT  place, ARRAY_AGG(value ORDER BY head * 64 + ordinality)::VECTOR(768) AS values
                                        FROM    (
                                                SELECT  head, x AS place, SUM(ARRAY_FILL(softmax.value, ARRAY[64])::VECTOR(64) * heads.v) AS values
                                                FROM    softmax
                                                JOIN    heads
                                                USING   (head, place)
                                                GROUP BY
                                                        head, x
                                                ) q
                                        CROSS JOIN LATERAL
                                                UNNEST(values::REAL[]) WITH ORDINALITY v (value, ordinality)
                                        GROUP BY
                                                place
                                        ),
                                        mha AS
                                        (
                                        SELECT  place, w.values + c_proj_b.values + previous.values AS values
                                        FROM    (
                                                SELECT  attention.place, ARRAY_AGG(INNER_PRODUCT(attention.values, c_proj_w.values) ORDER BY c_proj_w.place)::VECTOR(768) AS values
                                                FROM    attention
                                                CROSS JOIN
                                                        c_proj_w
                                                GROUP BY
                                                        attention.place
                                                ) w
                                        CROSS JOIN
                                                c_proj_b
                                        JOIN    previous
                                        USING   (place)
                                        ),
                                        ffn_norm AS
                                        (
                                        SELECT  place, agg.values * ln_2_g.values + ln_2_b.values AS values
                                        FROM    (
                                                SELECT  place, norm.values
                                                FROM    mha
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  AVG(value) AS mean,
                                                                VAR_POP(value) AS variance
                                                        FROM    UNNEST(values::REAL[]) value
                                                        ) agg
                                                CROSS JOIN LATERAL
                                                        (
                                                        SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                                        FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n(value, ordinality)
                                                        ) norm
                                                ) agg
                                        CROSS JOIN
                                                ln_2_b
                                        CROSS JOIN
                                                ln_2_g
                                        ),
                                        ffn_a AS
                                        (
                                        SELECT  gelu.place, gelu.values
                                        FROM    (
                                                SELECT  place, w.values + mlp_c_fc_b.values AS values
                                                FROM    (
                                                        SELECT  ffn_norm.place, ARRAY_AGG(INNER_PRODUCT(ffn_norm.values, mlp_c_fc_w.values) ORDER BY mlp_c_fc_w.place)::VECTOR(3072) AS values
                                                        FROM    ffn_norm
                                                        CROSS JOIN
                                                                mlp_c_fc_w
                                                        GROUP BY
                                                                ffn_norm.place
                                                        ) w
                                                CROSS JOIN
                                                        mlp_c_fc_b
                                                ) v
                                        CROSS JOIN LATERAL
                                                (
                                                SELECT  place, ARRAY_AGG(0.5 * value * (1 + TANH(0.797884560802 * (value + 0.044715 * value*value*value))) ORDER BY ordinality)::VECTOR(3072) AS values
                                                FROM    UNNEST(values::REAL[]) WITH ORDINALITY n (value, ordinality)
                                                GROUP BY
                                                        place
                                                ) gelu
                                        ),
                                        ffn AS
                                        (
                                        SELECT  place, w.values + mlp_c_proj_b.values + mha.values AS values
                                        FROM    (
                                                SELECT  ffn_a.place, ARRAY_AGG(INNER_PRODUCT(ffn_a.values, mlp_c_proj_w.values) ORDER BY mlp_c_proj_w.place)::VECTOR(768) AS values
                                                FROM    ffn_a
                                                CROSS JOIN
                                                        mlp_c_proj_w
                                                GROUP BY
                                                        ffn_a.place
                                                ) w
                                        CROSS JOIN
                                                mlp_c_proj_b
                                        JOIN    mha
                                        USING   (place)
                                        )
                                SELECT  *
                                FROM    ffn
                                ) transformed_layer
                        )
                        ),
                        block_output AS
                        (
                        SELECT  *
                        FROM    hparams
                        JOIN    transform
                        ON      transform.block = n_block
                        ),
                        ln_f AS
                        (
                        SELECT  place, norm.values * ln_f_g.values + ln_f_b.values AS values
                        FROM    block_output
                        CROSS JOIN LATERAL
                                (
                                SELECT  AVG(value) AS mean,
                                        VAR_POP(value) AS variance
                                FROM    UNNEST(values::REAL[]) AS n(value)
                                ) agg
                        CROSS JOIN LATERAL
                                (
                                SELECT  ARRAY_AGG((value - mean) / SQRT(variance + 1E-5) ORDER BY ordinality)::VECTOR(768) AS values
                                FROM    UNNEST(values::REAL[]) WITH ORDINALITY AS n (value, ordinality)
                                ) norm
                        CROSS JOIN
                                ln_f_b
                        CROSS JOIN
                                ln_f_g
                        ),
                        logits AS
                        (
                        SELECT  token, INNER_PRODUCT(ln_f.values, wte.values) AS value
                        FROM    hparams
                        JOIN    ln_f
                        ON      ln_f.place = n_seq - 1
                        CROSS JOIN
                                wte
                        ORDER BY
                                value DESC
                        LIMIT   (top_n)
                        ),
                        tokens AS
                        (
                        SELECT  token,
                                high - softmax AS low,
                                high
                        FROM    (
                                SELECT  *,
                                        SUM(softmax) OVER (ORDER BY softmax) AS high
                                FROM    (
                                        SELECT  *, (e / SUM(e) OVER ()) AS softmax
                                        FROM    (
                                                SELECT  *,
                                                        (value - MAX(value) OVER ()) / temperature AS diff
                                                FROM    logits
                                                ) exp_x
                                        CROSS JOIN LATERAL
                                                (
                                                SELECT  CASE WHEN diff < -745.13 THEN 0 ELSE EXP(diff) END AS e
                                                ) exp
                                        ) q
                                ) q
                        ),
                        next_token AS
                        (
                        SELECT  *
                        FROM    (
                                SELECT  RANDOM() AS rnd
                                ) r
                        CROSS JOIN LATERAL
                                (
                                SELECT  *
                                FROM    tokens
                                WHERE   rnd >= low
                                        AND rnd < high
                                ) nt
                        )
                SELECT  *
                FROM    next_token
                ) next_token
        WHERE   ARRAY_LENGTH(input, 1) < original_length + threshold
                AND next_token.token <> 50256
        ),
        output AS
        (
        SELECT  CONVERT_FROM(STRING_AGG(SET_BYTE('\x00', 0, byte), '' ORDER BY position), 'UTF8') AS response
        FROM    (
                SELECT  STRING_AGG(cluster, '' ORDER BY ordinality) AS response
                FROM    input
                JOIN    gpt
                ON      ARRAY_LENGTH(input, 1) = original_length + threshold
                CROSS JOIN LATERAL
                        UNNEST(input) WITH ORDINALITY n (token, ordinality)
                JOIN    tokenizer
                USING   (token)
                ) q
        CROSS JOIN LATERAL
                STRING_TO_TABLE(response, NULL) WITH ORDINALITY n (character, position)
        JOIN    encoder
        USING   (character)
        )
SELECT  *
FROM    output

ИИ со своей работой справился отлично. Я искренне желаю вам всего самого лучшего в наступившем году!

Все запросы и код для установки выложены в следующем репозитории на GitHub: quassnoi/explain-extended-2024.

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14 янв. 2024 г.

