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Н Новости

Тернарная нейронка на C#

Оглавление

Введение

Давайте заранее договоримся, в статье термин емкость означает информационную емкость, разрядность, битность (в двоичной логике). Емкость (количество) - это то, сколько всего бит/трит/квадрит выделено на число. Точность (качество) - насколько детально можно представить число в рамках данной емкости.

Любой кто когда либо запускал локальную нейронку, сталкивался с таким понятием как "квантизация". Квантизация - это фактически упрощение нейронки, позволяющее запускать ее на слабом железе. Чем сильнее квантизация - тем меньше весит файл модели, но хуже качество инференса. Изначально модели обучают используя веса с высокой точностью. Но размеры файла модели занимают слишком много места. Поэтому народ активно такие модели квантует, чтобы они "влезли" в ОЗУ видеокарты для локального запуска.

Квантизация - творческий процесс. Люди ищут оптимальный баланс между размером модели и способностью "нормально" работать. Это не отменяет того факта, что для обучения модели нужны большие траты на железо, особенно - на память. А память сейчас - дорогое удовольствие.

Но есть и другие варианты облегчить себе жизнь. Один из них - перейти на нейронки с меньшей точностью. Зачем обучать на FP32, а потом квантовать до INT4 (Q4), когда можно сразу обучать на INT4? Меньше требования к железу, меньше требования к ОЗУ. А значит - дешевле?

А вот и нет

Если всю модель полностью перевести на более слабую емкость (с FP32 на INT4) - модель будет обучатся нестабильно, градиенты могут "застрять" на локальных минимумах. Поэтому самые чувствительные места (градиенты, состояния оптимизатора Adam) оставляют как у обычных моделей в FP32/BF16.

Но, давайте сначала чуток освежим знания.

>> Вас всю жизнь обманывали

Когда мы смотрим на эти красивые "форматы сжатия", кажется что всё это - нативно поддерживаемые форматы современных компьютеров. Такое же ощущение появляется, когда вы видите в своем любимом языке программирования типы byte, int, float, double...

На самом деле всё это - разные интерпретации одной и той же двоичной последовательности, в основе которой - бит, который имеет всего два возможных значения: 0 или 1. Аппаратно поддерживаются не все варианты: где-то поддерживаются операции над байтами, целыми числами и числами с плавающей запятой. А где-то поддержки чисел с плавающей запятой нет вовсе. Все зависит от железа. Но на фундаментальном уровне - везде один лишь бит.

Что значит "поддерживаются"? Это значит что в железе присутствуют аппаратные инструкции которые умеют работать с разными представлениями значения: складывать/умножать/делить значения представленные группами битов, например в double. Аппаратные - значит прямо на чипе/кремнии физически есть транзисторы, объединённые в логические схемы, реализующие операции над определёнными представлениями данных. На самом деле даже значения 0 и 1 не существует - это просто уровень заряда, напряжения, тока, магнитного состояния и т.д.

Когда мы видим новость "выпущен ускоритель AMD MI300 аппаратно поддерживающий вычисления на FP8", это значит что в нем есть аппаратные инструкции работающие с битами объединенными в представление FP8.

Сравнительная таблица форматов и систем счисления. Сюда намеренно внесены чужеродные (для бинарной) системы счисления: трит (три состояния, троичная логика), квадрит (четыре состояния), квинтит (пять состояний), секстит (шесть состояний), септит (семь состояний), октит (восемь состояний), нонит (девять состояний) и децит (десять состояний).

Представление/формат/система счисления

Информационная ёмкость в битах

Кол-во
состояний

Диапазон

Binary / Бит / Двоичная

1

2

0, 1

Ternary / Трит / Троичная

1.585

3

−1, 0, +1

Quaternary / Квадрит / Четвертичная

2

4

−2, −1, +1, +2

INT2

2

4

−2 … +1

Quinary / Квинтит / Пятеричная

2.322

5

−2, −1, 0, +1, +2

Senary / Секстит / Шестеричная

2.585

6

−3, −2, −1, +1, +2, +3

Septenary / Септит / Семеричная

2.807

7

−3 … +3

INT4

4

16

−8 … +7

Octal / Октит / Восьмиричная

3

8

−4, −3, −2, −1, +1, +2, +3, +4

Nonary / Нонит / Девятичная

3.170

9

−4 … +4

Decimal / Децит / Десятичная

3.322

10

0 ... 9

INT8

8

256

−128 … +127

FP8 E4M3

8

256

≈ −448 … +448

FP8 E5M2

8

256

≈ −57 344 … +57 344

INT16

16

65 536

−32 768 … +32 767

BF16

16

65 536

≈ −3.39×10³⁸ … +3.39×10³⁸

FP16

16

65 536

≈ −65 504 … +65 504

INT32

32

4.29×10⁹

−2.147×10⁹ … +2.147×10⁹

FP32

32

4.29×10⁹

≈ −3.403×10³⁸ … +3.403×10³⁸

INT64

64

1.84×10¹⁹

−9.22×10¹⁸ … +9.22×10¹⁸

FP64

64

1.84×10¹⁹

≈ −1.798×10³⁰⁸ … +1.798×10³⁰⁸

INT128

128

3.40×10³⁸

−2¹²⁷ … +2¹²⁷−1

FP128

128

3.40×10³⁸

≈ −1.190×10⁴⁹³² … +1.190×10⁴⁹³²

Квадрит и INT2 это одно и то же?

