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[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 completionДавайте 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.
-
07.09.23 16:24
CherryTeam
Cherry Team atlyginimų skaičiavimo programa yra labai naudingas įrankis įmonėms, kai reikia efektyviai valdyti ir skaičiuoti darbuotojų atlyginimus. Ši programinė įranga, turinti išsamias funkcijas ir patogią naudotojo sąsają, suteikia daug privalumų, kurie padeda supaprastinti darbo užmokesčio skaičiavimo procesus ir pagerinti finansų valdymą. Štai keletas pagrindinių priežasčių, kodėl Cherry Team atlyginimų skaičiavimo programa yra naudinga įmonėms: Automatizuoti ir tikslūs skaičiavimai: Atlyginimų skaičiavimai rankiniu būdu gali būti klaidingi ir reikalauti daug laiko. Programinė įranga Cherry Team automatizuoja visą atlyginimų skaičiavimo procesą, todėl nebereikia atlikti skaičiavimų rankiniu būdu ir sumažėja klaidų rizika. Tiksliai apskaičiuodama atlyginimus, įskaitant tokius veiksnius, kaip pagrindinis atlyginimas, viršvalandžiai, premijos, išskaitos ir mokesčiai, programa užtikrina tikslius ir be klaidų darbo užmokesčio skaičiavimo rezultatus. Sutaupoma laiko ir išlaidų: Darbo užmokesčio valdymas gali būti daug darbo jėgos reikalaujanti užduotis, reikalaujanti daug laiko ir išteklių. Programa Cherry Team supaprastina ir pagreitina darbo užmokesčio skaičiavimo procesą, nes automatizuoja skaičiavimus, generuoja darbo užmokesčio žiniaraščius ir tvarko išskaičiuojamus mokesčius. Šis automatizavimas padeda įmonėms sutaupyti daug laiko ir pastangų, todėl žmogiškųjų išteklių ir finansų komandos gali sutelkti dėmesį į strategiškai svarbesnę veiklą. Be to, racionalizuodamos darbo užmokesčio operacijas, įmonės gali sumažinti administracines išlaidas, susijusias su rankiniu darbo užmokesčio tvarkymu. Mokesčių ir darbo teisės aktų laikymasis: Įmonėms labai svarbu laikytis mokesčių ir darbo teisės aktų, kad išvengtų baudų ir teisinių problemų. Programinė įranga Cherry Team seka besikeičiančius mokesčių įstatymus ir darbo reglamentus, užtikrindama tikslius skaičiavimus ir teisinių reikalavimų laikymąsi. Programa gali dirbti su sudėtingais mokesčių scenarijais, pavyzdžiui, keliomis mokesčių grupėmis ir įvairių rūšių atskaitymais, todėl užtikrina atitiktį reikalavimams ir kartu sumažina klaidų riziką. Ataskaitų rengimas ir analizė: Programa Cherry Team siūlo patikimas ataskaitų teikimo ir analizės galimybes, suteikiančias įmonėms vertingų įžvalgų apie darbo užmokesčio duomenis. Ji gali generuoti ataskaitas apie įvairius aspektus, pavyzdžiui, darbo užmokesčio paskirstymą, išskaičiuojamus mokesčius ir darbo sąnaudas. Šios ataskaitos leidžia įmonėms analizuoti darbo užmokesčio tendencijas, nustatyti tobulintinas sritis ir priimti pagrįstus finansinius sprendimus. Pasinaudodamos duomenimis pagrįstomis įžvalgomis, įmonės gali optimizuoti savo darbo užmokesčio strategijas ir veiksmingai kontroliuoti išlaidas. Integracija su kitomis sistemomis: Cherry Team programinė įranga dažnai sklandžiai integruojama su kitomis personalo ir apskaitos sistemomis. Tokia integracija leidžia automatiškai perkelti atitinkamus duomenis, pavyzdžiui, informaciją apie darbuotojus ir finansinius įrašus, todėl nebereikia dubliuoti duomenų. Supaprastintas duomenų srautas tarp sistemų padidina bendrą efektyvumą ir sumažina duomenų klaidų ar neatitikimų riziką. Cherry Team atlyginimų apskaičiavimo programa įmonėms teikia didelę naudą - automatiniai ir tikslūs skaičiavimai, laiko ir sąnaudų taupymas, atitiktis mokesčių ir darbo teisės aktų reikalavimams, ataskaitų teikimo ir analizės galimybės bei integracija su kitomis sistemomis. Naudodamos šią programinę įrangą įmonės gali supaprastinti darbo užmokesčio skaičiavimo procesus, užtikrinti tikslumą ir atitiktį reikalavimams, padidinti darbuotojų pasitenkinimą ir gauti vertingų įžvalgų apie savo finansinius duomenis. Programa Cherry Team pasirodo esanti nepakeičiamas įrankis įmonėms, siekiančioms efektyviai ir veiksmingai valdyti darbo užmokestį. https://cherryteam.lt/lt/
-
08.10.23 01:30
davec8080
The "Shibarium for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH. The Plot Thickens. Someone posted the actual transactions!!!! https://bscscan.com/tx/0xa846ea0367c89c3f0bbfcc221cceea4c90d8f56ead2eb479d4cee41c75e02c97 It seems the article is true!!!! And it's also FUD. Let me explain. Check this link: https://bscscan.com/token/0x5a752c9fe3520522ea88f37a41c3ddd97c022c2f So there really is a "Shibarium" token. And somebody did a rug pull with it. CONFIRMED. But the "Shibarium" token for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH.