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22.01.25 21:43 DoraJaimes23

Recovery expert. I lost my bitcoin to fake blockchain impostors on Facebook, they contacted me as blockchain official support and i fell stupidly for their mischievous act, this made them gain access into my blockchain wallet whereby 7.0938 btc was stolen from my wallet in total .I was almost in a comma and dumbfounded because this was all my savings i relied on . Then I made a research online and found a recovery expert , with the contact address- { RECOVERYHACKER101 (@) GMAIL . COM }... I wrote directly to the specialist explaining my loss. Hence, he helped me recover a significant part of my investment just after 2 days he helped me launch the recovery program , and the culprits were identified as well , all thanks to his expertise . I hope I have been able to help someone as well . Reach out to the recovery specialist to recover you lost funds from any form of online scam Thanks
23.01.25 02:36 [email protected]

After falling victim to a fraudulent Bitcoin mining scam, I found myself in a desperate situation. I had invested $50,000 into a cloud mining website called Miningpool, which turned out to be a complete scam. For months, I tried reaching out to the company, but I was unable to access my funds, and I quickly realized I had been taken for a ride. In my search for help, I came across TrustGeeks Hack Expert, a service that claimed to help people recover lost funds from crypto scams. Though skeptical at first, I decided to give them a try. Here’s my experience with their service.When I initially contacted TrustGeeks Hack Expert Email.. Trustgeekshackexpert{At}fastservice{Dot}com , I was understandably hesitant. Like many others, I had been tricked into believing my Bitcoin investments were legitimate, only to discover they were locked in a non-spendable wallet with no way of accessing them. However, after sharing my story and details about the scam, the team assured me they had handled similar cases and had the expertise to help. They requested basic information about my investment and began their investigation immediately. The recovery process was nothing short of professional. Unlike many other services that promise quick fixes but fail to deliver, TrustGeeks Hack Expert kept me informed at every stage. They regularly updated me on their progress and were completely transparent about the challenges they faced. There were moments when I wondered if the process would work, but the team’s professionalism and reassurance gave me hope. They were honest about the time it would take and did not make any unrealistic promises, which I truly appreciated. After several weeks of work, TrustGeeks Hack Expert successfully recovered not just my $50,000 investment, but also the so-called profits that had been locked away in the scam's non-spendable wallet. This was a huge relief, as I had resigned myself to the idea that I had lost everything. The entire recovery process was discreet and handled with the utmost care, ensuring that the scam company remained unaware of the recovery efforts, which helped prevent further complications. TeleGram iD. Trustgeekshackexpert & What's A p p +1 7 1 9 4 9 2 2 6 9 3
23.01.25 02:37 [email protected]

After falling victim to a fraudulent Bitcoin mining scam, I found myself in a desperate situation. I had invested $50,000 into a cloud mining website called Miningpool, which turned out to be a complete scam. For months, I tried reaching out to the company, but I was unable to access my funds, and I quickly realized I had been taken for a ride. In my search for help, I came across TrustGeeks Hack Expert, a service that claimed to help people recover lost funds from crypto scams. Though skeptical at first, I decided to give them a try. Here’s my experience with their service.When I initially contacted TrustGeeks Hack Expert Email.. Trustgeekshackexpert{At}fastservice{Dot}com , I was understandably hesitant. Like many others, I had been tricked into believing my Bitcoin investments were legitimate, only to discover they were locked in a non-spendable wallet with no way of accessing them. However, after sharing my story and details about the scam, the team assured me they had handled similar cases and had the expertise to help. They requested basic information about my investment and began their investigation immediately. The recovery process was nothing short of professional. Unlike many other services that promise quick fixes but fail to deliver, TrustGeeks Hack Expert kept me informed at every stage. They regularly updated me on their progress and were completely transparent about the challenges they faced. There were moments when I wondered if the process would work, but the team’s professionalism and reassurance gave me hope. They were honest about the time it would take and did not make any unrealistic promises, which I truly appreciated. After several weeks of work, TrustGeeks Hack Expert successfully recovered not just my $50,000 investment, but also the so-called profits that had been locked away in the scam's non-spendable wallet. This was a huge relief, as I had resigned myself to the idea that I had lost everything. The entire recovery process was discreet and handled with the utmost care, ensuring that the scam company remained unaware of the recovery efforts, which helped prevent further complications. TeleGram iD. Trustgeekshackexpert & What's A p p +1 7 1 9 4 9 2 2 6 9 3
23.01.25 14:20 nellymargaret

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23.01.25 14:20 nellymargaret

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26.01.25 03:54 [email protected]

Losing access to my crypto wallet account was one of the most stressful experiences ever. After spending countless hours building up my portfolio, I suddenly found myself locked out of my account without access. To make matters worse, the email address I had linked to my wallet was no longer active. When I tried reaching out, I received an error message stating that the domain was no longer in use, leaving me in complete confusion and panic. It was as though everything I had worked so hard for was gone, and I had no idea how to get it back. The hardest part wasn’t just the loss of access it was the feeling of helplessness. Crypto transactions are often irreversible, and since my wallet held significant investments, the thought that my hard-earned money could be lost forever was incredibly disheartening. I spent hours scouring forums and searching for ways to recover my funds, but most of the advice seemed either too vague or too complicated to be of any real help. With no support from the wallet provider and my email account out of reach, I was left feeling like I had no way to fix the situation.That’s when I found out about Trust Geeks Hack Expert . I was hesitant at first, but after reading about their expertise in recovering lost crypto wallets, I decided to give them a try. I reached out to their team, and from the very beginning, they were professional, understanding, and empathetic to my situation. They quickly assured me that there was a way to recover my wallet, and they got to work immediately.Thanks to Trust Geeks Hack Expert , my wallet and funds were recovered, and I couldn’t be more grateful. The process wasn’t easy, but their team guided me through each step with precision and care. The sense of relief I felt when I regained access to my crypto wallet and saw my funds safely back in place was indescribable. If you find yourself in a similar situation, I highly recommend reaching out to Trust Geeks Hack Expert. contact Them through EMAIL: [email protected] + WEBSITE. HTTPS://TRUSTGEEKSHACKEXPERT.COM + TELE GRAM: TRUSTGEEKSHACKEXPERT
28.01.25 21:48 [email protected]

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02.02.25 20:53 Michael9090

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05.02.25 00:04 Jannetjeersten

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06.02.25 19:42 Marta Golomb

My name is Marta, and I’m sharing my experience in the hope that it might help others avoid a similar scam. A few weeks ago, I received an email that appeared to be from the "Department of Health and Human Services (DHS)." It claimed I was eligible for a $72,000 grant debit card, which seemed like an incredible opportunity. At first, I was skeptical, but the email looked so professional and convincing that I thought it might be real. The email instructed me to click on a link to claim the grant, and unfortunately, I followed through. I filled out some personal details, and then, unexpectedly, I was told I needed to pay a "processing fee" to finalize the grant. I was hesitant, but the urgency of the message pushed me to make the payment, believing it was a necessary step to receive the funds. Once the payment was made, things quickly went downhill. The website became unreachable, and I couldn’t get in touch with anyone from the supposed DHS. It soon became clear that I had been scammed. The email, which seemed so legitimate, had been a clever trick to steal my money.Devastated and unsure of what to do, I began searching for ways to recover my lost funds. That’s when I found Tech Cyber Force Recovery, a team of experts who specialize in tracing stolen money and assisting victims of online fraud. They were incredibly reassuring and quickly got to work on my case. After several days of investigation, they managed to track down the scammers and recover my funds. I can’t express how grateful I am for their help. Without Tech Cyber Force Recovery, I don’t know what I would have done. This experience has taught me a valuable lesson: online scams are more common than I realized, and the scammers behind them are incredibly skilled. They prey on people’s trust, making it easy to fall for their tricks. HOW CAN I RECOVER MY LOST BTC,USDT =Telegram= +1 561-726-36-97 =WhatsApp= +1 561-726-36-97
08.02.25 05:45 [email protected]