Казалось бы, у них всё совпадает: емкость, количество состояний. Но нет.

INT2 — это конкретный способ интерпретации двух битов как целого числа. Но это именно интерпретация битов имеющих любые комбинации 00, 01, 10, 11!

Основные интерпретации бинарного INT2:

  • беззнаковое (UINT2): 0, +1, +2, +3

  • дополнительный код (two's complement): −2, −1, 0, +1

  • обратный код (one's complement): +0, +1, −1, −0

  • прямой код (sign-magnitude): +0, +1, −0, −1

Квадрит же сам по себе не определяет, какие именно значения соответствуют его четырём состояниям. Это могут быть 0, 1, 2, 3| −2, −1, +1, +2| A, B, C, D или вообще четыре произвольных символа.

Иными словами, INT2 - это интерпретация четырёх состояний бинарной системы как целого числа, а квадрит — информационная единица, имеющая четыре различимых состояния.

Значения диапазона в этой таблице - условные: в том же "квадрите" значения могут быть какими угодно:

  • −2, −1, 0, +1

  • −2, −1, +1, +2

  • 0, 1, 2, 3

  • A, B, C, D

  • 𓂀\hspace{0.2em}, 𓃠\hspace{0.2em}, 𓆣\hspace{0.2em}, \hspace{0.2em}𓇼

Даже информационная емкость в данном случае интерпретируется через бинарное представление: Q = \log_2(N), где:

  • Q - информационная ёмкость в битах

  • N - количество состояний

Например "трит", в бинарной системе счисления имеет информационную емкость Q=log_2​(3)≈1.585 бит.

Пример того, как 32 бита можно интерпретировать в разных форматах. Видно что в FP32 может влезть два FP16/BF16, либо четыре INT8, либо восемь INT4.
Пример того, как 32 бита можно интерпретировать в разных форматах. Видно что в FP32 может влезть два FP16/BF16, либо четыре INT8, либо восемь INT4.
Для справки: что такое экспонента, мантисса...
  • Экспонента определяет диапазон значений

  • Мантисса определяет точность представления

Пример для экспоненты:

Экспонента

Максимальное значение

4 бита

~256

5 бит

~65 504

8 бит

~3.4 × 10^38

Пример для мантиссы:

Мантисса

Число

3 бита

0.125

7 бит

0.1234

23 бита

0.12345679

Получается, на физическом уровне, уровень заряда (и другие виды реализации логики) интерпретируется как 0 или 1. Затем последовательности этих значений интерпретируются в разное представление: uint8, int32, float32, float64 и т.д. Потом и эти представления объединяются и интерпретируются как структуры данных: массивы, объекты. И всё это в итоге объединяется и интерпретируется как: текст, изображение, звук.

a52d6f8c7dc656018a85b50e832de93e.png

То есть, люди придумали уровни абстракции и правила интерпретации физических состояний, а затем построили поверх них всё то многообразие, которое мы называем данными, типами, форматами. Проще говоря - от интерпретации зависит всё. Купил ардиунку, не прочитал документацию, подал 220В на контакты - спалил ардуинку. Печаль.

>> Градиент

Давайте немного поясним что это за "градиент" был в самом начале статьи, и какое отношение он имеет к FP32, FP16, BF16.

Нейронка состоит из слоёв, где каждый слой - это массив чисел, весА. Как раз веса состоят из чисел с плавающей запятой. В нашем случае - из чисел с точностью FP32.

Из чего состоит GPT-2 можно глянуть в этой статье.

Конечно вес - это не всегда сам нейрон. Обычно нейрон это вес + смещение (bias). Когда на вход нейрона подают входящий сигнал, сначала сигнал умножается на вес, а потом добавляется смещение, применяется функция активации... Вес - это направление и важность сигнала (усилить или ослабить), смещение - корректировка порога срабатывания нейрона.

Схематичный нейрон, схематично "обрабатывает" сигнал.
Схематичный нейрон, схематично "обрабатывает" сигнал.

В некоторых нейронках (LLaMA, Gemma, Mistral, OLMo) смещение намеренно отключено в линейных слоях. В тритовой нейронке его вообще нет, но об этом позже.

Обучение нейронки происходит так: ей на вход подают последовательность токенов, и после "прохода" через слои сеть пытается предсказать следующий токен. Результат сравнивается с правильным ответом (следующим токеном), вычисляя связь между ними. Чем хуже связь - тем больше ошибка. Чтобы уменьшить эту ошибку, веса нейронки нужно подкорректировать (увеличить или уменьшить).

Градиент - это мера виновности каждого конкретного веса в общей ошибке нейросети. Фактически это инструмент для оптимизатора, показывающий в какую сторону и насколько сильно нужно изменить вес нейросети, чтобы она совершала меньше ошибок.

Оптимизатор - это алгоритм подкручивающий веса модели, исходя из значений градиента. Самые распространенные: SGD (Stochastic Gradient Descent), Adam, AdamW.

Так вот, чем больше емкость из которых состоят веса нейронки, тем точнее вычисляется градиент, тем стабильнее идет обучение. Имея высокую емкость FP32, алгоритм может улавливать тончайшие взаимосвязи между токенами и делать микроскопические, но очень важные поправки в весах.

>> Проблема FP32

Долгое время при обучении нейронок, "золотым стандартом" считался формат FP32: высокая емкость позволяла достаточно успешно бороться с затуханием градиентов.