-
24.06.24 04:31
tashandiarisha
Web-site. https://trustgeekshackexpert.com/ Tele-Gram, trustgeekshackexpert During the pandemic, I ventured into the world of cryptocurrency trading. My father loaned me $10,000, which I used to purchase my first bitcoins. With diligent research and some luck, I managed to grow my investment to over $350,000 in just a couple of years. I was thrilled with my success, but my excitement was short-lived when I decided to switch brokers and inadvertently fell victim to a phishing attack. While creating a new account, I received what seemed like a legitimate email requesting verification. Without second-guessing, I provided my information, only to realize later that I had lost access to my email and cryptocurrency wallets. Panic set in as I watched my hard-earned assets disappear before my eyes. Desperate to recover my funds, I scoured the internet for solutions. That's when I stumbled upon the Trust Geeks Hack Expert on the Internet. The service claimed to specialize in recovering lost crypto assets, and I decided to take a chance. Upon contacting them, the team swung into action immediately. They guided me through the entire recovery process with professionalism and efficiency. The advantages of using the Trust Geeks Hack Expert Tool became apparent from the start. Their team was knowledgeable and empathetic, understanding the urgency and stress of my situation. They employed advanced security measures to ensure my information was handled safely and securely. One of the key benefits of the Trust Geeks Hack Expert Tool was its user-friendly interface, which made a complex process much more manageable for someone like me, who isn't particularly tech-savvy. They also offered 24/7 support, so I never felt alone during recovery. Their transparent communication and regular updates kept me informed and reassured throughout. The Trust Geeks Hack Expert Tool is the best solution for anyone facing similar issues. Their swift response, expertise, and customer-centric approach set them apart from other recovery services. Thanks to their efforts, I regained access to my accounts and my substantial crypto assets. The experience taught me a valuable lesson about online security and showed me the incredible potential of the Trust Geeks Hack Expert Tool. Email:: trustgeekshackexpert{@}fastservice{.}com WhatsApp + 1.7.1.9.4.9.2.2.6.9.3
-
26.06.24 18:46
Jacobethannn098
LEGAL RECOUP FOR CRYPTO THEFT BY ADRIAN LAMO HACKER
-
26.06.24 18:46
Jacobethannn098
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-
04.07.24 04:49
ZionNaomi
For over twenty years, I've dedicated myself to the dynamic world of marketing, constantly seeking innovative strategies to elevate brand visibility in an ever-evolving landscape. So when the meteoric rise of Bitcoin captured my attention as a potential avenue for investment diversification, I seized the opportunity, allocating $20,000 to the digital currency. Witnessing my investment burgeon to an impressive $70,000 over time instilled in me a sense of financial promise and stability.However, amidst the euphoria of financial growth, a sudden and unforeseen oversight brought me crashing back to reality during a critical business trip—I had misplaced my hardware wallet. The realization that I had lost access to the cornerstone of my financial security struck me with profound dismay. Desperate for a solution, I turned to the expertise of Daniel Meuli Web Recovery.Their response was swift . With meticulous precision, they embarked on the intricate process of retracing the elusive path of my lost funds. Through their unwavering dedication, they managed to recover a substantial portion of my investment, offering a glimmer of hope amidst the shadows of uncertainty. The support provided by Daniel Meuli Web Recovery extended beyond mere financial restitution. Recognizing the imperative of fortifying against future vulnerabilities, they generously shared invaluable insights on securing digital assets. Their guidance encompassed crucial aspects such as implementing hardware wallet backups and fortifying security protocols, equipping me with recovered funds and newfound knowledge to navigate the digital landscape securely.In retrospect, this experience served as a poignant reminder of the critical importance of diligence and preparedness in safeguarding one's assets. Thanks to the expertise and unwavering support extended by Daniel Meuli Web Recovery, I emerged from the ordeal with renewed resilience and vigilance. Empowered by their guidance and fortified by enhanced security measures, I now approach the future with unwavering confidence.The heights of financial promise to the depths of loss and back again has been a humbling one, underscoring the volatility and unpredictability inherent in the digital realm. Yet, through adversity, I have emerged stronger, armed with a newfound appreciation for the importance of diligence, preparedness, and the invaluable support of experts like Daniel Meuli Web Recovery.As I persist in traversing the digital landscape, I do so with a judicious blend of vigilance and fortitude, cognizant that with adequate safeguards and the backing of reliable confidants, I possess the fortitude to withstand any adversity that may arise. For this, I remain eternally appreciative. Email Danielmeuliweberecovery @ email . c om WhatsApp + 393 512 013 528
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13.07.24 21:13
michaelharrell825
In 2020, amidst the economic fallout of the pandemic, I found myself unexpectedly unemployed and turned to Forex trading in hopes of stabilizing my finances. Like many, I was drawn in by the promise of quick returns offered by various Forex robots, signals, and trading advisers. However, most of these products turned out to be disappointing, with claims that were far from reality. Looking back, I realize I should have been more cautious, but the allure of financial security clouded my judgment during those uncertain times. Amidst these disappointments, Profit Forex emerged as a standout. Not only did they provide reliable service, but they also delivered tangible results—a rarity in an industry often plagued by exaggerated claims. The positive reviews from other users validated my own experience, highlighting their commitment to delivering genuine outcomes and emphasizing sound financial practices. My journey with Profit Forex led to a net profit of $11,500, a significant achievement given the challenges I faced. However, my optimism was short-lived when I encountered obstacles trying to withdraw funds from my trading account. Despite repeated attempts, I found myself unable to access my money, leaving me frustrated and uncertain about my financial future. Fortunately, my fortunes changed when I discovered PRO WIZARD GIlBERT RECOVERY. Their reputation for recovering funds from fraudulent schemes gave me hope in reclaiming what was rightfully mine. With a mixture of desperation and cautious optimism, I reached out to them for