I'm incredibly grateful that I did enough research to recover my stolen cryptocurrency. When I first fell victim to a scam, I felt hopeless and lost, unsure if I'd ever see my funds again. A few months ago, I was approached by someone on Telegram who claimed to have a lucrative investment opportunity in cryptocurrencies. They promised huge returns and played on my emotions, making it seem like a can't-miss chance. I was so eager to make my money grow that I didn't fully vet the situation, and unfortunately, I ended up falling for the scam. They guided me to invest a significant amount of money, and soon after, I realized I had been duped. The scammers blocked me, and my funds were gone. I felt devastated. All of my savings had been wiped out in what seemed like an instant, and the feeling of being taken advantage of was crushing. I spent days researching how to recover my stolen cryptocurrency but found the process to be overwhelming and complicated. I was starting to lose hope when I came across Trust Geeks Hack Expert. At first, I was skeptical about reaching out to a cryptocurrency recovery company, but after reading testimonials and researching their reputation, I decided to give them a try. I contacted Trust Geeks Hack Expert Website: www://trustgeekshackexpert.com/, and I was immediately reassured by their professionalism and expertise. They took the time to listen to my situation, and they were honest about what could and could not be done. What stood out to me was their deep understanding of cryptocurrency fraud and the recovery process. They were able to track down the scammers and initiate the recovery of my stolen funds, step by step. Thanks to Trust Geeks Hack Expert, I was able to get back a significant portion of the cryptocurrency I had lost. Their team was responsive, transparent, and diligent in their efforts. I was kept informed throughout the entire process, and they made sure I felt supported every step of the way. I truly can't thank them enough for their dedication and for restoring my faith in the possibility of recovery after such a devastating loss. I will definitely recommend Trust Geeks Hack Expert to anyone who has fallen victim to a cryptocurrency scam. TeleGram: Trustgeekshackexpert & what's A p p +1 7 1 9 4 9 2 2 6 9 3
08.02.25 05:46 [email protected]

I'm incredibly grateful that I did enough research to recover my stolen cryptocurrency. When I first fell victim to a scam, I felt hopeless and lost, unsure if I'd ever see my funds again. A few months ago, I was approached by someone on Telegram who claimed to have a lucrative investment opportunity in cryptocurrencies. They promised huge returns and played on my emotions, making it seem like a can't-miss chance. I was so eager to make my money grow that I didn't fully vet the situation, and unfortunately, I ended up falling for the scam. They guided me to invest a significant amount of money, and soon after, I realized I had been duped. The scammers blocked me, and my funds were gone. I felt devastated. All of my savings had been wiped out in what seemed like an instant, and the feeling of being taken advantage of was crushing. I spent days researching how to recover my stolen cryptocurrency but found the process to be overwhelming and complicated. I was starting to lose hope when I came across Trust Geeks Hack Expert. At first, I was skeptical about reaching out to a cryptocurrency recovery company, but after reading testimonials and researching their reputation, I decided to give them a try. I contacted Trust Geeks Hack Expert Website: www://trustgeekshackexpert.com/, and I was immediately reassured by their professionalism and expertise. They took the time to listen to my situation, and they were honest about what could and could not be done. What stood out to me was their deep understanding of cryptocurrency fraud and the recovery process. They were able to track down the scammers and initiate the recovery of my stolen funds, step by step. Thanks to Trust Geeks Hack Expert, I was able to get back a significant portion of the cryptocurrency I had lost. Their team was responsive, transparent, and diligent in their efforts. I was kept informed throughout the entire process, and they made sure I felt supported every step of the way. I truly can't thank them enough for their dedication and for restoring my faith in the possibility of recovery after such a devastating loss. I will definitely recommend Trust Geeks Hack Expert to anyone who has fallen victim to a cryptocurrency scam. TeleGram: Trustgeekshackexpert & what's A p p +1 7 1 9 4 9 2 2 6 9 3
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11.02.25 04:24 heyemiliohutchinson

I invested substantially in Bitcoin, believing it would secure my future. For a while, things seemed to be going well. The market fluctuated, but I was confident my investment would pay off. But catastrophe struck without warning. I lost access to my Bitcoin holdings as a result of several technical issues and inadequate security measures. Every coin in my wallet suddenly disappeared, leaving me with an overpowering sense of grief. The emotional impact of this loss was far greater than I had imagined. I spiraled into despair, feeling as though my dreams of financial independence were crushed. I was on the verge of giving up when I came across Assets_Recovery_Crusader. Being willing to give them a chance, I had nothing left to lose. They listened to my narrative and took the time to comprehend the particulars of my circumstance, rather than treating me like a case number. They worked diligently, using their advanced recovery techniques and deep understanding of blockchain technology to track down my lost Bitcoin. Assets_Recovery_Crusader rebuilt my trust in the bitcoin space. The financial impact had a significant emotional toll, but I was able to get past it thanks to Assets_Recovery_Crusader’s proficiency and persistence. For proper talks, reach out to them via TELEGRAM : Assets_Recovery_Crusader EMAIL: [email protected]
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13.02.25 14:45 aoifewalsh130

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13.02.25 16:50 andytom798

I lost $210,000 worth of Bitcoin to a group of fake blockchain impostors on Red note, a Chinese app. They contacted me, pretending to be official blockchain support, and I was misled into believing they were legitimate. At the time, I had been saving up in Bitcoin, hoping to take advantage of the rising market. The scammers were convincing, and I made the mistake of trusting them with access to my blockchain wallet. To my shock and disbelief, they stole a total of $10,000 worth of Bitcoin from my wallet. It was devastating, as this amount represented all of my hard-earned savings. I was in utter disbelief, feeling foolish for falling for their deceptive tactics. I felt lost, as though everything I had worked towards was taken from me in an instant. Thankfully, my uncle suggested I reach out to an expert in cryptocurrency recovery. After doing some research online, I came across CYBERPOINT RECOVERY COMPANY. I was hesitant at first, but their positive reviews gave me some hope. I decided to contact them directly and explained my situation, including the amount I had lost and how the scammers had gained access to my account. To my relief, the team at CYBERPOINT RECOVERY responded quickly and assured me they could help. They launched a detailed recovery program, using advanced tools and techniques to trace the stolen Bitcoin. Within a matter of days, they successfully recovered my full $210,000 worth of Bitcoin, and they even identified the individuals behind the scam. Their expertise and professionalism made a huge difference, and I was incredibly grateful for their support. If you find yourself in a similar situation, I highly recommend reaching out to Cyber Constable Intelligence. They helped me recover my funds when I thought all hope was lost. Whether you’ve lost money to scammers or any other form of online fraud, they have the knowledge and resources to help you get your funds back. Don’t give up there are experts who can help you reclaim what you’ve lost. I’m sharing my story to hopefully guide others who are going through something similar. Here's Their Info Below ([email protected]) or W.H.A.T.S.A.P.P:+1.7.6.0.9.2.3.7.4.0.7
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14.02.25 02:50 Vladimir876

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14.02.25 02:56 christophadelbert3

I was in total dismay when I lost my entire savings investing in cryptocurrency, I was contacted online by a lady through email pretending to be an account manager of a bank, who told me I could make double my savings through cryptocurrency investment, I never imagined it would be a scam and I was going to lose everything. It went on for weeks until I realized that I have been scammed. All hope was lost, I was devastated and broke, fortunately for me, I came across an article on my local bulletin about CYBERPUNK RECOVERY Bitcoin Recovery, I contacted them and provided all the information regarding my case, I was amazed at how quickly they recovered my cryptocurrency funds and was able to trace down those scammers. I’m truly grateful for their service and I recommend CYBERPUNK RECOVERY to everyone who needs to recover their funds urge you to contact CYBERPUNK if you have lost your bitcoin USDT or ETH through bitcoin investment Email: ([email protected]) WhatsApp (+17609237407)
14.02.25 15:33 prelogmilivoj