Модели росли не по дням, а по часам. Но внезапно индустрия ML (Machine learning) при обучении нейронок уперлась в пропускную способность памяти видеокарт (bottleneck). Высокая емкость из спасителя превратилась в тяжелую ношу для видеокарт: при обучении моделей в миллиарды параметров, видеокартам пришлось перегонять через себя огромные объемы данных между памятью и вычислительными ядрами. При этом, вычислительные ядра стали простаивать в ожидании информации.

Что бы облегчить видеокартам жизнь, ML-инженеры придумали схему: оригинальные веса в FP32 копировались в веса в формате FP16, на этой копии производились умножения, а результат (градиент) применялся к оригинальным мастер-весам. Назвали это - "смешанной точностью" (mixed precision). То есть нейронку в FP32 мы обучаем во временном пониженном формате.

Стадии обучения:

  1. Мастер-веса хранятся в FP32 - это оригинал.

  2. Копия: из мастера создаётся рабочая копия весов в пониженном формате (FP16 / BF16 / FP8 / MXFP4).

  3. Forward: тензорные ядра перемножают квантованные тензоры-копии; суммы накапливаются в FP32 (предсказание и loss).

  4. Backward: градиенты считаются на тех же квантованных тензорах; накопление в FP32.

  5. Оптимизатор: готовые градиенты применяются к мастер-весам.

  6. см. пункт 2.

Но маленький диапазон значений FP16 приводил к двум проблемам: маленькие значения приводили к обнулению градиента, большие значения улетали в бесконечность. Костыли вроде Loss Scaling (искусственное раздувание градиента) боролись с обнулением градиентов. Но вторая проблема с переполнением градиентов оставалась.

>> BF16

Тогда инженеры Google пошли на хитрость и создали формат BF16 (Brain Float 16), устраняющий проблему с переполнением градиентов. Они оставили такую же емкость в 16 бит, но увеличили экспоненту до 8 бит как у FP32: урезали точность округления, но оставили такой же диапазон значений как в FP32.

Схематичное изображение формата. Лучи - все возможные значения.
Схематичное изображение формата. Лучи - все возможные значения.

Сравнение максимального числа (бинарный вид и значение):

  • FP32

    • 0 | 11111110 | 11111111111111111111111

    • \approx \mathbf{3.4\times 10}^{\mathbf{38}}

  • BF16

    • 0 | 11111110 | 1111111

    • \approx \mathbf{3.4\times 10}^{\mathbf{38}}

  • FP16

    • 0 | 11110 | 1111111111

    • 65 504

И что же мы видим? FP16 хуже по диапазону возможных значений чем FP32 и BF16 в:

\frac{3.40282 \times 10^{38}}{65504} \approx 5.195 \times 10^{33} раза. Т.е. в 5 дециллионов раз.

Подсчет разницы диапазонов через максимальное значение - рабочий, потому что FP32 FP16 и BF16 - знаковые и симметричные. А вот посчитать разницу диапазонов между например INT32 и UINT16 через максимальное значение было бы некорректным. Надо делить количество всех состояний.

То есть FP16 и BF16 имеет одинаковое количество значений (2¹⁶ = 65 536). Но у BF16 диапазон значений почти как у FP32 и он размазан с худшей точностью чем у FP32.

FP32:

  • 1,0000001192092896

  • 1,0000002384185791

  • 1,0000003576278687

BF16:

  • 1,0078125

  • 1,0156250

  • 1,0234375

>> FP8

Следующим шагом стал переход на FP8 (256 комбинаций), который разделили на "подформаты":

  • E4M3 - используется для прямого прохода (активации и веса)

  • E5M2 - для обратного прохода (расчет градиентов)

E4M3 - буквально экспонента 4 бита, мантисса 3 бита.

Правильнее было бы назвать S1E4M3 - где S это бит знака.

Оказалось, что для разных процессов можно использовать разную емкость. При прямом проходе (forward) активации в E4M3 требуют меньше данных для передачи и ускоряют вычисления. При обратном проходе (backward pass, backpropagation) операции в E5M2 выполняются в разы быстрее.

E4M3 (4 бита экспоненты + 3 бита мантиссы): здесь активации лежат в узком диапазоне, поэтому широкий диапазон не нужен, но важна точность (меньше экспоненты, больше мантиссы).

E5M2 (5 бит экспоненты + 2 бита мантиссы): градиенты имеют огромный разброс, поэтому критичен широкий диапазон значений, а точность можно принести в жертву (больше экспоненты, меньше мантиссы).

>> FP4? MXFP4!

Так, стоп, а где FP6?

"На бумаге" это идеальный компромисс: он точнее чем FP4, и экономичнее чем FP8. Но в реальной жизни он "неудобен" для железа ориентированного на степени двойки. Существует так называемое "выравнивание байтов": способ размещения данных в оперативной памяти компьютера, при котором адрес начала переменной в памяти должен быть кратен её размеру.

Помните в ассемблере непонятная директива align? Или в паскале для передачи байта по сети например, писали TMyRecord = packed record, потому что без этого структура раздувалась?

Выравнивание байтов необходимо для ускорения работы с данными: грубо говоря процессор считывает данные из памяти не по одному байту, а "словами" (блоками по 4, 8, 16 и т.д. байт за раз).