assistance. PRO WIZARD GIlBERT RECOVERY impressed me from the start with their professionalism and deep understanding of financial disputes. They took a methodical approach, using advanced techniques to track down the scammers responsible for withholding my funds. Throughout the process, their communication was clear and reassuring, providing much-needed support during a stressful period. Thanks to PRO WIZARD GIlBERT RECOVERY's expertise and unwavering dedication, I finally achieved a resolution to my ordeal. They successfully traced and retrieved my funds, restoring a sense of justice and relief. Their intervention not only recovered my money but also renewed my faith in ethical financial services. Reflecting on my experience, I've learned invaluable lessons about the importance of due diligence and discernment in navigating the Forex market. While setbacks are inevitable, partnering with reputable recovery specialists like PRO WIZARD GIlBERT RECOVERY can make a profound difference. Their integrity and effectiveness have left an indelible mark on me, guiding my future decisions and reinforcing the value of trustworthy partnerships in achieving financial goals. I wholeheartedly recommend PRO WIZARD GIlBERT RECOVERY to anyone grappling with financial fraud or disputes. Their expertise and commitment to client satisfaction are unparalleled, offering a beacon of hope in challenging times. Thank you, PRO WIZARD GIlBERT RECOVERY, for your invaluable assistance in reclaiming what was rightfully mine. Your service not only recovered my funds but also restored my confidence in navigating the complexities of financial markets with greater caution and awareness. Email: prowizardgilbertrecovery(@)engineer.com Homepage: https://prowizardgilbertrecovery.xyz WhatsApp: +1 (516) 347‑9592
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17.07.24 02:26
thompsonrickey
In the vast and often treacherous realm of online investments, I was entangled in a web of deceit that cost me nearly $45,000. It all started innocuously enough with an enticing Instagram profile promising lucrative returns through cryptocurrency investment. Initially, everything seemed promising—communications were smooth, and assurances were plentiful. However, as time passed, my optimism turned to suspicion. Withdrawal requests were met with delays and excuses. The once-responsive "investor" vanished into thin air, leaving me stranded with dwindling hopes and a sinking feeling in my gut. It became painfully clear that I had been duped by a sophisticated scheme designed to exploit trust and naivety. Desperate to recover my funds, I turned to online forums where I discovered numerous testimonials advocating for Muyern Trust Hacker. With nothing to lose, I contacted them, recounting my ordeal with a mixture of skepticism and hope. Their swift response and professional demeanor immediately reassured me that I had found a lifeline amidst the chaos. Muyern Trust Hacker wasted no time in taking action. They meticulously gathered evidence, navigated legal complexities, and deployed their expertise to expedite recovery. In what felt like a whirlwind of activity, although the passage of time was a blur amidst my anxiety, they achieved the seemingly impossible—my stolen funds were returned. The relief I felt was overwhelming. Muyern Trust Hacker not only restored my financial losses but also restored my faith in justice. Their commitment to integrity and their relentless pursuit of resolution were nothing short of remarkable. They proved themselves as recovery specialists and guardians against digital fraud, offering hope to victims like me who had been ensnared by deception. My gratitude knows no bounds for Muyern Trust Hacker. Reach them at muyerntrusted @ m a i l - m e . c o m AND Tele gram @ muyerntrusthackertech
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18.07.24 20:13
austinagastya
I Testify For iBolt Cyber Hacker Alone - For Crypto Recovery Service I highly suggest iBolt Cyber Hacker to anyone in need of bitcoin recovery services. They successfully recovered my bitcoin from a fake trading scam with speed and efficiency. This crew is trustworthy, They kept me updated throughout the procedure. I thought my bitcoin was gone, I am so grateful for their help, If you find yourself in a similar circumstance, do not hesitate to reach out to iBolt Cyber Hacker for assistance. Thank you, iBOLT, for your amazing customer service! Please be cautious and contact them directly through their website. Email: S u p p o r t @ ibolt cyber hack . com Cont/Whtp + 3. .9 .3. .5..0. .9. 2. 9. .0 .3. 1 .8. Website: h t t p s : / / ibolt cyber hack . com /
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27.08.24 12:50
James889900
All you need is to hire an expert to help you accomplish that. If there’s any need to spy on your partner’s phone. From my experience I lacked evidence to confront my husband on my suspicion on his infidelity, until I came across ETHICALAHCKERS which many commend him of assisting them in their spying mission. So I contacted him and he provided me with access into his phone to view all text messages, call logs, WhatsApp messages and even her location. This evidence helped me move him off my life . I recommend you consult ETHICALHACKERS009 @ gmail.com OR CALL/TEXT +1(716) 318-5536 or whatsapp +14106350697 if you need access to your partner’s phone
-
27.08.24 13:06
James889900
All you need is to hire an expert to help you accomplish that. If there’s any need to spy on your partner’s phone. From my experience I lacked evidence to confront my husband on my suspicion on his infidelity, until I came across ETHICALAHCKERS which many commend him of assisting them in their spying mission. So I contacted him and he provided me with access into his phone to view all text messages, call logs, WhatsApp messages and even her location. This evidence helped me move him off my life . I recommend you consult ETHICALHACKERS009 @ gmail.com OR CALL/TEXT +1(716) 318-5536 or whatsapp +14106350697 if you need access to your partner’s phone
-
02.09.24 20:24
[email protected]
If You Need Hacker To Recover Your Bitcoin Contact Paradox Recovery Wizard Paradox Recovery Wizard successfully recovered $123,000 worth of Bitcoin for my husband, which he had lost due to a security breach. The process was efficient and secure, with their expert team guiding us through each step. They were able to trace and retrieve the lost cryptocurrency, restoring our peace of mind and financial stability. Their professionalism and expertise were instrumental in recovering our assets, and we are incredibly grateful for their service. Email: support@ paradoxrecoverywizard.com Email: paradox_recovery @cyberservices.com Wep: https://paradoxrecoverywizard.com/ WhatsApp: +39 351 222 3051.
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06.09.24 01:35
Celinagarcia
HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.
-
06.09.24 01:44
Celinagarcia
HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.