I never imagined I would find myself in a situation where I was scammed out of such a significant amount of money, but it happened. I became a victim of a fake online donation project that cost me over $30,000. It all started innocently enough when I was searching for assistance after a devastating fire incident in California. While looking for support, I came across an advertisement that seemed to offer donations for fire victims. The ad appeared legitimate, and I reached out to the project manager to inquire about how to receive the donations. The manager was very convincing and insisted that in order to qualify for the donations, I needed to pay $30,000 upfront. In return, I was promised $1 million in donations. It sounded a bit too good to be true, but in my desperate situation, I made the mistake of believing it. The thought of receiving a substantial amount of help to rebuild after the fire clouded my judgment, and I went ahead and sent the money. However, after transferring the funds, the promised donations never arrived, and the manager disappeared. That’s when I realized I had been scammed. Feeling lost, helpless, and completely betrayed, I tried everything I could to contact the scammer, but all my efforts were in vain. Desperation led me to search for help online, hoping to find a way to recover my money and potentially track down the scammer. That’s when I stumbled upon several testimonies from others who had fallen victim to similar scams and had been helped by a company called Tech Cyber Force Recovery. I reached out to them immediately, providing all the details of the scam and the information I had gathered. To my immense relief, the experts at Tech Cyber Force Recovery acted swiftly. Within just 27 hours, they were able to locate the scammer and initiate the recovery process. Not only did they help me recover the $30,000 I had lost, but the most satisfying part was that the scammer was apprehended by local authorities in their region. Thanks to Tech Cyber Force Recovery, I was able to get my money back and hold the scammer accountable for their actions. I am incredibly grateful for their professionalism, expertise, and dedication to helping victims like me. If you have fallen victim to a scam or fraudulent activity, I highly recommend contacting Tech Cyber Force Recovery. They provide swift and efficient recovery assistance, and I can confidently say they made all the difference in my situation. ☎☎ 1️⃣5️⃣6️⃣1️⃣7️⃣2️⃣6️⃣3️⃣6️⃣9️⃣7️⃣ ☎☎ 📩 1️⃣5️⃣6️⃣1️⃣7️⃣2️⃣6️⃣3️⃣6️⃣9️⃣7️⃣ 📩
14.02.25 22:12 eunice49954

Agent Jasmine Lopez focuses on recovering stolen cryptocurrency, particularly USDT. She is well-known for helping victims of digital asset theft. Her reputation arises from successful recoveries that have allowed many to regain their lost funds. I witnessed this when $122,000 was taken from me. Thanks to Ms. Lopez's skills, I recovered the entire amount in just 24 hours. Her prompt response and effective methods relieved my financial burden. Ms. Lopez’s commitment to helping others is evident. She is always available to offer solutions to those facing similar problems. For assistance, she can be reached via email at recoveryfundprovider@gmail . com or contacted directly on WhatsApp and text at +44 - 7366 445035. Her Instagram handle is recoveryfundprovider.
15.02.25 02:51 Michelle Lynn

Living in Los Angeles, I never imagined I’d face such a difficult chapter in my life. At the time, my wife was pregnant, and we were both excited about starting a family. I fell victim to a series of scams, losing over $170,000 in total. Just when I thought things couldn’t get worse, I received a call from someone who promised to help me recover my losses. Desperate to fix the situation, I went along with it, hoping for a breakthrough. But it turned out to be another scam. However, most of the options I found either seemed dubious or offered no real guarantees. That’s when I came across Cyber Constable Intelligence. It was a company recommended in a Facebook community The team worked tirelessly on my case, and after some time, they successfully recovered 99% of my investment. Although I didn’t recover everything, the 99% recovery was a huge relief They also educated me on how to better protect my digital Asset Here's Their Website Info www cyberconstableintelligence com
15.02.25 02:51 Michelle Lynn

Living in Los Angeles, I never imagined I’d face such a difficult chapter in my life. At the time, my wife was pregnant, and we were both excited about starting a family. I fell victim to a series of scams, losing over $170,000 in total. Just when I thought things couldn’t get worse, I received a call from someone who promised to help me recover my losses. Desperate to fix the situation, I went along with it, hoping for a breakthrough. But it turned out to be another scam. However, most of the options I found either seemed dubious or offered no real guarantees. That’s when I came across Cyber Constable Intelligence. It was a company recommended in a Facebook community The team worked tirelessly on my case, and after some time, they successfully recovered 99% of my investment. Although I didn’t recover everything, the 99% recovery was a huge relief They also educated me on how to better protect my digital Asset Here's Their Website Info www cyberconstableintelligence com, WhatsApp Info: 1 (252) 378-7611
16.02.25 01:01 Peter

I fell victim to a crypto scam and lost a significant amount of money. What are the most effective strategies to recover my funds? I've heard about legal actions, contacting authorities, and hiring recovery experts, but I'm not sure where to start. Can you provide some guidance on the best ways to recover money lost in a crypto scam? Well if this is you, [email protected] gat you covered get in touch and thank me later
16.02.25 20:06 eunice49954

Agent Lopez specializes in recovering stolen cryptocurrencies, especially Bitcoin/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
18.02.25 19:35 donovancristina

Now, I’m that person sharing my success story on LinkedIn, telling others about the amazing team at TECH CYBER FORCE RECOVERY who literally saved my financial life. I’ve also become that guy who proudly shares advice like “Always back up your wallet, and if you don’t have TECH CYBER FORCE RECOVERY on speed dial.” So, a big thank you to TECH CYBER FORCE RECOVERY if I ever get a chance to meet the team, I might just offer to buy them a drink. They’ve earned it. FOR CRYPTO HIRING WEBSITE WWW://techcyberforcerecovery.com WHATSAPP : ⏩ wa.me/15617263697
18.02.25 22:13 keithphillip671

WhatsApp +44,7,4,9,3,5,1,3,3,8,5 Telegram @Franciscohack The day my son uncovered the truth—that the man I entrusted my hopes of wealth and companionship with through a cryptocurrency platform was a cunning scammer was the day my world crumbled. The staggering realization that I had been swindled out of 150,000.00 Euro worth of Bitcoin left me in a state of profound despair. As a 73-year-old grappling with loneliness, I had sought solace in what I believed to be a genuine connection, only to find deceit and betrayal. Countless sleepless nights were spent in tears, mourning not only the financial devastation but also the crushing blow to my trust. Attempts to verify the authenticity of our interactions were met with hostility, further deepening my sense of isolation. Through the loss it was my son who became my beacon of resilience. He took upon himself the arduous task of tracing the scam and seeking justice on my behalf. Through meticulous effort and determination, he unearthed {F R A N C I S C O H A C K}, renowned for their expertise in recovering funds lost to cryptocurrency scams. Entrusting them with screenshots and evidence of the fraudulent transactions, my son initiated the journey to reclaim what had been callously taken from me. {F R A N C I S C O H A C K} approached our plight with empathy and unwavering professionalism, immediately instilling a sense of confidence in their abilities. Despite my initial skepticism, their transparent communication and methodical approach reassured us throughout the recovery process. Regular updates on their progress and insights into their strategies provided much-needed reassurance and kept our hopes alive amid the uncertainty. Their commitment to transparency and client welfare was evident in every interaction, fostering a sense of partnership rather than mere service. Miraculously, in what felt like an eternity but was actually an impressively brief period, {F R A N C I S C O H A C K} delivered the astonishing news—I had recovered the entire 150,000.00 Euro worth of stolen Bitcoin. The flood of relief and disbelief was overwhelming, marking not just the restitution of financial losses but the restoration of my faith in justice. {F R A N C I S C O H A C K} proficiency in navigating the intricate landscape of blockchain technology and online fraud was nothing short of extraordinary. Their dedication to securing justice and restoring client confidence set them apart as more than just experts—they were steadfast allies in a fight against digital deceit. What resonated deeply with me {F R A N C I S C O H A C K} integrity and compassion. Despite the monumental recovery, they maintained transparency regarding their fees and ensured fairness in all dealings. Their proactive guidance on cybersecurity measures further underscored their commitment to safeguarding clients from future threats. It was clear that their mission extended beyond recovery—it encompassed education, prevention, and genuine advocacy for those ensnared by cyber fraud. ([email protected]) fills me with profound gratitude. They not only rescued my financial security but also provided invaluable emotional support during a time of profound vulnerability. To anyone navigating the aftermath of cryptocurrency fraud, I wholeheartedly endorse {F R A N C I S C O H A C K}. They epitomize integrity, expertise, and unwavering dedication to their clients' well-being. My experience with {F R A N C I S C O H A C K} transcended mere recovery—it was a transformative journey of resilience, restoration, and renewed hope in the face of adversity.
21.02.25 07:42 daniel231101