Пример:

  • Если 4-байтовое число выровнено (например, лежит по адресу 0x04), процессор прочитает его за 1 цикл

  • Если число не выровнено (например, лежит по адресу 0x03), оно окажется на стыке двух блоков памяти. Процессору придется сделать 2 цикла чтения, а затем аппаратно "склеивать" эти байты

  • Если число занимает два блока памяти: процессору опять придется сделать 2 цикла чтения. Это наш случай.

Вот и получается, что 6-битное число не укладывается в сетку памяти: оно меньше байта, поэтому не может иметь собственного адреса, и его пакуют впритык с соседями - по 4 штуки в 3 байта. Из-за этого часть чисел оказывается на стыке двух байтов: что бы прочитать одно, приходится считывать сразу два, сдвигать и вырезать нужные биты.

Конечно есть ускоритель от AMD Instinct MI350 у которого FP6 поддерживается на аппаратном уровне (вынужденная конкуренция с архитектурой NVIDIA Blackwell). Вернее формат MXFP6 из открытого стандарта Microscaling. Но о блочном формате - дальше.

Итак, у FP4 всего 16 комбинаций. В 16 комбинаций запихнуть достаточный для обучения диапазон и точность невозможно - битов физически не хватает на сколько то значимую экспоненту и мантиссу. То есть реализовать каждый вес в формате FP4 бесполезно.

Поэтому инженеры пошли на хитрость и объединили веса FP4 (S1E2M1 - знак 1 бит, экспонента 2 бита, мантисса 1 бит) в блок по 32 элемента и добавили одну общую 8 битную экспоненту (E8M0 - экспонента 8 бит) для всех весов в блоке. Эта экспонента является рычагом для изменения диапазона значений для каждого элемента в блоке. В простонародье - "зум". Так появился блочный формат MXFP4.

Блок MXFP4. Развернул представление, что бы влезло на экран.
Блок MXFP4. Развернул представление, что бы влезло на экран.

Зачем каждому FP4 своя экспонента, если есть общая аж на 8 бит? Мини-экспонента в FP4 не дает округлить значение каждого веса во время обучения нейронки.

Главный выигрыш в обучении, помимо уменьшения объемов занимаемой памяти заключается в том, что в MXFP4 дешевле арифметика (перемножаются простые целые 4-битные числа), а масштаб применяется один раз после накопления всей суммы - одним сдвигом экспоненты.

>> Бит vs Трит

Мы уже рассматривали FP4 как рабочий вариант для построения полноценной нейронки, правда пришлось пойти на трюк, объединяя такой формат в блок из 32 штук, и вынос экспоненты.

Так может взять и сразу перепрыгнуть на Бит? Сделать однобитовую нейронку?

Давайте подумаем, что такое нейрон? Нейрон это обучаемый элемент имеющий внутреннее состояние, с помощью которого он может видоизменять проходящий через себя сигнал. Обучаемый - значит способный менять внутреннее состояние. Полноценный нейрон может делать три вещи: усиливать сигнал, ослаблять сигнал, и "молчать".

Главная фундаментальная проблема битового нейрона - у него физически не может быть трех вариантов внутреннего состояния, поэтому он либо только усиливает и ослабляет [-1,+1], либо только "молчит" и усиливает [0,1].

В контексте нейросети из таких нейронов - это приводит к перекосу при обучении:

  • [-1,+1] Слабые и нерелевантные признаки постоянно вносят свой вклад и фонят шумом, поэтому сеть не может стать избирательной, и ее обобщающая способность падает

  • [0, +1] Сеть умеет только наращивать сигнал, из-за чего ей недоступны немонотонные функции (например, "исключающее ИЛИ")

И тут, весь в белом пальто на сцену выходит трит - тот самый, полноценный нейрон. У него есть три состояния [−1, 0, +1], позволяющие построить обучаемую нейронку. Да конечно два бита (условный формат FP2) [-1, 0, +1, +2] например тоже подходит для полноценной нейронки, но в качестве минимально возможного нейрона - трит, вне конкуренции.

Схематичный пример прохода сигнала через нейроны. Серый цвет - нейрон неактивный (имеет значение 0).
Схематичный пример прохода сигнала через нейроны. Серый цвет - нейрон неактивный (имеет значение 0).

На картинке видно, что в тритовой/тернарной нейронке много неактивных нейронов выделенных серым цветом (т.е. имеющих состояние 0 - "молчу"), это называется "разряженность" (sparse). Разреженность дает полезные вещи:

  • Подавление шума: слабые признаки отключаются, и не вносят вклад в сигнал

  • Экономия на вычислениях: неактивные нейроны не участвуют в вычислениях

  • Обобщение: сеть вынуждена строить "правильные" пути движения сигнала, что снижает переобучение

Глядя на серые неактивные нейроны в тритовой нейронке, кажется, что сеть работает неэффективно: столько нейронов неактивно, столько простаивает! Но... в выключенном состоянии они тоже "выполняют работу" - не позволяют тратить вычислительные ресурсы на неэффективные связи между нейронами.

Напомню: изначально, перед обучением нейронки, ее веса имеют произвольные хаотичные значения, без структуры, без смысла. Обучение в том и заключается, что бы обучающие данные пробурили в весах разветвленную сеть прохождения сигнала, как в природе вода вытачивает со временем замысловатые узоры в скалах. И каждый раз, конфигурация, "рисунок" нейронных связей при обучении с нуля, будет уникальным, не смотря на то что железо - не поменялось. Выключенные нейроны - это часть уникального узора нейросети.