-
16.09.24 00:10
marcusaustin
Bitcoin Recovery Services: Restoring Lost Cryptocurrency If you've lost access to your cryptocurrency and unable to make a withdrawal, I highly recommend iBolt Cyber Hacker Bitcoin Recovery Services. Their team is skilled, professional, and efficient in recovering lost Bitcoin. They provide clear communication, maintain high security standards, and work quickly to resolve issues. Facing the stress of lost cryptocurrency, iBolt Cyber Hacker is a trusted service that will help you regain access to your funds securely and reliably. Highly recommended! Email: S u p p o r t @ ibolt cyber hack . com Cont/Whtp + 3. .9 .3. .5..0. .9. 2. 9. .0 .3. 1 .8. Website: h t t p s : / / ibolt cyber hack . com /
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16.09.24 00:11
marcusaustin
Bitcoin Recovery Services: Restoring Lost Cryptocurrency If you've lost access to your cryptocurrency and unable to make a withdrawal, I highly recommend iBolt Cyber Hacker Bitcoin Recovery Services. Their team is skilled, professional, and efficient in recovering lost Bitcoin. They provide clear communication, maintain high security standards, and work quickly to resolve issues. Facing the stress of lost cryptocurrency, iBolt Cyber Hacker is a trusted service that will help you regain access to your funds securely and reliably. Highly recommended! Email: S u p p o r t @ ibolt cyber hack . com Cont/Whtp + 3. .9 .3. .5..0. .9. 2. 9. .0 .3. 1 .8. Website: h t t p s : / / ibolt cyber hack . com /
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23.09.24 18:56
matthewshimself
At first, I was admittedly skeptical about Worldcoin (ref: https://worldcoin.org/blog/worldcoin/this-is-worldcoin-video-explainer-series), particularly around the use of biometric data and the WLD token as a reward mechanism for it. However, after following the project closer, I’ve come to appreciate the broader vision and see the value in the underlying tech behind it. The concept of Proof of Personhood (ref: https://worldcoin.org/blog/worldcoin/proof-of-personhood-what-it-is-why-its-needed) has definitely caught my attention, and does seem like a crucial step towards tackling growing issues like bots, deepfakes, and identity fraud. Sam Altman’s vision is nothing short of ambitious, but I do think he & Alex Blania have the chops to realize it as mainstay in the global economy.
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01.10.24 14:54
Sinewclaudia
I lost about $876k few months ago trading on a fake binary option investment websites. I didn't knew they were fake until I tried to withdraw. Immediately, I realized these guys were fake. I contacted Sinew Claudia world recovery, my friend who has such experience before and was able to recover them, recommended me to contact them. I'm a living testimony of a successful recovery now. You can contact the legitimate recovery company below for help and assistance. [email protected] [email protected] WhatsApp: 6262645164
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02.10.24 22:27
Emily Hunter
Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.
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18.10.24 09:34
freidatollerud
The growth of WIN44 in Brazil is very interesting! If you're looking for more options for online betting and casino games, I recommend checking out Casinos in Brazil. It's a reliable platform that offers a wide variety of games and provides a safe and enjoyable experience for users. It's worth checking out! https://win44.vip
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31.10.24 00:13
ytre89
Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.
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02.11.24 14:44
diannamendoza732
In the world of Bitcoin recovery, Pro Wizard Gilbert truly represents the gold standard. My experience with Gilbert revealed just how exceptional his methods are and why he stands out as the premier authority in this critical field. When I first encountered the complexities of Bitcoin recovery, I was daunted by the technical challenges and potential risks. Gilbert’s approach immediately distinguished itself through its precision and effectiveness. His methods are meticulously designed, combining cutting-edge techniques with an in-depth understanding of the Bitcoin ecosystem. He tackled the recovery process with a level of expertise and thoroughness that was both impressive and reassuring. What sets Gilbert’s methods apart is not just their technical sophistication but also their strategic depth. He conducts a comprehensive analysis of each case, tailoring his approach to address the unique aspects of the situation. This personalized strategy ensures that every recovery effort is optimized for success. Gilbert’s transparent communication throughout the process was invaluable, providing clarity and confidence during each stage of the recovery. The results I achieved with Pro Wizard Gilbert’s methods were remarkable. His gold standard approach not only recovered my Bitcoin but did so with an efficiency and reliability that exceeded my expectations. His deep knowledge, innovative techniques, and unwavering commitment make him the definitive expert in Bitcoin recovery. For anyone seeking a benchmark in Bitcoin recovery solutions, Pro Wizard Gilbert’s methods are the epitome of excellence. His ability to blend technical prowess with strategic insight truly sets him apart in the industry. Call: for help. You may get in touch with them at ; Email: (prowizardgilbertrecovery(@)engineer.com) Telegram ; https://t.me/Pro_Wizard_Gilbert_Recovery Homepage ; https://prowizardgilbertrecovery.info
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12.11.24 00:50
TERESA
Brigadia Tech Remikeable recovery has exhibited unparalleled strength in the realm of recovery. They stand out as the premier team to collaborate with if you encounter withdrawal difficulties from the platform where you’ve invested. Recently, I engaged with them to recover over a million dollars trapped in an investment platform I’d been involved with for months. I furnished their team with every detail of the investment, including accounts, names, and wallet addresses to which I sent the funds. This decision proved to be the best I’ve made, especially after realizing the company had scammed me. Brigadia Tech Remikeable recovery ensures exemplary service delivery and ensures the perpetrators face justice. They employ advanced techniques to ensure you regain access to your funds. Understandably, many individuals who have fallen victim to investment scams may still regret engaging in online services again due to the trauma of being scammed. However, I implore you to take action. Seek assistance from Brigadia Tech Remikeable Recovery Experts today and witness their remarkable capabilities. I am grateful that I resisted their enticements, and despite the time it took me to discover brigadia tech recovery, they ultimately fulfilled my primary objective. Without Brigadia Tech Recovery's intervention, I would have remained despondent and perplexed indefinitely. Also if you are looking for the best and safest investment company you can contact them, for wallet recovery, difficult withdrawal, etc. I am so happy to keep getting my daily BTC, all I do is keep 0.1 BTC in my mining wallet with the help of Brigadia Tech. They connected me to his mining stream and I earn 0.4 btc per day with this, my daily profit. I can get myself a new house and car. I can’t believe I have thousands of dollars in my bank account. Now you can get in. ([email protected]) Telegram +1 (323)-9 1 0 -1 6 0 5
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17.11.24 09:31
Vivianlocke223
Have You Fallen Victim to Cryptocurrency Fraud? If your Bitcoin or other cryptocurrencies were stolen due to scams or fraudulent activities, Free Crypto Recovery Fixed is here to help you recover what’s rightfully yours. As a leading recovery service, we specialize in restoring lost cryptocurrency and assisting victims of fraud — no matter how long ago the incident occurred. Our experienced team leverages cutting-edge tools and expertise to trace and recover stolen assets, ensuring swift and secure results. Don’t let scammers jeopardize your financial security. With Free Crypto Recovery Fixed, you’re putting your trust in a reliable and dedicated team that prioritizes recovering your assets and ensuring their future protection. Take the First Step Toward Recovery Today! 📞 Text/Call: +1 407 212 7493 ✉️ Email: [email protected] 🌐 Website: https://freecryptorecovery.net Let us help you regain control of your financial future — swiftly and securely.