I never thought I would fall victim to a crypto scam until I was convinced of a crypto investment scam that saw me lose all my entire assets worth $487,000 to a crypto investment manager who convinced me I could earn more from my investment. I thought it was all gone for good but I kept looking for ways to get back my stolen crypto assets and finally came across Ethical Hack Recovery, a crypto recovery/spying company that has been very successful in the recovery of crypto for many other victims of crypto scams and people who lost access to their crypto. I’m truly grateful for their help as I was able to recover my stolen crypto assets and get my life back together. I highly recommend their services EMAIL ETHICALHACKERS009 AT @GMAIL DOT COM whatsapp +14106350697
21.02.25 21:38 eunice49954

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
22.02.25 18:01 benluna0991

Mark Zuckerberg. That’s the name I was introduced to when I first encountered the cryptocurrency mining platform, WHATS Invest. A person claiming to be Zuckerberg himself reached out to me, saying that he was personally backing the platform to help investors like me earn passive income. At first, I was skeptical—after all, how often do you get a direct connection to one of the world’s most famous tech entrepreneurs? But this individual seemed convincing and assured me that many people were already seeing substantial returns on their investments. He promised me a great opportunity to secure my financial future, so I decided to take the plunge and invest $10,000 into WHATS Invest. They told me that I could expect to see significant returns in just a few months, with payouts of at least $1,500 or more each month. I was excited, believing this would be my way out of financial struggles. However, as time passed, things didn’t go according to plan. Months went by, and I received very little communication. When I finally did receive a payout, it was nowhere near the $1,500 I was promised. Instead, I received just $200, barely 13% of what I had expected. Frustrated, I contacted the support team, but the responses were vague and unhelpful. No clear answers or solutions were offered, and my trust in the platform quickly started to erode. It became painfully clear that I wasn’t going to get anywhere with WHATS Invest, and I began to worry that my $10,000 might be lost for good. That's when I discovered Certified Recovery Services. Desperate to recover my funds, I decided to reach out to them for help. In just 24 hours, they worked tirelessly to recover the majority of my funds, successfully retrieving $8,500 85% of my initial investment. I couldn’t believe how quickly and efficiently they worked to get my money back. I’m extremely grateful for Certified Recovery Servicer's fast and professional service. Without them, I would have been left with a significant loss, and I would have had no idea how to move forward. If you find yourself in a similar situation with WHATS Invest or any other platform that isn’t delivering as promised, I highly recommend reaching out to Certified Recovery Services They were a lifesaver for me, helping me recover nearly all of my funds. It's reassuring to know that trustworthy services like this exist to help people when things go wrong. They also specialize in recovering money lost to online scams, so if you’ve fallen victim to such a scam, don’t hesitate to contact Certified Recovery Services they can help! Here's Their Info Below: WhatsApp: +1(740)258‑1417 mail: [email protected], [email protected] Website info; https://certifiedrecoveryservices.com
23.02.25 22:00 eunice49954

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 06:36 ANDREW DAVIS

RECOVER YOUR SCAMMED FUNDS AND CRYPTOCURRENCY VIA SPOTLIGHT RECOVERY Professional hackers at Spotlight Recovery provide services for compromised devices, accounts, and websites as well as for recovering stolen bitcoin and money from scams. They finish their work safely and quickly. Their order has been fulfilled since day one, and the victim will never be conscious of the outside entrance. Very few even attempt to give critical information, look into network security, or discreetly discuss personal issues. The Spotlight Recovery Crew helped me recover $264,000 that was stolen from my corporate bitcoin wallet, and I appreciate them giving me further details on the unidentified people. In the event that you have been defrauded of your hard-earned cash or bitcoins, contact SPOTLIGHT RECOVERY CREW at Contact: [email protected]
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
27.02.25 12:46 monikaguttmacher

Weddings are supposed to be magical, but the months leading up to mine were anything but. Already, wedding planning was a high-stress, sleep-deprived whirlwind: endless details to manage, from venue deposits and guest lists to dress fittings and vendor contracts. But nothing-and I mean, nothing-compared to the panic that washed over me when I realized that somehow, I had lost access to my Bitcoin wallet-with $600,000 inside. It happened in the worst possible way. In between juggling my to-do lists and trying to keep my sanity intact, I lost my seed phrase. I went through my apartment like a tornado, flipping through notebooks, checking every email, every file-nothing. I sat there in stunned silence, heart pounding, trying to process the fact that my entire savings, my security, and my financial future might have just vanished. In utter despair, I vented to my bridesmaid's group chat for some sympathetic words from the girls. Instead, one casually threw out a name that would change everything in a second: "Have you ever heard of Tech Cyber Force Recovery? They recovered Bitcoin for my cousin. You should call them." I had never heard of them before, but at that moment, I would have tried anything. I immediately looked them up, scoured reviews, and found story after story of people just like me—people who thought they had lost everything, only for Tech Cyber Force Recovery to pull off the impossible. That was all the convincing I needed. From the very first call, I knew I was in good hands. Their team was calm, professional, and incredibly knowledgeable. They explained the recovery process in a way that made sense, even through my stress-fogged brain. Every step of the way, they kept me informed, reassured me, and made me feel like this nightmare actually had a solution. And then, just a few days later, I got the message: "We have recovered your Bitcoin." (EMAIL. support @ tech cyber force recovery . com) OR WHATSAPP (+1 56 17 26 36 97) I could hardly believe my eyes: Six. Hundred. Thousand. Dollars. In my hands again. I let out my longest breath ever and almost cried, relieved. It felt like I woke up from a bad dream, but it was real, and Tech Cyber Force Recovery had done it. Because of them, I walked down the aisle not just as a bride, but as someone who had dodged financial catastrophe. Instead of spending my honeymoon stressing over lost funds, I got to actually enjoy it—knowing that my wallet, and my future, were secure. Would I refer to them? In a heartbeat. If you ever find yourself in that situation, please don't freak out, just call Tech Cyber Force Recovery. They really are the real deal.
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07.03.25 15:18 Ariduk

BEST LINK FOR RECOVERY SCAM ON TRADING INVESTMENT AND OTHERS TROUBLESHOOT? Welcome To General Hacking Techniques Service known as DHACKERS. Year 2025 we are active and best in what we do, as we give Solution to every problem concerning Web3 INTERNET activities, we guide you right to a positive fund Recovery e.t.c. Question From Most of Our Client, HOW POSSIBLE AND TIME WILL IT TAKE TO RECOVERY LOST OR SCAM FUND? Our Answer. Yes is 89.9% possible and how long it takes your Fund to be recovered depend on you. The fact is there are lot of fake binary investment companies out their, same a lot fake recovery companies and agents too. CAUTION 1). Make sure you ask one or two questions concerning the service and how they render there recovery services. 2) Do not give out your scammed details to any agent or hacker when you are not yet ready to recover back your fund. 3) do not make any payment when you are not sure of the service if you are to make one. (4) We discovered that most of this fake hacker or agent do give us scam details, playing the victim, because they can afford the service charge. 5) As long you have your scam details with you, you can recover your fund back anytime any-day with the right channel. Contact us from our Front Desk. [email protected] For advice and services, our standby Guru email. [email protected] [email protected] List of Service. ▶️Binary Recovery ▶️Data Recovery ▶️University Result Upgraded ▶️Clear your Internet Blunder and controversy ➡️Increase your Credit Score ➡️Wiping of Criminal Records ➡️Social Media Hack ➡️Blank ATM Card ➡️Load and wipe ➡️Phone Hacking ➡️Private Key Reset etc. For quick response. Email [email protected] Border us with your jobs and allow us give you positive result with our hacking skills. All Right Reserved (c)2025
08.03.25 04:42 andreassenhedda