>> B1.58

Microsoft решила реализовать нейронку в тритах, и назвала ее BitNet 1.58. Но если до этого обучение велось на пониженных форматах, а целью была полноценная нейронка на FP32 (BF16). То в этот раз наоборот: обучение ведется в мастер-весах BF16, а тернарные веса получаются путем квантования мастер-весов в триты (на каждом forward-проходе).

После обучения, можно спокойно выкинуть BF16 мастер-веса, и использовать тернарную нейронку для инференса.

Страничка на huggingface, веса в gguf, движок для инференса bitnet.cpp

В обучении используется трюк STE (Straight-Through Estimator). Суть трюка: градиент, который Backward принёс от loss к триту, пропускается сквозь квантователь к оптимизатору без изменений. Благодаря этому мастер-веса плавно дрейфуют под потоком градиентов, накапливая микроизменения, а сами триты меняются дискретно - "переключаются" (из нуля в ±1) в тот момент, когда мастер пересекает порог (среднее значение модулей весов слоя).

Все понятно?
Он - все понял
Он - все понял

Проще говоря, мастер-веса при обучении плавно меняют значения (что то типа увеличить вес нейрона на +0.0001), а трит - он дискретный. У него всего три состояния между которыми он может переключаться. Как понять в какой момент нужно переключать трит? Для этого и вводится некий "порог" значения нейрона в мастер-весах, после достижения которого и переключается трит. При этом порог - не фиксированный, он вычисляется отдельно для каждого слоя и равен среднему значению модулей всех мастер-весов этого слоя.

Но стОит отметить: нет никакого точечного изменения каждого трита. Блок мастер-весов при каждом forward проходе переводится в тритовый и полностью перезаписывает старый тритовый блок:

БЛОК МАСТЕР-ВЕСОВ (BF16)
┌───────────────────────────────────┐
│  0.03  │ -0.41  │  0.27  │ -0.09  │
│  0.18  │  0.55  │ -0.33  │  0.11  │
│ -0.22  │  0.07  │ -0.48  │  0.39  │
└───────────────────────────────────┘
                  │
                  │ вычисляем порог
                  │ среднее модулей всех весов
                  │ (0.03-0.41+0.27-...+0.39) / 12 ≈ 0.26
                  │
                  ▼
            КВАНТИЗАЦИЯ
        ┌───────────────────┐
        │  вес > +0.26 → +1 │
        │  вес < -0.26 → -1 │
        │  иначе       →  0 │
        └───────────────────┘
                  │
                  ▼
БЛОК ТЕРНАРНЫХ ВЕСОВ (триты)
┌───────────────────────────────────┐
│   0    │  -1    │  +1    │   0    │
│   0    │  +1    │  -1    │   0    │
│  -1    │   0    │  -1    │  +1    │
└───────────────────────────────────┘

Конечно в результате не все слои нейронки полностью тернарные. Нельзя например перевести в триты входящий слой, связывающий ID токенов с его числовым описанием (вектором). А так же последний слой, переводящий внутреннее состояние модели в вероятность следующего слова.

>> Ternary LLM

Ну штош, давайте попробуем сделать максимально минимальную нейронку на тритах. В статье Обучение LLM с нуля на c# и экспорт в GGUF. OpenCL против CUDA мы уже реализовали нейронку, которая после экспорта в формат GGUF стала занимать на диске 422Кб.

Возьмем ее за основу, но переделаем на архитектуру Llama, и оставим обучение на CPU. Llama - дешевле при обучении чем GPT-2.

Наша задача - натянуть логику стандартной архитектуры современных моделей основанных на transformer на триты, поэтому обучение ведется на FP32, а потом квантизация в тернарные веса.

Скрытый текст
e435298631e78ae49a1a6cfe436e3145.png

...Как собственно это же делает сам Bitnet1.58. Других устаканившихся рабочих рецептов полноценного обучения сразу на тритах, на данный момент нет, ну или я о них не знаю.

Архитектура нейронки:

  • BPETokenizer токенизатор.
    Превращает текст в токены (индексы).

  • MultiPlaneEmbedding слой (с динамическим квантованием весов / QAT).
    Превращает токены в векторы. Модель не может работать просто с индексами, потому что индекс - это просто номер. Динамическое квантование (QAT) нужно для того чтобы модель сразу училась работать с тернарными весами. Во время обучения модель уже видит квантованные веса и приспосабливается к ним.

  • TernaryLlamaBlock блок (RMSNorm, GQA Self-attention + KV cache, SwiGLU FFN, Residual connections).
    Понимает контекст и обрабатывает векторы.

    • RMSNorm приводит векторы к нормальному масштабу.

    • GQA (Grouped-Query Attention) - экономная "голова внимания": несколько Q-голов используют общие K и V.

    • KV кэш ускоряет инференс, что бы при генерации каждого токена не пересчитывать предыдущие токены заново.

    • SwiGLU FFN усиливает важные признаки и отбрасывает лишние.

    • Residual connections для стабилизации обучения.

  • Final RMSNorm
    Приводит финальный вектор в порядок.

  • MultiPlaneLinear
    Превращает вектор в вероятности следующих токенов - логиты.