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19.11.24 03:06
[email protected]
My entire existence fell apart when a malevolent hacker recently gained access to my online accounts. I felt violated and extremely uneasy after discovering that the digital platforms I depended on for communication, employment, and finances had been compromised. Regaining control and restoring my digital security was an overwhelming task in the immediate aftermath. To help me navigate the difficult process of recovering my accounts and getting my peace of mind back, TRUST GEEKS HACK EXPERT came into my life as a ray of hope. They immediately put their highly skilled professionals to work, thoroughly examining the vulnerability and methodically preventing unwanted access. They guided me through each stage soothingly, explaining what was occurring and why, so I never felt lost or alone. They communicated with service providers to restore my legitimate access while skillfully navigating the complex labyrinth of account recovery procedures. My digital footprint was cleaned and strengthened against future attacks thanks to their equally amazing ability to remove any remaining evidence of the hacker's presence. However, TRUST GEEKS HACK EXPERT actual worth went beyond its technical aspects. They offered constant emotional support during the ordeal, understanding my fragility and sense of violation. My tense nerves were calmed by their comforting presence and kind comments, which served as a reminder that I wasn't alone in this struggle. With their help, I was able to reestablish my sense of security and control, which enabled me to return my attention to the significant areas of my life that had been upended. Ultimately, TRUST GEEKS HACK EXPERT all-encompassing strategy not only recovered my online accounts but also my general peace of mind, which is a priceless result for which I am incredibly appreciative of their knowledge and kindness. Make the approach and send a message to TRUST GEEKS HACK EXPERT Via Web site <> www://trustgeekshackexpert.com/-- E>mail: Trustgeekshackexpert(At)fastservice..com -- TeleGram,<> Trustgeekshackexpert
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19.11.24 03:07
[email protected]
My entire existence fell apart when a malevolent hacker recently gained access to my online accounts. I felt violated and extremely uneasy after discovering that the digital platforms I depended on for communication, employment, and finances had been compromised. Regaining control and restoring my digital security was an overwhelming task in the immediate aftermath. To help me navigate the difficult process of recovering my accounts and getting my peace of mind back, TRUST GEEKS HACK EXPERT came into my life as a ray of hope. They immediately put their highly skilled professionals to work, thoroughly examining the vulnerability and methodically preventing unwanted access. They guided me through each stage soothingly, explaining what was occurring and why, so I never felt lost or alone. They communicated with service providers to restore my legitimate access while skillfully navigating the complex labyrinth of account recovery procedures. My digital footprint was cleaned and strengthened against future attacks thanks to their equally amazing ability to remove any remaining evidence of the hacker's presence. However, TRUST GEEKS HACK EXPERT actual worth went beyond its technical aspects. They offered constant emotional support during the ordeal, understanding my fragility and sense of violation. My tense nerves were calmed by their comforting presence and kind comments, which served as a reminder that I wasn't alone in this struggle. With their help, I was able to reestablish my sense of security and control, which enabled me to return my attention to the significant areas of my life that had been upended. Ultimately, TRUST GEEKS HACK EXPERT all-encompassing strategy not only recovered my online accounts but also my general peace of mind, which is a priceless result for which I am incredibly appreciative of their knowledge and kindness. Make the approach and send a message to TRUST GEEKS HACK EXPERT Via Web site <> www://trustgeekshackexpert.com/-- E>mail: Trustgeekshackexpert(At)fastservice..com -- TeleGram,<> Trustgeekshackexpert
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21.11.24 04:14
ronaldandre617
Being a parent is great until your toddler figures out how to use your devices. One afternoon, I left my phone unattended for just a few minutes rookie mistake of the century. I thought I’d take a quick break, but little did I know that my curious little genius was about to embark on a digital adventure. By the time I came back, I was greeted by two shocking revelations: my toddler had somehow managed to buy a $5 dinosaur toy online and, even more alarmingly, had locked me out of my cryptocurrency wallet holding a hefty $75,000. Yes, you heard that right a dinosaur toy was the least of my worries! At first, I laughed it off. I mean, what toddler doesn’t have a penchant for expensive toys? But then reality set in. I stared at my phone in disbelief, desperately trying to guess whatever random string of gibberish my toddler had typed as a new password. Was it “dinosaur”? Or perhaps “sippy cup”? I felt like I was in a bizarre game of Password Gone Wrong. Every attempt led to failure, and soon the laughter faded, replaced by sheer panic. I was in way over my head, and my heart raced as the countdown of time ticked away. That’s when I decided to take action and turned to Digital Tech Guard Recovery, hoping they could solve the mystery that was my toddler’s handiwork. I explained my predicament, half-expecting them to chuckle at my misfortune, but they were incredibly professional and empathetic. Their confidence put me at ease, and I knew I was in good hands. Contact With WhatsApp: +1 (443) 859 - 2886 Email digital tech guard . com Telegram: digital tech guard recovery . com website link :: https : // digital tech guard . com Their team took on the challenge like pros, employing their advanced techniques to unlock my wallet with a level of skill I can only describe as magical. As I paced around, anxiously waiting for updates, I imagined my toddler inadvertently locking away my life savings forever. But lo and behold, it didn’t take long for Digital Tech Guard Recovery to work their magic. Not only did they recover the $75,000, but they also gave me invaluable tips on securing my wallet better like not leaving it accessible to tiny fingers! Who knew parenting could lead to such dramatic situations? Crisis averted, and I learned my lesson: always keep my devices out of reach of little explorers. If you ever find yourself in a similar predicament whether it’s tech-savvy toddlers or other digital disasters don’t hesitate to reach out to Digital Tech Guard Recovery. They saved my funds and my sanity, proving that no challenge is too great, even when it involves a toddler’s mischievous fingers!