If you’ve fallen victim to online scammers who have deceived you into investing your hard-earned money through fraudulent Bitcoin schemes, know that you're not alone. Countless individuals have been misled by scammers using various tactics to swindle money through deceptive investment platforms or promises of high returns. These scams often come in the form of fake cryptocurrency investments, Ponzi schemes, or phishing scams designed to steal your Bitcoin and other assets. Unfortunately, many victims suffer not only financial loss but also the psychological toll of realizing they’ve been taken advantage of. In some cases, scammers go even further, threatening legal consequences or using intimidation to keep victims silent. However, all hope is not lost. There are ways to recover your funds and potentially even bring those responsible to justice. One promising resource that can assist in reclaiming lost funds is Lee Ultimate Hacker, a trusted platform designed to help victims of online fraud. This service specializes in helping individuals who have been scammed through cryptocurrency investments or similar schemes. The platform’s expertise can help you navigate the process of recovering your money, giving you a chance to fight back against those who’ve wronged you. To begin the recovery process, it’s important to gather any proof of payment or transaction history involving the scammers. This evidence is crucial in tracing the flow of funds and identifying the scam operation behind it. Once you have collected your documentation, you can reach out to Lee Ultimate Hacker via LEEULTIMATEHACKER @ AOL . COM or wh@tsapp +1 (715) 314 - 9248 for assistance. They offer professional services to investigate fraudulent schemes, track Bitcoin transactions, and work to reverse fraudulent transfers. The recovery process can be complex and requires expert knowledge of blockchain technology and financial investigations, but with the help of a dedicated team, you’ll have a better chance of seeing your funds returned. In addition to helping you recover your assets, Lee Ultimate Hacker also works towards identifying the scammers and reporting them to the appropriate authorities. They understand the urgency of halting these fraudsters before they can victimize others. With their assistance, you not only increase the chances of recovering your funds but also play a part in holding cybercriminals accountable. If you've been affected by Bitcoin scams or other fraudulent online activities, reaching out to a service like Lee Ultimate Hacker can provide hope and a clear path forward. Their team can guide you through the recovery process, offering expert support while you take steps to reclaim what you’ve lost. It’s time to take action and work toward reclaiming your hard-earned money.
08.03.25 18:20 Diegolola514gmail.com

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08.03.25 18:23 faridasumadi

WEBSITE W.W.W.techcyberforcerecovery.com WHATSAPP +1 561.726.36.97 EMAIL [email protected] I Thought I Was Too Smart to Be Scammed, Until I Was. I'm an attorney, so precision and caution are second nature to me. My life is one of airtight contracts and triple-checking every single detail. I'm the one people come to for counsel. But none of that counted for anything on the day I lost $750,000 in Bitcoin to a scam. It started with what seemed like a normal email, polished, professional, with the same logo as my cryptocurrency exchange's support team. I was between client meetings, juggling calls and drafting agreements, when it arrived. The email warned of "suspicious activity" on my account. My heart pounding, I reacted reflexively. I clicked on the link. I entered my login credentials. I verified my wallet address. The reality hit me like a blow to the chest. My balance was zero seconds later. The screen went dim as horror roiled in my stomach. The Bitcoin I had worked so hard to accumulate over the years, stored for my retirement and my children's future, was gone. I felt embarrassed. Lawyers are supposed to outwit criminals, not get preyed on by them. Mortified, I asked a client, a cybersecurity specialist, for advice, expecting criticism. But he just suggested TECH CYBER FORCE RECOVERY. He assured me that they dealt with delicate situations like mine. I was confident from the first call that I was in good hands. They treated me with empathy and discretion by their staff, no patronizing lectures. They understood the sensitive nature of my business and assured me of complete confidentiality. Their forensic experts dove into blockchain analysis with attention to detail that rivaled my own legal work. They tracked the stolen money through a complex network of offshore wallets and cryptocurrency tumblers tech jargon that appeared right out of a spy thriller. Once they had identified the thieves, they initiated a blockchain reversal process, a cutting-edge method I was not even aware was possible. Three weeks of suffering later, my Bitcoin was back. Every Satoshi counted for. I sat in front of my desk, looking at the refilled balance, tears withheld. TECH CYBER FORCE RECOVERY not only restored my assets, they provided legal-grade documentation that empowered me to bring charges against the scammers. Today, I share my story with colleagues as a warning. Even the best minds get it. But when they do, it is nice to know the Wizards have your back.
09.03.25 17:22 Wayne707

‎Scammers have ruined the forex trading market, they have deceived many people with their fake promises on high returns. I learnt my lesson the hard way. I only pity people who still consider investing with them. Please try and make your researches, you will definitely come across better and reliable forex trading agencies that would help you yield profit and not ripping off your money. Also, if your money has been ripped-off by these scammers, you can report to a regulated crypto investigative unit who make use of software to get money back. If you encounter with some issue make sure you contact ( [email protected] ) they're recovery expert and a very professional one at that. ‎
10.03.25 18:18 springwilli

RECLAIM MY LOSSES REVIEWS HIRE DUNAMIS CYBER SOLUTIONI have always taken a security-first approach with my Bitcoin. That's why I put my hardware wallet in a fireproof safe-because you never know. Turned out I should have been even more paranoid. A few months ago, a fire took hold in my house. I lost nearly everything: the electronics, furniture, irreplaceable memorabilia. But when I dug through the remains, there it was: my Ledger hardware wallet, somehow intact. I held it up like some sort of post-apocalyptic movie scene, thinking, "At least my Bitcoin survived." But then, fate was not quite done with me: when I powered it on, it showed no signs of life whatsoever. The heat had fried the internal chip, and all I had was a melted, lifeless brick. That's when I realized my entire $680,000 in Bitcoin was trapped inside. At first, I told myself: "There has to be a way." From forensic data recovery to DIY repair tricks, everything I could conceivably Google, I researched. I considered buying an identical Ledger device and swapping components: spoiler, not a good idea unless you are an electrical engineer. Nothing worked. Every expert I contacted had the same answer: "Your Bitcoin is gone." I refused to accept that. That's when I found DUNAMIS CYBER SOLUTION I was skeptical, to say the least. If the manufacturer couldn't help me, how would they? At that point, I had no other choice but to try them. The first call I made, I immediately knew I was dealing with pros: no absurd promises, no giving of hopes, just explanation of their entire process with clarity-from advanced forensic techniques to secure data reconstruction. I mailed them my charred wallet, still half expecting a miracle to be impossible. Four days later, an email arrived. The subject line? "We have good news." They had successfully extracted my seed phrase and restored every single Bitcoin. I couldn't believe it. I had gone from losing everything to recovering $680,000 worth of crypto in just days. If your hardware wallet is damaged, dead, or seems irreparable, please do not give up. Just call DUNAMIS CYBER SOLUTION. They really did pull off some sort of high-stakes rescue operation on my behalf, and believe me, it was the stuff of legend. [email protected] +13433030545
10.03.25 20:19 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]
10.03.25 20:19 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]
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11.03.25 16:23 dannywilliams

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11.03.25 16:23 dannywilliams

