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Долгая дорога к DiT (часть 2)

Новая задача

Продолжаем то, на чём остановились в первой части. Напомню, нам удалось создать модель, которая может трансформировать простое (нормальное) распределение в целевое. Вот только работала она лишь с точками на плоскости, иными словами, в пространстве тензоров с шейпом (2). Короче, это была лишь тренировка на простых данных (2-размерных векторах). Надо браться за что-то посерьезнее. Как насчёт того, чтобы замоделировать превращение нормального распределения в изображения цифр и букв? Для такого как раз есть подходящий датасет - EMNIST называется. Содержатся в нём чёрно-белые изображения размером 28x28 пикселей. Так что сэмплы (выборки) целевого распределения это уже не две точки представленные тензором с шейпом (2), а целая картинка, представленная уже тензором (28, 28).

Задача опять та же: Мы хотим извлекать сэмплы из целевого распределения (узнаваемые черно-белые изображения), но просто так взять и получить изображение мы не можем, зато можем научить нейросеть трансформировать нормально распределение (шум) в целевое (картинки из датасета EMNIST). И как только мы натренируем такую нейросеть, мы сможем генерить бесконечное количество картинок - достаточно просто взять сэмпл из нормального распределения, и прогнать его через нашу модель. Давайте перефразирую: Если модель способна трансформировать распределение А в распределение В, то это значит, что, имея в распоряжении сэмпл распределения А, можно, используя эту модель, получить сэмпл из распределения В. В нашем случае распределение А - это гауссовый шум, сэмлпы которого очень просто получить, а распределение В (целевое) - это черно-белые изображения букв и цифр.

Кривой датасет

Пора поближе познакомиться с датасетом. На этот раз мы не создаём его сами, а просто скачиваем полгигабайта из интернета:

from torchvision.datasets import EMNIST

dataset = EMNIST(
    root="./emnst",  # в какую папку сохранять
    split="balanced",  # часть датасета
    download=True,  # если False, то будет ожидать что датасет уже скачен
)

Параметр split="balanced" означает, что датасет будет содержать только часть классов. Погодите, что ещё за "классы"? Сейчас объясню. Дело в том, что датасет это не просто набор картинок, это набор пар текст -> изображение. Вот этот текст и называется class или label. В датасете EMNIST классы - это просто буквы и цифры, например:

"j" -> image_1
"j" -> image_2
"a" -> image_3
...

Вот только класса "j" в нашем датасете не будет - мы выбрали вариацию "balanced", в котором изображения, привязанные к каждому классу должны выглядеть уникально. Например, убран класс "o", ведь уже есть класс "O", выглядящей идентично. Только не стоит забывать, что когда мы запрашиваем данные из датасета, то возвращает он нам не сами значения классов, а их индексы.

Давайте уже посмотрим из чего состоит этот датасет. Просто вытягиваем сэмплы, обращаясь к датасету по индексу:

# Готовимся показать 4 картинки в ряд
fig, plots = plt.subplots(1, 4, figsize=(16, 4))
for i in range(4):
    image, clazz = dataset[i]  # Я же говорил, что датасет состоит из пар
    plots[i].imshow(image)
plt.show()

Если что, plt взялся вот отсюда:

import matplotlib.pyplot as plt

PyPlot - это удобная библиотека для визуализации. Она ещё и с Numpy и PyTorch совместима. И привыкайте к plt.subplots- в статье такого будет много.

Вызвав этот код у нас на экране появится вот такое изображение сэмпла из датасета EMNIST:

f5mRk1h.png

Шкала тут явно не к месту, так что давайте её уберём. Заодно и цвет поменяем: 

fig, plots = plt.subplots(1, 4, figsize=(16, 4))
for i in range(4):
    image, clazz = dataset[i]
    plots[i].imshow(image, cmap="gray")  # цвет неба - серый
    plots[i].axis("off")  # отключить
plt.show()
r4hKQy5.png

Выглядит хорошо, но кажется осталась проблема. Проблема в том, что сэмплы из датасета криво отображаются! А знаете почему? Потому что эти буквы по умолчанию отзеркалены и повёрнуты на 90 градусов.

Этого так оставлять нельзя, надо их "раскрутить" обратно. По счастью, при работе с torchvision датасетами, можно передать им "инструкцию" о том, как трансформировать каждый сэмпл:

dataset = EMNIST(
    root="./emnst", 
    split="balanced", 
    download=True, 
    transform=transforms,  # указываем как модифицировать (аугментировать) сэмплы
)

А откуда transform возьмётся? Из этого объявления:

from torchvision.transforms import v2 as T  # версия 2, ага

transforms = T.Compose([  # группа последовательных трансформаций
	# выбираем случайный угол поворота между -90 и -90 градусов.
    T.RandomRotation(degrees=(-90, -90)),  
    T.RandomHorizontalFlip(p=1),  # с вероятностью 100% зеркалим сэмпл
    T.ToTensor()  # и сразу в тензоры конвертируем, чтобы 2 раза не вставать
])

И не надо удивляться RandomRotation и RandomHorizontalFlip, ведь основное предназначение torchvision.transforms - это аугментация изображений. Ну то есть для того, чтобы искусственно увеличить датасет. Например, представьте, что у нас есть датасет из фотографий, но нам его мало, так как данных всегда мало. Что мы можем сделать? Мы можем искусственно "раздуть" датасет в два раза, если отразим каждую фотографию по горизонтали. Правда, на фотографиях городских пейзажей все надписи получатся отзеркаленными, но вот изображения природы зеркалить можно без проблем. А ещё можно crop делать. Загляните в документацию, если интересно.