Как мы уже знаем, один бит - всего два значения. Но если объединить несколько битов - будет намного более ёмкая единица информации: byte, short, int, float и т.д. Что нам мешает увеличить емкость тритовой нейронки таким же макаром? Правильно, ничего. Поэтому был придуман параметр planes: количество тритов на нейрон, "плоскость", как слои пирога. Больше значение - более ёмкие тритовые слои у нейронки.

Самая минимальная нейронка на точно таком же корпусе как в LLMGPT2, но уже на Llama архитектуре позволяет сделать такую конфигурацию (106496 параметров):

  Embedding dim = 64
  FFN hidden dim = 64
  Num heads = 1
  Num KV heads = 1
  Num layers = 1
  Max seq len = 512
  BPE vocab size = 16000
  Trit planes = 1

Обучение удалось довести до Loss=0,26.
При этом размер мастер-модели (веса + токенизатор): 420 КБ.
А размер тернарной нейронки: 28,9 КБ (из них 3,71 КБ - данные токенизатора).


И, барабанная дробь, самая экстремальная конфигурация (49152 параметров):

  Embedding dim = 32
  FFN hidden dim = 32
  Num heads = 1
  Num KV heads = 1
  Num layers = 1
  Max seq len = 512
  BPE vocab size = 16000
  Trit planes = 1

Обучение удалось довести до Loss=0,42, ниже - не получается.
При этом размер мастер-модели (веса + токенизатор): 196 КБ
А размер тернарной нейронки: 17,1 КБ (из них 3,71 КБ - всё так же данные токенизатора).
Моделька может хуже отвечать в интерактивном чате.

0f2f443ea24d348783cc13bd24a79293.pngТа самая модель размером 17,1 КБ
Та самая модель размером 17,1 КБ

>> Итого

Щепотка терпения, горсть нервных клеток, ложка промптов
e74ff7bdb4d056b1d5e5308b6d1e34b0.png

Поймал себя на мысли, что ежедневное общение и спор с превосходящим меня интеллектом в миллиарды китайских и американских нейронов, это уникальная возможность получить себе интересного собеседника, которого в реальной жизни, получить практически невозможно.

Данный проект - попытка понять насколько малую (но полноценную в плане архитектуры) модель можно сделать на модных нынче тритах. Обучение по прежнему ресурсозатратное, поэтому и был выбран самый "щадящий" корпус, что бы каждый мог попробовать обучить модель на своем железе.

Для тех кто хочет проверить сразу:
Исходный код: https://github.com/virex-84/LLamaTritLLM
Релиз (отдельно два варианта моделей): https://github.com/virex-84/LLamaTritLLM/releases/tag/v1.0

А на сегодня всё...

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  • 24.06.26 14:16 Universina da Mota

    Becoming a victim of an investment scam is never anyone's intention it often happens because fraudsters exploit trust and a lack of awareness. I would like to express my sincere gratitude to the dedicated team at ResQpro for their professionalism and commitment to helping victims of online investment fraud. Their efforts in assisting individuals with the recovery of stolen assets and holding scammers accountable are truly commendable. If you need assistance or would like to learn more, you can contact them through: Email: [email protected] Alternative Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146

  • 24.06.26 14:21 Elizabeth Thompson

    If you believe you have been the victim of an investment scam, it is important to act promptly and gather all relevant information. Keep records of transaction receipts, wallet addresses, communication logs, account details, and any other evidence related to the incident. Providing accurate documentation can help investigators, financial institutions, legal professionals, or recovery specialists review your case and determine what options may be available. Be cautious of anyone who guarantees the recovery of lost funds or requests large upfront payments. For additional information, you may contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146

  • 24.06.26 15:33 Júlia Castro

    If you have fallen victim to an investment scam, it is important to act quickly and gather all available evidence related to the incident. This may include transaction records, wallet addresses, screenshots of conversations, emails, account details, and any information connected to the individuals or entities involved. Having complete documentation can help professionals assess your situation and explore possible recovery options. Always exercise caution when seeking assistance and carefully verify the credentials of any service provider before proceeding. For further information, you may contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146

  • 24.06.26 22:01 robertalfred175

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

  • 24.06.26 22:01 robertalfred175

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

  • 25.06.26 21:13 Emilie Safi

    A fraudulent investment scheme operated by BTCMining.limited functions as a fake return scam. In this setup, scammers lure victims with false promises of high returns. Through manipulative tactics, they gain individuals' trust and convince them to invest, ultimately leading to financial loss. If you have ever faced a cyber threat or fallen victim to an online crypto scam and need to reach the authorities, I recommend contacting [email protected], [email protected], WhatsApp +19852969146, telegram @resqprofirm. They are a legitimate team that helps victims of online crypto scams using advanced tools.

  • 25.06.26 21:25 Emilie Safi

    So I ended up losing $38,000 to this platform. At first, they kept asking me to put in more money so I could get into my portfolio. I did that, but then they wouldn’t let me withdraw anything—just kept asking for more deposits. It got way too suspicious, so I stopped. I found this company called ResQProfirm on Google and told them what happened. They got in touch, asked me to walk them through everything, and I gave them all the proof I had. They did an amazing job tracking down my money and getting it back. Big thanks to them at [email protected] and on WhatsApp at +19852969146. Please be careful out there and always research before investing.