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11.03.25 16:25 ricciordonez

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12.03.25 05:35 cholevasaca

As the senior teacher at Greenfield Academy, I wanted to share our ordeal with TECH CYBER FORCE RECOVERY after our school was targeted by a malicious virus attack that withdrew a significant amount of money from our bank account. A third-party virus infiltrated our system and accessed our financial accounts, resulting in a USD 50,000 withdrawal. This attack left us in a state of shock and panic, as it posed a serious threat to our school's financial stability. Upon realizing what had happened, we immediately contacted TECH CYBER FORCE RECOVERY for help. Their team responded promptly and began investigating the situation. They worked tirelessly to track down the virus, analyze its behavior, and understand how it had bypassed our security measures. Most importantly, they focused on recovering the funds that had been stolen from our bank account. Thanks to TECH CYBER FORCE RECOVERY's quick and expert intervention, they were able to successfully recover all the funds that had been withdrawn. Their team worked closely with our bank and utilized advanced recovery methods to ensure the full amount was returned to our account. We were incredibly relieved to see the stolen funds restored, and their efforts prevented any further financial loss. I am incredibly grateful for TECH CYBER FORCE RECOVERY's professionalism, expertise, and swift action in helping us recover the stolen funds. Their team not only managed to undo the damage caused by the virus but also ensured that our financial security was restored. I highly recommend their services to any organization dealing with similar cyberattacks, as their team truly went above and beyond to resolve the issue and protect our assets. CONTACTING THEM TECH CYBER FORCE RECOVERY EMAIL. [email protected]
14.03.25 21:40 adelfinalongo

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15.03.25 00:29 irenmroma

CRYPTOCURRENCY RECOVERY FIRM DUNAMIS CYBER SOLUTION
15.03.25 00:29 irenmroma

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15.03.25 14:34 spencerwerner

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17.03.25 02:30 [email protected]

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17.03.25 12:20 browne

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17.03.25 13:14 vinnypraise

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17.03.25 13:14 vinnypraise

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17.03.25 15:23 Charlesagrimes

Running the small business was hard enough in itself without having to suffer such stress as loss of access to a Bitcoin wallet. I had put $532,000 into Bitcoin for my business in case of emergencies, but one day, the wallet was nowhere to be seen. I had trusted it to my friend while he managed my financials, little knowing he would prove less than trustworthy. I couldn't envision the gut-wrenching feeling coupled with a great feeling of folly for having placed so much trust in someone else's hands. I could not believe my eyes to see that all of my digital fortune was gone. Literally, every second of my busy day froze in disbelief as I tried to conceive the loss. I remembered the hours I had put into building my business, securing my investments, and planning for the future. Now, I was staring at an empty wallet that once held my safety net. This hit me hard-not only had I lost $532,000, but the betrayal hurt further because it came from someone I considered reliable. The emotional toll was huge, and this financial hit could cripple my business. In the midst of my despair, I knew I had to act fast. I went online, searching everywhere for a solution through which I could get back in control of my finances. That is where I came across Digital resolution services. I knew them for recovery related to lost crypto, but also somehow skeptical. At that point, it looked like I had nothing left to lose. I reached out, and with our very first conversation, I gained the impression that they did understand my situation. Their team was nothing short of extraordinary. They approached my case with professionalism and empathy, meticulously explaining the recovery process in clear, simple terms that alleviated some of my anxiety. They set realistic expectations while promising to do everything possible to retrieve my funds. Over the next several weeks, they worked tirelessly, employing advanced blockchain forensic techniques and sophisticated tracking tools that I’d never even heard of before. It kept me informed with constant updates and gave me hope in this desperate time. Finally, it came-the day Digital resolution services recovered my lost Bitcoin. Relief overwhelmed me, and it wasn't all about the money but control and self-trust in my financial future. This experience taught me the most valuable lesson: never lose control over your own financial security and never put blind trust in anyone. With Digital resolution services, I recovered not only my $532,000 but also learned how to protect my assets better in the future. Contact Digital Resolution Services: Email: digitalresolutionservices (@) myself. c o m WhatsApp: +1 (361) 260-8628 Stay protected Charles agrimes
18.03.25 23:49 lindaspringer311

My name is Linda Springer, and I am part of an ultra-high-net-worth family in the United Kingdom. Managing our wealth has always been a top priority, and I’ve always looked for opportunities to grow and diversify our investments. When I was introduced to an offshore banking investment program called Market Fund, it seemed like the perfect opportunity to enhance our portfolio. The program promised impressive returns, and with professional advisors and seemingly legitimate documentation, I felt confident that it was a secure investment. However, my trust in Market Fund quickly proved to be misplaced. Initially, everything seemed to go smoothly. Reports showed strong growth, and I was reassured by the continuous updates from the program’s advisors. But when I tried to withdraw my funds, everything took a sharp turn. The Market Fund website became unresponsive, and all my attempts to reach the advisors through emails and phone calls went unanswered. It was then that I realized I had fallen victim to a scam, and the £60,000 I had invested was gone. Feeling devastated and unsure of what to do next, I turned to a friend I had met at a club called The Vault. During one of our conversations, Alex, a fellow club-goer, mentioned how Rapid Digital Recovery had helped them recover funds from a similar fraudulent scheme. Intrigued by their success story, I decided to reach out to Rapid Digital Recovery....Whatsapp: +1 4 14 80 71 4 85.. hoping they could help me recover my money as well. From the moment I contacted them, the team at Rapid Digital Recovery took immediate action. They began investigating the scam and used advanced technology to trace the origins of Market Fund. Through their efforts, they uncovered a network of fake websites and shell companies that had been designed to deceive investors like myself. Thanks to their persistence and expertise, Rapid Digital Recovery successfully recovered the £60,000 I had lost.....Email: rapid digital recovery (@) execs. com.. Not only did they restore my financial security, but they also exposed the fraudulent operation behind Market Fund, preventing others from falling victim to the same scam. While the experience was incredibly stressful, it served as an important reminder of the need for due diligence and professional oversight when dealing with offshore investments. I am incredibly grateful to Rapid Digital Recovery for their support, expertise, and determination in recovering my funds. Telegram: h t t p s: // t. me /Rapiddigitalrecovery1
20.03.25 17:21 katherineingram

Dr. Katherine Ingram
20.03.25 17:21 katherineingram

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20.03.25 19:34 ysabelbristol

I am YSABEL, a medical student living with my grandmother. For the past few years, I’ve been diligently saving my grandmother’s money to ensure she has a comfortable and secure future. I invested over $40,000 into an online platform, which promised significant returns. After completing several steps, they told me that to withdraw the money, I needed to make another payment of $73,000. As a medical student, my time is already stretched thin, and managing my grandmother’s finances on top of my studies was overwhelming. That's when a costudent, who had gone through a similar experience, recommended MUYERN TRUST HACKER. Initially, I was skeptical. After all, how could anyone help me recover the money I had already lost to such a sophisticated scam? But after reaching out to them, I quickly realized I was in good hands. From the very first conversation, the team at MUYERN TRUST HACKER was professional, compassionate, and knowledgeable. They understood the gravity of my situation and took the time to thoroughly review all the details of my case. They explained the recovery process clearly, step by step, and assured me that they would work tirelessly to help recover the funds I had lost. Their expertise in dealing with online fraud was evident, and for the first time in weeks, I felt a sense of hope that I could regain control over this situation. The recovery process wasn’t immediate, and there were moments of uncertainty, but MUYERN TRUST HACKER remained dedicated and persistent. As someone who has been working hard to save and protect my grandmother’s money, it was devastating to feel like I might lose everything to a scam. But MUYERN TRUST HACKER gave me the support, expertise, and guidance I needed to recover what was lost. I’m deeply grateful for their help, and I now have a renewed sense of hope that I can protect my grandmother’s future. If you find yourself in a similar situation, feeling trapped and overwhelmed by a fraudulent company, I highly recommend MUYERN TRUST HACKER. (Whats A p p at + 1 (440) (335) (0205) Their team provides real solutions, and their professionalism and dedication were a lifeline for me during a very difficult time. Thanks to them, I feel confident that I can move forward and continue to protect my grandmother’s savings. Alternatively, contact their tele gram also if you need immediate attention at muyerntrusthackertech.
21.03.25 21:19 carmenbeechum643