А сейчас нам интересно на то как теперь выглядят изображения из датасета. Запускаем скрипт и..

TypeError: Invalid shape (1, 28, 28) for image data

Ну вот, imshow(image, cmap="gray") не хочет рисовать наши сэмплы. А виной всему вот эта строка:

T.ToTensor()

Тут дело в том, что при работе с изображениями PyTorch ожидает, что изображение будет представлено тензором вот с таким шейпом: (C, H, W). Давайте поясню, что означает здесь каждый символ:

  • C (channel) - это количество каналов. Для RGB-изображения каналов будет 3, для RGBA их будет 4 (красный, зелёный, синий и альфа-канал для прозрачности), а в нашем случае всего 1, так как изображение чёрно-белое.

  • H (height) - высота (всегда идёт прежде чем ширина).

  • W (width) - ширина (всегда после высоты).

Трансформатор ToTensor преобразует черно-белые изображения 28x28 из датасета MNIST в тензоры с шейпом (1, 28, 28). Мы передаём такое изображение функции imshow, но imshow может рисовать чёрно-белые изображения только если мы ему передадим тензор с шейпом (H, W) либо с шейпом (H, W, C). В общем, мы имеем на руках тензор с шейпом (C, H, W) - конкретно (1, 28, 28), а хотим получить тензор шейпом (H, W, C) - то есть (28, 28, 1). Количество элементов остаётся неизменным, просто элементы по-другому "упакованы". На самом деле, довольно банальная операция для PyTorch. Всего-то делов вызвать

image.permute(1, 2, 0)  # возвращает тензор с измененным порядком dimensions

Теперь всё работает без ошибок. Давайте сравним сэмплы до и после трансформации:

Было, стало (гифка)
Буквы теперь похожи на буквы.
Буквы теперь похожи на буквы.

Полный код:

import matplotlib.pyplot as plt
from torchvision.datasets import EMNIST
from torchvision.transforms import v2 as T

transforms = T.Compose([
    T.RandomRotation(degrees=(-90, -90)),
    T.RandomHorizontalFlip(p=1),
    T.ToTensor()
])

dataset = EMNIST(
    root="./emnst",  # в какую папку сохранять
    split="balanced",  # часть датасета
    download=True,  # если False, то будет ожидать что датасет уже скачен
    transform=transforms,  # указываем как модифицировать (аугментировать) сэмплы
)

# Готовимся показать 4 картинки в ряд
fig, plots = plt.subplots(1, 4, figsize=(16, 4))
for i in range(4):
    image, clazz = dataset[i]
    plots[i].imshow(image.permute(1, 2, 0), cmap="gray")
    plots[i].axis("off")
plt.show()

Приступаем к тренировке

Ладно, датасет скачали, сэмплы посмотрели. Пора использовать данные по назначению - натренировать модель.

Переиспользуем тренировочный код из прошлой статьи, внеся правки под новый датасет и модель:

BATCH_SIZE = 256
LR = 6e-4
DEVICE = 'cuda'
EPOCHS = 600

data_loader = torch.utils.data.DataLoader(
    dataset=dataset,
    batch_size=BATCH_SIZE,
    shuffle=True,
)
optimizer = torch.optim.AdamW(model.parameters(), lr=LR)

for epoch in range(EPOCHS):
    epoch_loss = 0
    for x0, clazz in data_loader:
        x0 = x0.to(DEVICE)
        clazz = clazz.to(DEVICE)
        time = torch.rand((x.size(0), 1), device=DEVICE)

        noise = torch.randn_like(x, device=DEVICE)

        true_velocity = x0 - noise
        # Помните, чем больше time, тем больше шума
        xt = x0 * (1 - time) + noise * time
        # Можно было написать вот так:
        # xt = noise + true_velocity * (1 - time)

        pred_velocity = model(xt, time)  # передаём в модель сэмплы и time
		
		# ошибка между ожидаемым и предсказанным значением
        loss = torch.mean((true_velocity - pred_velocity) ** 2)  
        epoch_loss += loss.item()  # накапливаем ошибку для логирования

        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

    if epoch % 50 == 0:  # Каждые 50 эпох отчитываемся о прогрессе
        print(f"Epoch {epoch + 1} completed.")
        print(f"Loss: {epoch_loss / len(subset) * 1000:.2f}")
        
# По окончании тренировки сохраняем модель в файл
safetensors.torch.save_model(model, "./mnist_model_1.sft")

И ещё раз напомню, что тут вообще происходит: Каждую итерацию цикла мы извлекаем из датасета набор (батч) 256 чёрно-белых изображений (сэмплов) размером 28 на 28 пикселей. Этот батч представляет собой тензор с шейпом (256, 1, 28, 28). Будь изображения цветные, то тензор был бы (256, 3, 28, 28). Чтобы натренировать модель нам нужны сэмплы с разной степенью "зашумлённости". Как нам их получить? Нужно создать тензор с шумом, при этом такого же размера, что и батч изображений, а потом просто линейно интерполировать между этими двумя тензорами. Вот только чтобы линейно интерполировать между двумя тензорами и получить новый (зашумлённый) тензор нам нужен какой-то коэффициент. То есть, коэффициент 0.5 означает что, полученный тензор будет ровно на полпути между изображением и шумом, а коэффициент 0.1 - шумным только на 10%. Легче это визуально показать:

Большая гифка про добавление шума
При коэффициенте выше 0.6 изображение растворяется в шуме
При коэффициенте выше 0.6 изображение растворяется в шуме

Тренировочный цикл практически 1 в 1 то, что было в предыдущей статье. Пока проигнорируем тот факт, что model мы до сих пор не создали, посмотрим вот на эту строку:

xt = x * (1 - time) + noise * time

Тут мы хотим получить частично зашумлённые сэмплы линейно интерполируя между целевыми сэмплами и шумом используя time в качестве коэффициента. Всё хорошо, вот только этот код упадёт с ошибкой. Чтобы понять в чём дело, распишем какой шейп имеют все 3 тензора:

x0     (256, 1, 28, 28)
noise  (256, 1, 28, 28)
time   (256, 1)

При попытке умножить noise на time PyTorch выдаст нам такую ошибку:

RuntimeError: The size of tensor a (64) must match the size of tensor b (28) at non-singleton dimension 2

А оно и понятно, вот просто подумайте, мы хотим умножить набор из 200704 (256 x 1 x 28 x 28) чисел на другой набор уже из 256 (256 x 1) чисел, чтобы в итоге получить ещё одни набор из 200704 чисел. И как, спрашивается, PyTorch должен это сделать? Так-то мы хотим умножить каждое число из тензора noise на соответствующее ему из тензора time. У нас бы всё получилось если бы тензор time имел такую же форму (шейп) как и тензор noise (256, 1, 28, 28). И мы можем этого достичь, нужно просто размножить (расширить) тензор:

(256, 1) -> (256, 1, 28, 28)

Всего-то и делов - добавить 2 дополнительных измерения, а потом скопировать единственное число пока не получится матрица 28x28. При чём добавлять измерений мы можем тензору сколько угодно - количество элементов в нём не изменится. То есть тензор с шейпом (256, 1) содержит столько же элементов сколько и тензор с шейпом (256, 1, 1, 1). Для этого как раз подходит метод reshape:

ext_time = time.reshape(time.size(0), 1, 1, 1)  # будет (256, 1, 1, 1)

Осталось только скопи.... А не надо ничего копировать больше! PyTorch вполне способен превратить тензор (256, 1, 1, 1) в тензор (256, 1, 28, 28) ориентируясь на размер второго тензора в операции умножения. Загляните в документацию по broadcasting, если хотите подробностей.

И, кстати, небольшое пояснение к time.size(0) - можно было бы просто написать BATCH_SIZE, вот только проблема в том, что когда мы итерируемся по датасету и извлекаем из него один батч за другим в самой последней итерации может оказаться меньше элементов чем BATCH_SIZE.
Поясню этот момент. Представьте, что у нас есть вот такой список:

[1, 2, 3, 6, 5, 7, 3, 2]

И мы решаем проитерировать его по 3 элемента за раз:

[1, 2, 3]
[6, 5, 7]
[3, 2]

Как видите последний "батч" вышел короче чем другие. Надеюсь стало понятнее.

Возвращаемся к коду. Заменяем вот эту строку:

xt = x0 * (1 - time) + noise * time

на

ext_time = time.reshape(time.size(0), 1, 1, 1)
xt = x0 * (1 - ext_time) + noise * ext_time

Ладно, с этим разобрались, приступаем к самой модели

Собираем модель

В качестве отправной точки возьмём модель из предыдущей статьи:

class DenoiserBlock(nn.Module):  
    def __init__(self, hidden_dim, mlp_ratio):  
        super().__init__()  
        self.ln = nn.LayerNorm(hidden_dim)  
        self.mlp = nn.Sequential(  
            nn.Linear(hidden_dim, hidden_dim * mlp_ratio),  
            nn.SiLU(),  
            nn.Linear(hidden_dim * mlp_ratio, hidden_dim),  
        )  
  
    def forward(self, x):  
        z = self.ln(x)
        z = self.mlp(z)
        return z  
  
  
class Denoiser(nn.Module):  
    def __init__(self, hidden_dims, num_blocks):  
        super().__init__()  
        self.input_encoder = nn.Linear(2, hidden_dims)  
        block_list = [DenoiserBlock(hidden_dims, 4) for _ in range(num_blocks)]  
        self.blocks = nn.ModuleList(block_list)  
        self.output_decoder = nn.Linear(hidden_dims, 2)  
        self.time_linear = nn.Sequential(  
            nn.Linear(1, hidden_dims),  
            nn.LayerNorm(hidden_dims)
        )  
  
    def forward(self, x, t):  
        hidden = self.input_encoder(x)  # (B, 2) -> (B, 16)  
        time_embedding = self.time_linear(t)
        for block in self.blocks:  
	        hidden = hidden + block(hidden + time_embedding)  
        return self.output_decoder(hidden)  # (B, 16) -> (B, 2)

Сейчас она принимает 2 параметра - тензор точек с шейпом (B, 2) и тензор времени (шаг, timestep) с шейпом (B, 1). Нам надо работать не с точками на плоскости, а с изображениями, поэтому первым параметром наша модель должна принимать 4D тензор с шейпом (B, 1, 28, 28). B - это размер батча, если кто забыл, 256 в нашем случае.