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21.11.24 08:02
Emily Hunter
If I hadn't found a review online and filed a complaint via email to support@deftrecoup. com , the people behind this unregulated scheme would have gotten away with leaving me in financial ruins. It was truly the most difficult period of my life.
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22.11.24 04:41
[email protected]
I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT
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22.11.24 15:26
cliftonhandyman
Your Lost Bitcoins Are Not Gone Forever? Enquire From iBolt Cyber Hacker iBolt Cyber Hacker is a cybersecurity service that specializes in Bitcoin and cryptocurrency recovery. Even if your Bitcoin is locked away in a scammer inaccessible wallet, they have the tools and expertise to retrieve it. Many people, including seasoned cryptocurrency investors, face the daunting possibility of never seeing their lost funds again. iBolt cyber hacker service is a potential lifeline in these situations. I understand the concerns many people might have about trusting a third-party service to recover their Bitcoin. iBolt Cyber Hacker takes security seriously, implementing encryption and stringent privacy protocols. I was assured that no sensitive data would be compromised during the recovery process. Furthermore, their reputation in the cryptocurrency community, based on positive feedback from previous clients, gave me confidence that I was in good hands. Whtp +39, 351..105, 3619 Em.ail: ibolt @ cyber- wizard. co m
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22.11.24 23:43
teresaborja
all thanks to Tech Cyber Force Recovery expert assistance. As a novice in cryptocurrency, I had been carefully accumulating a modest amount of Bitcoin, meticulously safeguarding my digital wallet and private keys. However, as the adage goes, the best-laid plans can often go awry, and that's precisely what happened to me. Due to a series of technical mishaps and human errors, I found myself locked out of my Bitcoin wallet, unable to access the fruits of my digital labors. Panic set in as I frantically searched for a solution, scouring the internet for any glimmer of hope. That's when I stumbled upon the Tech Cyber Force Recovery team, a group of seasoned cryptocurrency specialists who had built a reputation for their ability to recover lost or inaccessible digital assets. Skeptical at first, I reached out, desperate for a miracle. To my utter amazement, the Tech Cyber Force Recovery experts quickly assessed my situation and devised a meticulous plan of attack. Through their deep technical knowledge, unwavering determination, and a keen eye for detail, they were able to navigate the complex labyrinth of blockchain technology, ultimately recovering my entire Bitcoin portfolio. What had once seemed like a hopeless endeavor was now a reality, and I found myself once again in possession of my digital wealth, all thanks to the incredible efforts of the Tech Cyber Force Recovery team. This experience has not only restored my faith in the cryptocurrency ecosystem. Still, it has also instilled in me a profound appreciation for the critical role that expert recovery services can play in safeguarding one's digital assets. ENAIL < Tech cybers force recovery @ cyber services. com > WEBSITE < ht tps : // tech cyber force recovery. info > TEXT < +1. 561. 726. 3697 >
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24.11.24 02:21
[email protected]
I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT
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25.11.24 02:19
briankennedy
COMMENT ON I NEED A HACKER TO RECOVER MONEY FROM BINARY TRADING. HIRE FASTFUND RECOVERY
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25.11.24 02:20
briankennedy
After countless hours of research and desperate attempts to find a solution, I stumbled upon FASTFUND RECOVERY. It was like finding an oasis in the middle of a desert. Their website promised to help victims of scams reclaim what was rightfully theirs, and I instantly knew I had to give them a shot. Before diving headfirst into the recovery process, I wanted to make sure that FASTFUND RECOVERY was the real deal. So, I did my due diligence and looked into their expertise and reputation. To my relief, I found that they had an impeccable track record, successfully assisting countless individuals in recovering their lost funds. Their team consisted of experts in cybersecurity and financial fraud, armed with the knowledge and tools needed to tackle even the most intricate scams. With their reputation preceding them, I felt a renewed sense of hope. FASTFUND RECOVERY successfully came to my aid and got back the amount I lost to these scammers and for this, I am sending this article for clarification. The info of FASTFUND RECOVERY is email: Fastfundrecovery8 (@)Gmail (.) com. Web fastfundrecovery(.)com. (W/A 1 807/500/7554)
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26.11.24 21:59
[email protected]