  • 26.06.26 01:04 robertalfred175

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

  • 26.06.26 01:04 robertalfred175

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

  • 26.06.26 02:48 Miriam Rocha

    I trusted this platform with $120,000 of my hard-earned money. Then they started asking for more deposits just so I could access my own portfolio. I paid, but every withdrawal request was denied. They kept pushing for more money. I finally stopped it just felt wrong. Desperate, I found ResQProfirm on Google. They didn't just hear me out; they truly listened. I shared all my proof, and they launched an investigation. Thanks to their hard work, they tracked and returned my funds. From the bottom of my heart, thank you to [email protected] and their WhatsApp +19852969146. Please stay safe and always verify a platform before investing

  • 26.06.26 02:52 Miško Bakić

    I got my $232,000 refund thanks to [email protected] and WhatsApp +19852969146. Highly recommended for anyone in a similar situation.

  • 26.06.26 02:56 Asunción Herrera

    A recovery of $48,330 was facilitated by [email protected]. Individuals who have experienced financial fraud may consider contacting this service.

  • 26.06.26 15:05 Riley Stephens

    If withdrawals keep getting denied, stay calm. I went through the same, and this firm helped me recover everything. Their assistance was outstanding. Contact: [ResQProFirm @Gmail|•|com], Telegram: ResQprofirm, WhatsApp: <+198> <5296> <9146>.

  • 26.06.26 15:09 Antonio Riley

    Withdrawal troubles shouldn’t stress you out. I faced a similar problem, and this firm stepped in and recovered my funds. Their support truly mattered. Contact them: [[email protected], ResQprofirm @aol.com], Telegram: ResQprofirm, WhatsApp: +19852969146.

  • 28.06.26 00:37 kimberlyhebertt673

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

  • 28.06.26 00:37 kimberlyhebertt673

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

  • 29.06.26 11:57 Lisadonato0726

    For 43 years, I struggled with bad credit due to my own poor decisions, and my credit score was around 490. When my girlfriend and I decided to buy a house, a mortgage broker informed us that it would be impossible to secure a mortgage with my credit score. As a result, she referred me to a company called HACK MAVENS CREDIT SPECIALIST, assuring me of their professionalism and ability to assist with credit improvement. Upon contacting them, I was impressed by their professionalism and they assured me that they could help. In less than 6 days, my credit score skyrocketed to 785, and they also successfully resolved issues in my credit report, including the bankruptcy. I am incredibly satisfied with their service and would highly recommend HACK MAVENS CREDIT SPECIALIST for reliable credit repairs. You can reach them at H A C K M A V E N S 5 [AT] G M A I L [DOT] COM or at [+] [1] [2 0 9] [4 1 7] – [1 9 5 7]. Thanks to their help, my girlfriend and I are now proud homeowners.

  • 29.06.26 22:37 riley777

    Back in 2025, I watched my life savings vanish. A thief took every cent. I felt desperate and went looking for a way to get it back. I found a guy here who said he was an expert haha. He talked about special software that could find my missing cash. I trusted him. That was a big mistake. He was just another scammer. I paid him a software fee and then he just stopped answering my texts and ran off with my money too. I felt so ashamed that I kept quiet about it for months. It is hard to admit you got fooled twice. Later on, I found a real pro. she did not use a fancy sales pitch. she just looked at the trans screenshots and followed the path the money took. she worked fast and got my funds back into my account. Having that money back changed everything. I can sleep again. her info; [email protected]. Call/chatroom on Whtasapp/ +44 7476618364.

  • 30.06.26 15:08 wendytaylor015

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

  • 30.06.26 15:08 wendytaylor015

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

  • 02.07.26 01:22 Lieneke Bonnema

    I highly recommend ResQprofirm for their professional asset recovery services of my $120,000 scammed funds. Their expertise, professionalism, and commitment to achieving results make them a reliable choice for anyone seeking dependable recovery assistance. [email protected], WhatsApp +19852969146, telegram @resqprofirm

  • 02.07.26 01:26 Clara Morin

    I want to extend my deepest appreciation for showing that circumstances do not define one’s potential for greatness. Your support has been a major source of inspiration during my trading journey, and I am sincerely grateful for your insight and mentorship. Thank you so much. [email protected], WhatsApp +19852969146, telegram ResQprofirm

  • 02.07.26 01:31 Robin Hale

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  • 04.07.26 15:32 Fraddy Pual

    There are few companies I trust as much as FUNDSRETRIEVER. When I lost $653,000 in Ethereum to a ruthless scam, I thought my life would never be the same. The betrayal cut deep, but I refused to give up. I searched tirelessly for a legitimate way to recover what was stolen, and finally found FUNDSRETRIEVER—the most competent and compassionate recovery team I could have imagined. They handled my case with precision and care, and in the end, my entire ETH wallet was restored. More than the money, they gave me back my hope and happiness. I'm sharing my story because I want others to know that recovery is possible. If a scam has taken from you, don't hesitate—contact FUNDSRETRIEVER today. Email: FUNDSRETRIEVER1@ Gmail.com | WhatsApp: +1 603-512-1448 | Telegram: @FUNDSRETRIEVER

  • 05.07.26 14:44 lydiassmith567

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

  • 05.07.26 14:44 lydiassmith567

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

  • 06.07.26 16:20 Olga Ognjanović

    Having trouble withdrawing funds from an investment platform? ResQprofirm provides fund recovery assistance for individuals seeking help with investment-related disputes. I reached out to them after experiencing problems with an investment platform, and I appreciated their professionalism and support throughout the process. If you're facing a similar situation, act promptly, keep records of your transactions and communications, and seek assistance from a qualified recovery service or the appropriate authorities. Contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 985 296 9146