Тут очень удобно получается, что в нашей модели уже есть слой input_encoder, который трансформирует входной тензор во внутреннее представление, и output_decoder, который проделывает обратную операцию. Так что всего лишь остаётся модифицировать эти слои, чтобы они работали с новыми входными данными:
Вот это

self.input_encoder = nn.Linear(2, hidden_dims)

Заменяем на

self.input_encoder = nn.Sequential(
	nn.Flatten(start_dim=1),  # (B, 1, 28, 28) -> (B, 784)
	nn.Linear(28*28, hidden_dims),
)

nn.Flatter - это просто операция слияния измерений в тензоре. Тренируемых параметров не содержит, в отличие уже знакомого нам nn.Linear.

Теперь с output decoder. Превращаем

self.output_decoder = nn.Linear(hidden_dims, 2)

В такое:

self.output_decoder = nn.Sequential(
	nn.Linear(hidden_dims, hidden_dims * 2),
	nn.SiLU(),
	nn.Linear(hidden_dims * 2, SIZE * SIZE),
	nn.Unflatten(1, (1, SIZE, SIZE)),  # (B, 784) -> (B, 1, SIZE, SIZE)
)

А ещё уберём time_embedding для чистоты эксперимента:

def forward(self, x, t):  
        hidden = self.input_encoder(x)
        time_embedding = self.time_linear(t)  # пока игнорируем
        for block in self.blocks:  
	        hidden = hidden + block(hidden)  
        return self.output_decoder(hidden)

Пока что наша новая модель не сильно отличается от предыдущей - всего-то адаптировали энкодер и декодер под новый формат. Пока что.

Ладно, давайте инициализировать модель и попробуем её натренировать

BATCH_SIZE = 256
LR = 6e-4
DEVICE = 'cuda'
EPOCHS = 600

subset = Subset(dataset, torch.randperm(4096 * 2))
data_loader = torch.utils.data.DataLoader(
    dataset=subset,
    batch_size=BATCH_SIZE,
    shuffle=True,
)
model = Denoiser(hidden_dims=600, num_blocks=2)  # вектор из 600 элементов
model.to(DEVICE)  # всё должно быть на одном девайсе
optimizer = torch.optim.AdamW(model.parameters(), lr=LR)

И получаем в итоге:

Всё очень плохо
Всё очень плохо

Как думаете, что пошло не так? Слишком большой датасет? Неудачная архитектура? Модель недостаточно глубокая? Я расскажу в чём дело, но давайте сначала разберёмся откуда вообще взялась эта картинка.

Понимаете, во время тренировки генеративной модели полезно не только следить за уменьшением показателя loss (ошибка), но и за тем какие изображения (сэмплы) модель способна генерить. Поэтому в моё коде тренировки логируется не только loss, но и генерируются и сохраняются сэмплы чтобы наглядно наблюдать как модель учится генерить изображения. Вот так это выглядит:

if epoch % ((EPOCHS - 1) // num_samples) == 0:
	with torch.no_grad():
		log_sample(sample_noise, model)  # генерим прямо походу обучения
if epoch % 50 == 0:  # Каждые 50 эпох отчитываемся о прогрессе
        print(f"Epoch {epoch + 1} completed.")
        print(f"Loss: {epoch_loss / len(subset) * 1000:.2f}")

Не буду здесь углубляться в то, что делает функция log_sample - всё равно можно посмотреть в финальном коде. Просто генерим 5 сэмплов несколько раз за время обучения и сохраняем их все в виде одного изображения - чтобы потом видеть "прогресс" в обучении. По рисунку выше видно, что модель уже после первых 20% времени обучения научилась генерить из шума бесформенных кляксы и на этом остановилась. А причина в том, что данные не нормализованы.

Я, конечно, мог бы поступить лениво и просто сказать, что нужно добавить T.Normalize((0.175,), (0.35,))
в конец списка трансформаторов:

transforms = T.Compose([
    T.RandomRotation(degrees=(-90, -90)),
    T.RandomHorizontalFlip(p=1),
    T.ToTensor(),
    T.Normalize((0.175,), (0.35,)),  # Вот так
])

Но я так не поступлю. Держите объяснение:

Давайте вспомним, что входной датасет у нас это одноканальные PIL-изображения, которые представляют собой набор пикселей каждый в интервале от 0 (черные) до 255 (белые). Наш трансформатор ToTensor() помимо всего прочего ещё и "сжимает" входное изображение в интервал от 0 (черные) до 1 (белые). А теперь припоминаем как мы создаём "зашумлённые" изображения во время тренировки - интерполируем между шумом и "чистыми" изображениями. Вот только чистые изображения у нас находятся в интервале [0, 1] а шум где-то в интервале [-2, 2] (да, я в курсе [-3\sigma, 3\sigma]) - получается что когда мы создаём наполовину зашумлённые изображения, то шум просто "скрывает" данные. По другому можно сказать, что 95% процентов времени обучения модель не видит данные в шуме - не может их различить и из-за этого не может нормально обучиться. Что же в таком случае сделает Normalize?