In a world brimming with enticing investment opportunities, it is crucial to tread carefully. The rise of digital currencies has attracted many eager investors, but along with this excitement lurk deceitful characters ready to exploit the unsuspecting. I learned this lesson the hard way, and I want to share my story in the hopes that it can save someone from making the same mistakes I did. It all began innocently enough when I came across an engaging individual on Facebook. Lured in by promises of high returns in the cryptocurrency market, I felt the electric thrill of potential wealth coursing through me. Initial investments returned some profits, and that exhilarating taste of success fueled my ambition. Encouraged by a meager withdrawal, I decided to commit even more funds. This was the moment I let my guard down, blinded by greed. As time went on, the red flags started to multiply. The moment I tried to withdraw my earnings, a cascade of unreasonable fees appeared like a thick mist, obscuring the truth. “Just a little more,” they said, “Just until the next phase.” I watched my hard-earned money slip through my fingers as I scraped together every last cent to pay those relentless fees. My trust had become my downfall. In the end, I lost not just a significant amount of cash, but my peace of mind about $1.1 million vanished into the abyss of false promises and hollow guarantees. But despair birthed hope. After a cascade of letdowns, I enlisted the help of KAY-NINE CYBER SERVICES, a team that specializes in reclaiming lost funds from scams. Amazingly, they worked tirelessly to piece together what had been ripped away, providing me with honest guidance when I felt utterly defeated. Their expertise in navigating the treacherous waters of crypto recovery was a lifeline I desperately needed. To anyone reading this, please let my story serve as a warning. High returns often come wrapped in the guise of deception. Protect your investments, scrutinize every opportunity, and trust your instincts. Remember, the allure of quick riches can lead you straight to heartbreak, but with cautious determination and support, it is possible to begin healing from such devastating loss. Stay informed, stay vigilant, and may you choose your investment paths wisely. Email: kaynine @ cyberservices . com
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26.11.24 23:12
rickrobinson8
FAST SOLUTION FOR CYPTOCURRENCY RECOVERY SPARTAN TECH GROUP RETRIEVAL
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26.11.24 23:12
rickrobinson8
Although recovering from the terrible effects of investment fraud can seem like an impossible task, it is possible to regain financial stability and go on with the correct assistance and tools. In my own experience with Wizard Web Recovery, a specialized company that assisted me in navigating the difficulties of recouping my losses following my fall prey to a sophisticated online fraud, that was undoubtedly the case. My life money had disappeared in an instant, leaving me in a state of shock when I first contacted Spartan Tech Group Retrieval through this Email: spartantechretrieval (@) g r o u p m a i l .c o m The compassionate and knowledgeable team there quickly put my mind at ease, outlining a clear and comprehensive plan of action. They painstakingly examined every aspect of my case, using their broad business contacts and knowledge to track the movement of my pilfered money. They empowered me to make knowledgeable decisions regarding the rehabilitation process by keeping me updated and involved at every stage. But what I valued most was their unrelenting commitment and perseverance; they persisted in trying every option until a sizable amount of my lost money had been successfully restored. It was a long and arduous journey, filled with ups and downs, but having Spartan Tech Group Retrieval in my corner made all the difference. Thanks to their tireless efforts, I was eventually able to rebuild my financial foundation and reclaim a sense of security and control over my life. While the emotional scars of investment fraud may never fully heal, working with this remarkable organization played a crucial role in my ability to move forward and recover. For proper talks, contact on WhatsApp:+1 (971) 4 8 7 - 3 5 3 8 and Telegram:+1 (581) 2 8 6 - 8 0 9 2 Thank you for your time reading as it will be of help.
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27.11.24 00:39
[email protected]
Although recovering lost or inaccessible Bitcoin can be difficult and unpleasant, it is frequently possible to get back access to one's digital assets with the correct help and direction. Regarding the subject at hand, the examination of Trust Geeks Hack Expert Website www://trustgeekshackexpert.com/ assistance after an error emphasizes how important specialized services may be in negotiating the difficulties of Bitcoin recovery. These providers possess the technical expertise and resources necessary to assess the situation, identify the root cause of the issue, and devise a tailored solution to retrieve the lost funds. By delving deeper into the specifics of Trust Geeks Hack Expert approach, we can gain valuable insights into the nuances of this process. Perhaps they leveraged advanced blockchain analysis tools to trace the transaction history and pinpoint the location of the missing Bitcoins. Or they may have collaborated with the relevant parties, such as exchanges or wallet providers, to facilitate the recovery process. Equally important is the level of personalized support and communication that Trust Geeks Hack Expert likely provided, guiding the affected individual through each step of the recovery effort and offering reassurance during what can be an anxious and uncertain time. The success of their efforts, as evidenced by the positive outcome, underscores the importance of seeking out reputable and experienced service providers when faced with a Bitcoin-related mishap, as they possess the specialized knowledge and resources to navigate these challenges and restore access to one's digital assets. Email.. [email protected]
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27.11.24 09:10
Michal Novotny
The biggest issue with cryptocurrency is that it is unregulated, wh ich is why different people can come up with different fake stories all the time, and it is unfortunate that platforms like Facebook and others only care about the money they make from them through ads. I saw an ad on Facebook for Cointiger and fell into the scam, losing over $30,000. I reported it to Facebook, but they did nothing until I discovered deftrecoup . c o m from a crypto community; they retrieved approximately 95% of the total amount I lost.