  • 06.07.26 16:31 Joseph Weigl

    Invest wisely and stay cautious. Don't be influenced by promises of unusually high returns or convincing sales pitches from brokers. I learned this the hard way after falling victim to an investment scam that promised huge profits. Fortunately, I acted quickly and reported the incident to a recovery firm for assistance. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146

  • 06.07.26 16:33 Jaran Løvlien

    A heartfelt thank you to RESQPRO FIRM for their commitment and professionalism throughout the investigation of my case. Their team worked diligently and helped recover assets valued at $88,000, which were returned to my wallet. I truly appreciate their support, clear communication, and dedication, and I'm grateful for the assistance I received. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146

  • 07.07.26 18:00 robertalfred175

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

  • 07.07.26 18:01 robertalfred175

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

  • 09.07.26 19:06 Toivo Walli

    I lost 8.56btc to a fake Bitcoin mining site, I tried withdrawing but couldn't approved my process, I reported to !R£SQPROFIRM! via °R£SQproFirm°àt°gmail•com° °tEL£°gram=R£SQprofirm °whaT°Zap+198°52°96°91°46

  • 09.07.26 19:10 Misty Alexander

    Ongoing messages demanding more money before approving withdrawals are a major red flag. Stop engaging and report the incident to a trusted re­covery team. For professional support, you can contact R£sQprofirm using °ResQproFirm°àt°g,*ma'il(•)¢m°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.

  • 09.07.26 19:13 Clara Soto

    Anyone receiving continued requests for additional deposits from a scam platform should immediately cut off communication and submit the case to a reputable re­covery service for investigation. R£sQprofirm is a dependable firm you can reach at °ResQproFirm°àt°g,*ma'il(•)¢om°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.

  • 12.07.26 03:30 Kora Baltacha

    Time is critical. Act now by reaching out to a reputable, seasoned recovery specialist who will guide you every step of the way. You'll need to submit transaction proof, scammer details, and any other useful information. Armed with this, the experts can trace and attempt to pull your money back from the scammers' hidden accounts or wallets. Best of all, R£sQprofirm provides recovery help without charging any upfront fees. Contact them immediately via Telegram @ResQprofirm, WhatsApp +19852969146, or email [email protected].

  • 12.07.26 03:33 Pahal Mathew

    It's important to move proactively by engaging an experienced recovery specialist. They will assist you throughout the process. To help them, provide: · Transaction evidence · Scammer information · Any additional relevant details The experts will then track and try to retrieve your funds from the scammers' hidden accounts or wallets. R£sQprofirm offers recovery assistance with no upfront fees. Contact: Telegram: @ResQprofirm WhatsApp: +19852969146 Email: [email protected]

  • 13.07.26 23:49 [email protected]

    One of the biggest concerns I have about cryptocurrency is the lack of regulation. It creates opportunities for scammers to invent convincing stories and fraudulent investment schemes. Unfortunately, some social media platforms continue to display these ads because they profit from them, even after users report them.I personally clicked on a Facebook advertisement for a company called Chickenfastmining and ended up losing more than $120,000 in a scam. I reported the ad, but nothing was done. Later, through a Reddit community, I found a recovery service called CYBERBERSPY that, in my personal experience, they helped me recover $110,000 of my lost funds. If you've been a victim of a cryptocurrency scam, don't lose hope. Explore your options carefully, and always verify the legitimacy of any recovery service before trusting them or paying any fees. Based on my own experience, CYBERBERSPY was helpful to me and i was able to recover my funds back, but I encourage everyone to do their own research before using any recovery service.i highly recommend: ([email protected])

  • 15.07.26 11:53 Sarah Green

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  • 04.08.26 11:05 Kisnoles

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

  • 19.08.26 14:50 BAYER7043

    My account was locked, and I couldn’t access my own information until [email protected] +447476618364 whats?up? helped me recover it. This lady hacker was kind and professional, but this experience showed me how risky account lockouts can be. If you’re facing the same problem, do not panic consult her A. S. A. P. Be careful with recovery agents outchea, and research their name, business, and reviews before sharing any details. Never send passwords, security codes, banking information, or copies of your ID unless you’ve confirmed who you’re dealing with. Be wary of promises that sound too good to be true, especially claims that require little information or guarantee instant access with outrageous fees.

  • 20.08.26 11:32 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 20.08.26 11:32 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.08.26 20:02 leslieyee

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

  • 25.08.26 13:44 lydiassmith567

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

  • 25.08.26 13:44 lydiassmith567

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

  • 30.08.26 15:37 [email protected]

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

  • 30.08.26 15:37 [email protected]

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

  • 01.09.26 11:16 lisawerth897

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

  • 01.09.26 11:16 lisawerth897

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

  • 01.09.26 17:34 Garry42

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

  • 01.09.26 17:34 Garry42

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

  • 02.09.26 03:43 kimberlyhebertt6877

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

  • 02.09.26 03:43 kimberlyhebertt6877

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

  • 04.09.26 21:51 Kovengray

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

  • 05.09.26 21:38 [email protected]

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

  • 09.09.26 21:31 lisawerth897

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

  • 09.09.26 21:31 lisawerth897

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

  • 09.09.26 23:22 Fraddy Pual

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

  • 11.09.26 03:23 kimberlyhebertt6877

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

  • 11.09.26 03:23 kimberlyhebertt6877

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

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