На самом деле всё просто - первое число (0.175) - это то что мы отнимем от каждого "пикселя" во входном изображении. Нужно это для того, чтобы средняя стала равняться 0. А откуда вообще взялось число 0.175? Да я просто посчитал среднее значения для всех пикселей в нашем датасете. Большинство пикселей равнялось 0 - чёрный фон ведь, поэтому вычисленное среднее смещено к 0. Значит, отняли среднее и теперь новое среднее значение это 0. Осталось лишь разделить 0.35. Может уже догадались, что 0.35 - это стандартное отклонение нашего датасета. Разделив все данные на это число мы получим новый набор данных, но теперь уже со средним 0 и стандартным отклонением 1.0 - как раз совпадающий со средним и стандартным отклонением гауссового шума, из которого мы берём наши "шумные" сэмплы. Таким образом, мы добились того, что и шум и чистые данные статистически равнозначны и обучение модели должно пройти лучше.

Запускаем тренировку и получаем:

Небо и земля
Небо и земля

Будем считать это нашей точкой отсчёта и начнём улучшать архитектуру нашей модели.

Версия 0 (downsample)

Добавляю нулевую версию, уже после того как почти дописал статью. В общем, тут такое дело: двухслойная модель шириной 600 скрытых параметров не потянула моделирование датасета изображений, каждое из которых 784 пикселей. Поэтому, признав поражение, приходится уменьшить разрешение целевых изображений. Будут 24x24 пикселя.

SIZE = 24
transforms = T.Compose([
    T.RandomRotation(degrees=(-90, -90)),
    T.RandomHorizontalFlip(p=1),
    T.Resize(SIZE),  # Как уменьшить фотку в фотошопе
    T.ToTensor(),
    T.Normalize((0.175,), (0.35,)),  # Вот так
])

Заменяем во всём коде 28 на SIZEи запускаем тренировку

24x24
24x24

Вот от этого теперь будем отталкиваться

Версия 1 (timestep condition)

Прежде всего, давайте вернём информацию о временном шаге (timestep), чтобы модели легче было распознавать на какой стадии "зашумления" находятся обучающие сэмплы.

Было:

    def forward(self, x, t):
        hidden = self.input_encoder(x)
        #  time_embedding = self.time_linear(t)
        #  hidden = hidden + time_embedding
        for block in self.blocks:
            hidden = hidden + block(hidden)
        return self.output_decoder(hidden)

Стало:

    def forward(self, x, t):
        hidden = self.input_encoder(x)
        time_embedding = self.time_linear(t)
        hidden = hidden + time_embedding  # информация о времени добавилась
        for block in self.blocks:
            hidden = hidden + block(hidden)
        return self.output_decoder(hidden)
Небольшая разница проглядывается
WecoteF.gif

Есть способ улучшить результат. Для этого нужно поменять то, как модель использует информацию.

Версия 2 (modulation)

Давайте сначала разберёмся с определениями. Вот какую информацию мы передаём модели, когда хотим что-то сгенерировать? Можно передать просто сэмлпы разной степени зашумлённости и тогда модель должна каким-то образом только только из этой информации определить степень зашумления и предсказать нужный вектор. Но ведь можно упростить модели задачу - передать ей на вход не только шумные сэмплы, но ещё и дополнительную подсказку (условие), которая "расскажет" модели сколько шума содержится в переданном сэмпле. Можно по другому сказать: на какой точки траектории находится находится сэмпл, он ближе к целевому распределению или к сэмплам гауссового шума. Эта дополнительная информация позволит модели легче произвести обобщение, а это, в общем-то, и есть цель обучения. С практической точки зрения тут понятно - если дать модели дополнительную информацию на вход, то результат будет лучше. Наглядно будет видно, когда мы дойдём до генерации по классам - качество генерации резко возрастёт. А пока надо запомнить, что когда мы передаём модели дополнительную информацию (помимо самого шумного сэмпла), то это называется условная генерация. А если подобной информации нет, то это безусловная генерация.

Сейчас в версии 1 единственное условие, которое мы передаём в модель - это время

def forward(self, x, t):  # t - это time
	hidden = self.input_encoder(x)
	time_embedding = self.time_linear(t)  # делаем тензор-условие
	hidden = hidden + time_embedding  # и просто прибавляем к данным

Сложение тензоров - это вполне себе рабочий способ добавить дополнительную информацию, но в случае диффузных моделей малоэффективный. Но как ещё мы можем повлиять на генерацию? Ответ мы найдём в публикации по диффузным трансформерам:

gompg9m.gif

На этой диаграмме подсвечен механизм управления генерацией через манипуляцию Scale и Shift. На самом деле, всё просто. Вот есть у нас (допустим) скрытое представление - одномерный тензор (вектор) вот с таким значениями:

[0, 1.2, 0.3, -0.9]

И два вот таких вектора Scale и Shift:

[1.1, 0.9, -1, -0.8] - это Scale

[0.1, 0.2, -0.07, 0] - а это Shift

Как эти 2 вектора повлияют на вектор скрытого представления?
А вот так:
[0, 1.2, 0.3, -0.9]
x
[1.1, 0.9, -1, -0.8]
=
[0, 1.08, -3, 0.72] - это после операции scale

И потом:
[0, 1.08, -3, 0.72]
+
[0.1, 0.2, -0.07, 0]
=
[0.1, 1.28, -3.07, 0.72] - это после операции shift

В коде это будет выглядеть вот так:

z = z * scale + shift  # z - это переменная скрытого представления

Выглядит как непонятно откуда взявшаяся операция, но вспомните, что мы моделируем - мы моделируем трансформацию исходного распределения в целевое. Скрытое представление, с которым мы проделываем все эти операции - это лишь одна "точка" из распределения. Умножая и прибавляя некие значения к каждой точке распределения приводит к тому, что распределение как бы сжимается или растягивается (умножение) и сдвигается в некотором направлении (сложение). И всё это происходит в некоем многомерном пространстве - в случае нашей модели пространство 600-мерное.