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01.12.24 17:21
KollanderMurdasanu
REACH OUT TO THEM WhatsApp + 156 172 63 697 Telegram (@)Techcyberforc We were in quite a bit of distress. The thrill of our crypto investments, which had once sparked excitement in our lives, was slowly turning into anxiety when my husband pointed out unusual withdrawal issues. At first, we brushed it off as minor glitches, but the situation escalated when we found ourselves facing login re-validation requests that essentially locked us out of our crypto wallet—despite entering the correct credentials. Frustrated and anxious, we sought advice from a few friends, only to hit a wall of uncertainty. Turning to the vast expanse of the internet felt daunting, but in doing so, we stumbled upon TECH CYBER FORCE RECOVERY. I approached them with a mix of skepticism and hope; after all, my understanding of these technical matters was quite limited. Yet, from our very first interaction, it was clear that they were the experts we desperately needed. They walked us through the intricacies of the recovery process, patiently explaining each mechanism—even if some of it went over my head, their reassurance was calming. Our responsibility was simple: to provide the correct information to prove our ownership of the crypto account, and thankfully, we remained on point in our responses. in a timely fashion, TECH CYBER FORCE RECOVERY delivered on their promises, addressing all our withdrawal and access issues exactly when they said they would. The relief we felt was immense, and the integrity they displayed made me confident in fully recommending their services. If you ever find yourself in a similar predicament with your crypto investments, I wholeheartedly suggest reaching out to them. You can connect with TECH CYBER FORCE RECOVERY through their contact details for assistance and valuable guidance. Remember, hope is only a reach away!
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02.12.24 23:02
ytre89
Online crypto investment can seem like a promising opportunity, but it's crucial to recognize that there are no guarantees. My experience serves as a stark reminder of this reality. I was drawn in by the allure of high returns and the persuasive marketing tactics employed by various brokers. Their polished presentations and testimonials made it seem easy to profit from cryptocurrency trading. Everything appeared to be legitimate. I received enticing messages about the potential for substantial gains, and the brokers seemed knowledgeable and professional. Driven by excitement and the fear of missing out, I invested a significant amount of my savings. The promise of quick profits overshadowed the red flags I should have noticed. I trusted these brokers without conducting proper research, which was a major mistake. As time went on, I realized that the promised returns were nothing but illusions. My attempts to withdraw funds were met with endless excuses and delays. It became painfully clear that I had fallen victim. The reality hit hard: my hard-earned money was gone, I lost my peace of mind and sanity. In my desperation, I sought help from a company called DEFTRECOUP. That was the turning point for me as I had a good conversation and eventually filed a complaint via DEFTRECOUP COM. They were quite delicate and ensured I got out of the most difficult situation of my life in one piece.
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04.12.24 22:24
andreygagloev
When I first heard about Bitcoin back in 2018, I was skeptical. The idea of a decentralized, digital currency seemed too good to be true. But I was intrigued as I learned more about the technology behind it and its potential. I started small, investing just a few hundred dollars, dipping my toes into the cryptocurrency waters. At first, it was exhilarating to watch the value of my investment grow exponentially. I felt like I was part of the future, an early adopter of this revolutionary new asset. But that euphoria was short-lived. One day, I logged into my digital wallet only to find it empty - my Bitcoin had vanished without a trace. It turned out that the online exchange I had trusted had been hacked, and my funds were stolen. I was devastated, both financially and emotionally. All the potential I had seen in Bitcoin was tainted by the harsh reality that with decentralization came a lack of regulation and oversight. My hard-earned money was gone, lost to the ether of the digital world. This experience taught me a painful lesson about the price of trust in the uncharted territory of cryptocurrency. While the technology holds incredible promise, the risks can be catastrophic if you don't approach it with extreme caution. My Bitcoin investment gamble had failed, and I was left to pick up the pieces, wiser but poorer for having placed my faith in the wrong hands. My sincere appreciation goes to MUYERN TRUST HACKER. You are my hero in recovering my lost funds. Send a direct m a i l ( muyerntrusted ( @ ) mail-me ( . )c o m ) or message on whats app : + 1 ( 4-4-0 ) ( 3 -3 -5 ) ( 0-2-0-5 )
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12.12.24 00:35
amandagregory
HOW TO HIRE A HACKER TO RECOVER STOLEN BITCOIN WITH FASTFUND RECOVERY
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12.12.24 00:35
amandagregory
HOW TO HIRE A HACKER TO RECOVER STOLEN BITCOIN WITH FASTFUND RECOVERY... A few months ago, I made a huge mistake. I invested in what seemed like a legitimate crypto opportunity, only to find out I’d been scammed. I lost a significant amount of money, and the scam platform vanished overnight. I felt completely lost.I had heard of Fastfund Recovery and decided to reach out, even though I was skeptical. From the first conversation, they made me feel heard and understood. They explained the recovery process clearly and kept me updated every step of the way.Within weeks, Fastfund Recovery successfully to recovered my lost funds—something I honestly didn’t think was possible. Their team was professional, transparent, and genuinely caring. I can’t thank them enough for turning a nightmare into a hopeful outcome. If you’re in a similar situation, don’t hesitate to contact them. They truly deliver on their promises. Gmail::: fastfundrecovery8(@)gmail com .....Whatsapp ::: 1::807::::500::::7554
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19.12.24 17:07
rebeccabenjamin
USDT RECOVERY EXPERT REVIEWS DUNAMIS CYBER SOLUTION It's great to hear that you've found a way to recover your Bitcoin and achieve financial stability, but I urge you to be cautious with services like DUNAMIS CYBER SOLUTION Recovery." While it can be tempting to turn to these companies when you’re desperate to recover lost funds, many such services are scams, designed to exploit those in vulnerable situations. Always research thoroughly before engaging with any recovery service. In the world of cryptocurrency, security is crucial. To protect your assets, use strong passwords, enable two-factor authentication, and consider using cold wallets (offline storage) for long-term storage. If you do seek professional help, make sure the company is reputable and has positive, verifiable reviews from trusted sources. While it’s good that you found a solution, it’s also important to be aware of potential scams targeting cryptocurrency users. Stay informed about security practices, and make sure you take every step to safeguard your investments. If you need help with crypto security tips or to find trustworthy resources, feel free to ask! [email protected] +13433030545 [email protected]
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