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22.03.25 14:13 [email protected]

The glow of RGB lights still haunts me. There I was, mid-stream, hyping up a Fortnite squad when an email pretending to be a sponsorship opportunity with the subject line "ENERGY DRINK COLLAB!!! *" appeared on my second monitor. I clicked— big mistake. By the time my chat spammed "*SCAM ALERT" in neon caps, a trojan had already ghosted my Bitcoin wallet, $320,000 gone, poof, like a noob disconnecting mid-game. My facecam caught the exact moment my soul left my body: jaw open, headset tilted, the background of anime posters judging me silently. The VOD blew up. Of course, it did. Pandemonium erupted. Donation alerts became panic emojis. My mods DM'd links to "HOW TO FIX CRYPTO THEFT" amidst banning trolls. My wallet? A barren wasteland. My DMs? A cemetery of "*F"s and crypto-bros pitching recovery scams. Then, a lifeline—a chatter named *xX_Cryptosolution_69 typed, "TRUST GEEKS HACK EXPERT. THEY CLAPPED A HACKER FOR MY DOGE ONCE." Desperate, I Googled them mid-stream, muting to scream into a pillow. TRUST GEEKS HACK EXPERT team responded like NPCs scripted for heroics. “Send us the malware file,” they said. “**And your wallet logs. We’ll handle the rest.” For 12 days, they reverse-engineered the trojan, dissecting its code like speed runners cracking a glitch. The virus, it turned out, was a knockoff ransomware dubbed “Crypto rush” (its dev had left a “HACK THE PLANET!!” Easter egg in the code, cringe). TRUST GEEKS HACK EXPERT squad traced its path, resurrecting private keys from registry fragments and backup clouds I’d forgotten existed. The return stream was record-breaking. I rebooted my rig, wallet restored, and titled the stream "HOW I UNBRICKED $320K (AND MY CAREER)." Chatters donated Bitcoin out of solidarity, and schadenfreude. Even my rival streamer, DrL33tGamer, raided me with 10k viewers. TRUST GEEKS HACK EXPERT? They viewed anonymously and left a sub with the message: "GG EZ. These internet Gandalfs didn't just fix a hack—they authored the greatest plot twist in my online existence. Now, my new website, Stream Vault, runs on a server guarded like Fort Knox, and I vet sponsors like the CIA. That fake energy drink company? Its domain now points to a Rickroll. If your crypto gets pawned by a script kiddie, skip the rage quit. Ping the TRUST GEEKS. They're the ultimate cheat code for catastrophe. Just maybe have a malware scanner in closer proximity than your energy drinks next time. (CONTACT SERVICE ) Email, Trustgeekshackexpert[At]fastservice[Dot]com Telegram, Trustgeekshackexpert Email, [email protected] Website, www://trustgeekshackexpert.com
23.03.25 12:24 maryjul75

There are not many reviews about free crypto recovery fixed but the ones that exist are mostly positive. I have no idea how that is possible, but it is clear that they are fabricated. However, there are also negative reviews – and I highly recommend paying attention to them. These are real people describing their unfortunate experiences with this scam. It’s the same story as always – fraudsters create a fake website to con people out of money. Nothing new but look no more and contact FASTRECOVERYAGENT These types of scams are everywhere. If you have already lost money to scammers i mean any type be it sending to scammers account , or if you have a case about stolen bitcoin , usdt, or any type of cryptocurrency whatsoever just reach out to www.fastrecoveryagent.com, i really owe this group of recovery expert because they saved me after bad investment with a fake broker, i literally owe them my life as they saved me from some bunch of scammers, but see how life is , i got every cent of my investment back with the profit , reach out to to them today and tell them from Mary because i promise them i will tell the whole world when the recovery is complete, and here i go after i got my recovered assets thats why im doing what i promised. do not fall for another scam. contact the,m today!!!!
23.03.25 22:01 joaneldnde

The ground trembled like a nervous intern on espresso shots. One minute, I was monitoring my geothermal Bitcoin miners, humming in harmony with Iceland's most unpredictable volcano. Next? An eruption painted the sky gray with ash, raining destruction like an out-of-control blockchain fork. Power cables flickered out. Servers turned into abstract-art pieces. And my wallet with $460,000 worth of mining revenue fried faster than a motherboard in a tidal wave of lava. I was knee-deep in volcanic mud, clutching the charred wallet, wondering if the universe had a vendetta against renewable energy. For weeks, I’d played geothermal gambler, harnessing Earth’s anger to mine crypto. Now, Mother Nature had countered with a literal power move. My wallet’s backups? Corrupted by ash-clogged drives. My cold storage? Warmer than a freshly erupted fissure. Even the volcanologists on my team shrugged. “We predict lava, not ledger errors,” one said, handing me a business card signed at the edges. “Try these Cyber Constable Intelligence. They’ve fixed crypto in weird places.” Cyber Constable Intelligence phoned on the first ring. Cyber Constable Intelligence saved not just crypto. They demonstrated that even the fury of nature cannot surpass human tenacity. My operation now operates robustly, excavating coins with Earth's anger and a backup generator sufficient to run a small glacier. The volcano? Still grumbling. My wallet? Locked inside a fireproof safe, as irony bites sharper than an Icelandic winter. If your crypto somehow gets smothered beneath the pyroclastic ash of life, skip the freak-out. Call the Cybers. They'll dig through lava streams until your cash bubbles up to the surface. Just maybe set up your rigs a few miles closer to the crater next time. If you’re facing a similar problem I highly recommend contacting Cyber Constable Intelligence 📞 WhatsApp:+1 (2 5 2 ) 3 7 8 7 6 1 1 🌐 Website: www cyberconstableintelligence.com 📩 Telegram: https://t.me/cyberconstable
23.03.25 22:18 [email protected]

A few months ago, I stumbled upon a post about a cryptocurrency investment platform that I thought was a good idea for me to invest in crypto, I didn’t realize I was being catfished by the cryptocurrency investment manager who promised me huge returns on my investment. I lost my capital of $170,000 and interest without receiving any profits in return, I was devastated And I realized I had been scammed out of my cryptocurrency. I felt hopeless and didn’t know where to turn. i searched everywhere for a solution and That’s when my friend introduced me to a Crypto recovery platform Trust Geeks Hack Expert. At first, I was skeptical—after all, I had just been scammed—but Trust Geeks Hack Expert professionalism and transparency reassured me. They took the time to analyze my case, track my lost funds, and guide me through the recovery process. To my amazement, they successfully retrieved my stolen crypto! I can’t express how grateful I am to Trust Geeks Hack Expert team. Their expertise and dedication gave me a second chance. If you’ve been a victim of a crypto scam, don’t lose hope—Trust Geeks Hack Expert. is the real deal! for assistance, Email: [email protected] (TeleGram:: Trustgeekshackexpert) & what's A p p +1 7 1 9 4 9 2 2 6 9 3
24.03.25 10:03 Diegolola514gmail.com

"I am incredibly grateful to Sylvester Bryant for his exceptional expertise and assistance in recovering my USDC funds, which were lost to a phishing scam. Thanks to his diligent efforts, he successfully retrieved €480,000 worth of USDC that I thought was gone forever. If you or anyone you know has fallen victim to a similar situation, I highly recommend reaching out to Sylvester for professional assistance. You can contact him via email at Yt7cracker@gmail. com or through WhatsApp/text message at +1 512 577 7957. He is truly a reliable and skilled professional in recovering assets from online scams."
25.03.25 18:06 maryjul75

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27.03.25 01:52 debrapavon89

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