Но вы спросите - откуда вообще берутся эти вектора Scale и Shift? Видите на диаграмме блок "MLP" справа внизу - он на вход получает вектор-условие, а на выходе у него вектор размера в три раза больше чем размер скрытого представления. Это для того, чтобы потом этот длинный вектор разделить на 3 части - Scale, Shift и Gate. Вот иллюстрация:

Из вектора-условия получаем 3 вектора модуляции
Из вектора-условия получаем 3 вектора модуляции

Наш 32-размерный вектор с условием проходит через MLP и трансформируется в 600 * 3 = 1800 размерный вектор. 600 - это размерность скрытого представления в нашей модели. Потом просто разделяем его на 3 равные части каждая размером в 600, которые становятся векторами Scale, Shift и Gate. Вам, наверное, хочется спросить, что это за Gate? На самом деле, но работает также как Scale (умножается на скрытое преставление), но служит немного для другой цели. Дочитайте до конца секции и поймёте.

Теперь воплотим это в коде:

    def __init__(self, hidden_dim, mlp_ratio, condition_dim):  # новый параметр
        super().__init__()
        self.ln = nn.LayerNorm(hidden_dim)
        self.mlp = nn.Sequential(
            nn.Linear(hidden_dim, hidden_dim * mlp_ratio),
            nn.SiLU(),
            nn.Linear(hidden_dim * mlp_ratio, hidden_dim),
        )
        self.modulator_mlp = nn.Sequential(  # MLP
            nn.Linear(condition_dim, condition_dim * 4),
            nn.SiLU(),
            nn.Linear(condition_dim * 4, hidden_dim * 3),
        )

	
    def forward(self, x, c):
	    # Вычисляем, разделяем на 3 куска и применяем
        scale, shift, gate = self.modulator_mlp(c).chunk(3, dim=1)
        z = self.ln(x)
        z = z * scale + shift  # после нормализации
        z = self.mlp(z)
        z = z * gate
        return z

self.modulator_mlp(c) вернёт нам тензор с шейпом (B, 1800), а вызов .chunk(3, dim=1) разделит его на 3 равные части: ((B, 600), (B, 600), (B, 600)), которые мы и будем использовать. Итак, подытожим: условная информация (время) - это вектор размером 32. Он проходит через дополнительную модель modulator_mlp, которая создаёт на его основе вектор размеров в три раз больше чем скрытое представление z. После этого мы рубим этот вектор на 3 части и используем их, чтобы "оказать влияние" на скрытое представление через умножение и складывание - операции, которые, по сути, трансформирует моделируемое распределение. Таким образом, каждый блок теперь "знает" условную информацию и имеет больше возможностей учесть эту дополнительную условную информацию в своей работе.

Ладно, думаю стало понятнее. Теперь, конечно, нужно дописать код - у нас ведь появился новый параметр в конструкторе блока: condition_dim, поэтому надо поправить размерность вектора, который выдаёт time_linear в основной модели:

Вместо

self.time_linear = nn.Sequential(  
    nn.Linear(1, hidden_dims),
    nn.LayerNorm(hidden_dims) 
)

Написать

self.time_linear = nn.Sequential(  
    nn.Linear(1, condition_dim),  
    nn.LayerNorm(condition_dim)  
)

condition_dim появится в конструкторе самой модели

def __init__(self, hidden_dims, num_blocks, condition_dim):

И теперь нужен при создании блоков:

block_list = [DenoiserBlock(hidden_dims, 4, condition_dim) for _ in range(num_blocks)]

Запускаем тренировку и видим, что результат особо не улучшился:

Незначительное улучшение
Незначительное улучшение

А дело вот в чём - изначально мы инициализируем modulator_mlp случайными весами, которые при добавлении к скрытому представлению оказывают дополнительную нагрузку на тренировку - сигнал становится слишком шумным. Но есть способ это поправить. Первый раз я узнал про него как раз в публикации про Diffuison Transformers - надо инициализировать веса modulator_mlp так, чтобы изначально выдаваемый её вектор был нулевым. Что значит нулевым? А то что и Scale, и Shift, и Gate будет содержать только 0, другими словами, получатся 3 вектора размером в 600 заполненные нулями. Но зачем нам векторы, заполненные нулями? Они дают нам возможность переписать метод forward у DenoiserBlock вот так: 

def forward(self, x, c):
        scale, shift, gate = self.modulator_mlp(c).chunk(3, dim=1)
        z = self.ln(x)
        z = z * (1 - scale) + shift
        z = self.mlp(z)
        z = z * gate
        return z

Подумайте, что будет происходить если все элементы векторов scale, shift и gate равны 0? Возвращаемое значение (z) будет равняться нулевому вектору, все значения которого равны 0! А сейчас вспомните как мы используем результат работы блока в основной модели-денойзере:

hidden = hidden + block(hidden, time_embedding)

hidden + нулевой вектор == hidden. Другими словами, мы полностью обнулили работу блока. Главным образом из-за вот этого "умножения на 0": z = z * gate. Вот для чего gate и нужен - сгладить сигнал для градиента. Главное тут понять, что "нулевым" вектора Scale, Shift и Gate будут только первую итерацию тренировки - после первого же вызова optimizer.step() градиент поменяет веса modulator_mlp и модель будет обучаться своим чередом. Но за счёт того, что изначально она инициализировалась нулями и не добавляла шум в сигнал, последующее обучение пройдёт более "гладко". Сейчас мы в этом убедимся. В конец конструктора блока добавляем код инициализации весов:

self.modulator_mlp = nn.Sequential(  
    nn.Linear(cond_dims, cond_dims * 4),  
    nn.SiLU(),  
    nn.Linear(cond_dims * 4, hidden_dim * 3)  # вот этот слой
)
#  Linear делает x * weight + bias
nn.init.zeros_(self.modulator_mlp[-1].weight)  # все weight теперь 0
nn.init.zeros_(self.modulator_mlp[-1].bias)    # все bias теперь 0

теперь modulator_mlp стартует обучение с нулевым вектором на выходе. Всё остальное не меняется. Запускаем тренировку и...

Вот теперь видно, что сэмплы стили чётче.
Вот теперь видно, что сэмплы стили чётче.

Версия 3 (class condition)

Вы ведь помните, что наш EMNIST датасет содержит не просто сэмплы-изображения, но ещё и их классы (лейблы). Вот тут видно как класс картинки clazz извлекается из data_loader вместе с самой картинкой x0:

for epoch in range(EPOCHS):
    epoch_loss = 0
    for x0, clazz in data_loader:

clazz здесь - это просто индекс класса - всего 47, от 0 до 46. А откуда мы узнали, что их 47? Да просто создав переменную num_classes сразу после объявления датасета:

subset = Subset(dataset, torch.randperm(4096 * 2))  
num_classes = len(dataset.classes)

И что мы будем с этими классами делать? С помощью них мы обучим модель новому условию (классу изображения) - научим её генерировать не просто сэмплы, похожие на какие-то картинки из датасета EMNIS, а на конкретные символы - 1, 2, 8, b, c, k, w и прочие. Что ж, приступим.

Как и в случае с time_embedding нам нужно получить вектор, кодирующий условие класса (class_embedding), но на руках у нас опять лишь единственное целочисленное дискретное число. В случае с time мы создавали вектор-условие прогоняя time через time_linear, но индексы класса - это не интервал, поэтому мы будем действовать по-другому: создадим ассоциативный массив (lookup table, мапа), где каждый индекс (класс) будет ассоциироваться с каким-то конкретным вектором. И как удачно получилось, что у Pytorch как раз есть для этого уже готовое решение: nn.Embedding. Добавляем его в начало конструктора Denoiser'a:

def __init__(self, hidden_dims, num_blocks, condition_dim):  
    super().__init__()  
    self.class_embeddings = nn.Embedding(num_classes, condition_dim)

nn.Embedding создаёт набор векторов размером condition_dim в количестве num_classes, и даёт возможность к ним обращаться вот так:

self.class_embeddings(19)

Вектора инициализируются случайными значениями, но по ходу тренировки до них доходит градиент, поэтому они тоже будут обучаться.

Помимо class_embeddings нам понадобится ещё один MLP. Объявим его на следующей строке:

def __init__(self, hidden_dims, num_blocks, condition_dim):  
    super().__init__()  
    self.class_embeddings = nn.Embedding(num_classes, condition_dim)  
    self.class_mlp = nn.Sequential(  
        nn.Linear(condition_dim, condition_dim * 4),  
        nn.SiLU(),  
        nn.Linear(condition_dim * 4, condition_dim),  
    )

Осталось лишь обновить метод forward:

def forward(self, x, t, c):  # тепеть метод принимает индекс класса  
    hidden = self.input_encoder(x)
    time_embedding = self.time_linear(t)  
    class_embedding = self.class_embeddings(c)  # вытаскиваем эмбеддинг
    class_condition = self.class_mlp(class_embedding)  # прогоняем его через mlp
    # формируем объединённый вектор-условие
    # time_embedding можно было бы переименовать в time_condition
    condition = time_embedding + class_condition 
    for block in self.blocks:  
	    # отправляем объединённый вектор-условие в блок
        hidden = hidden + block(hidden, condition)
    return self.output_decoder(hidden)

Ну и код тренировки тоже подправить надо:

Вместо

pred_velocity = model(xt, time)  # передаём в модель сэмплы и time

Пишем

pred_velocity = model(xt, time, clazz)  # передаём в модель сэмплы, time и класс

Запускаем теперь тренировку и

Og85bqC.png

Теперь символы (почти) отчётливо различимы, однако присутствует какая-то размытость. Пришлось потратить некоторое время, чтобы выяснить, что причина в излишне "жирном" output_decoder.

При удалении лишнего слоя из

self.output_decoder = nn.Sequential(
	nn.Linear(hidden_dims, hidden_dims * 2),
	nn.SiLU(),
	nn.Linear(hidden_dims * 2, SIZE * SIZE),
	nn.Unflatten(1, (1, SIZE, SIZE)),  # (B, 784) -> (B, 1, SIZE, SIZE)
)

Энкодер превращается в простое умножение на матрицу (плюс bias):

self.output_decoder = nn.Sequential(
	nn.Linear(hidden_dims, SIZE * SIZE),
	nn.Unflatten(1, (1, SIZE, SIZE)),  # (B, 784) -> (B, 1, SIZE, SIZE)
)

И финальный результат выглядит гораздо лучше:

92lDm82.gif

Чем это можно объяснить? Странно это выглядит, когда при уменьшении размера модели она начинает выдавать сэмплы лучшего качества. Я вижу объяснение в том, что "жирный" output_decoder хоть и обладает потенциально лучшим качеством генерации, но при ограниченности "вычислительных ресурсов" - у нас тут всего 8192 * 600 = 4915200 итераций - слишком мощный output_decoder оттягивает часть этих ресурсов на себя и из-за этого понижает качество сэмплов. Чтобы выяснить действительно ли моя гипотеза верна придётся произвести небольшое исследование, так что пока догадка остаётся догадкой.

В результате получилась модель весом 27Mb, способная генерировать узнаваемые символы из датасета EMNIST. Цель выполнена! И финальный код доступен по ссылке.

Заключение

Что мы сделали по ходу статьи:

  • Разобрались как работать с датасетом EMNIST

  • Адаптировали код тренировки к 4D тензорам (изображения)

  • Создали модель, способную генерировать чёрно-белые изображения

  • Постепенно улучшали архитектуру модели, узнав как задавать условие генерации через модуляцию

На самом деле даже такую маленькую модель есть куда улучшать - использовать нелинейный шедулер, например - у нас уже на 60% зашумления изображения от шума не отличить.

Самое главное, что можно вынести из этой статьи - это не работа с датасетом и 4D-тензорами, а механизм управления генерацией через Scale, Shift и Gate - то что называют modulation. Именно это приближает нас конечной цели - к созданию Diffusion Transformer. Чем мы и займёмся в третьей (финальной) части - продолжение следует..!

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

  • 14.10.25 08:46 robertalfred175

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

  • 15.10.25 18:07 crypto

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

  • 15.10.25 21:52 harristhomas7376

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

  • 15.10.25 21:52 harristhomas7376

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

  • 17.10.25 20:17 tyleradams

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  • 17.10.25 20:20 lindseyvonn

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  • 17.10.25 20:22 richardcharles

    I would recommend NVIDIA TECH HACKERS to anyone that needs this service. I decided to get into crypto investment and I ended up getting my crypto lost to an investor late last year. The guy who was supposed to be managing my account turned out to be a scammer all along. I invested 56,000 USD and at first, my reading and profit margins were looking good. I started getting worried when I couldn’t make withdrawals and realized that I’ve been scammed. I came across some of the testimonials that people said about NVIDIA TECH HACKERS and how helpful he has been in recovering their funds. I immediately contacted him in his mail at [email protected] so I can get his assistance. One week into the recovery process the funds were traced and recovered back from the scammer. I can't appreciate him enough for his professionalism.

  • 17.10.25 20:23 stevekalfman

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  • 17.10.25 21:42 marcushenderson624

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

  • 17.10.25 21:42 marcushenderson624

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

  • 17.10.25 21:42 marcushenderson624

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

  • 21.10.25 08:39 debby131

    Given how swiftly the cryptocurrency market moves, losing USDT may be a terrifying and upsetting experience. Whether you experienced a technical problem, a transaction error, or were the victim of fraud, it is important to understand the potential recovery routes. Marie can assist you in determining the specific actions you can take to attempt to regain your lost USDT when you need guidance and clarification. You can reach her via email at [email protected] and WhatsApp at +1 7127594675.

  • 21.10.25 11:45 harristhomas7376

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

  • 21.10.25 11:45 harristhomas7376

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

  • 22.10.25 04:48 MATT PHILLIP

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

  • 22.10.25 07:36 donnacollier

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  • 22.10.25 11:59 elizabethrush89

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  • 22.10.25 11:59 elizabethrush89

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  • 22.10.25 16:31 MATT PHILLIP

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

  • 23.10.25 01:52 marcushenderson624

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

  • 23.10.25 01:52 marcushenderson624

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

  • 23.10.25 15:47 MATT PHILLIP

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

  • 23.10.25 21:43 patricialovick86

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

  • 23.10.25 21:43 patricialovick86

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

  • 24.10.25 06:08 MATT PHILLIP

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

  • 24.10.25 06:40 elizabethrush89

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

  • 24.10.25 06:40 elizabethrush89

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

  • 24.10.25 06:54 MATT PHILLIP

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

  • 24.10.25 18:18 patricialovick86

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

  • 24.10.25 18:18 patricialovick86

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

  • 25.10.25 00:49 tyleradams

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  • 25.10.25 00:50 stevekalfman

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  • 25.10.25 05:05 victoriabenny463

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  • 25.10.25 10:13 wendytaylor015

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  • 25.10.25 10:13 wendytaylor015

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

  • 26.10.25 01:03 Christopherbelle

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

  • 26.10.25 18:09 victoriabenny463

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

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