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Н Новости

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:

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()

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.

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

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

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

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

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

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:

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

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

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.

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

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:

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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26 окт. 2025 г.

22.06.26 21:51 kimberlyhebert786

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
24.06.26 01:25 Fraddy Pual

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24.06.26 01:27 Fraddy Pual

I never thought it would happen to me—but I lost $256,100 in Bitcoin through a shady investment deal. I was shattered, panicked, and convinced my savings were gone forever. Just when I was about to give up, I stumbled upon reviews for FUNDSRETRIEVER, a cyber recovery team with a solid reputation. I decided to give it a shot, and to my absolute shock, they recovered every single cent in record time. Working with them was a lifesaver. If you've been tricked by fake investment platforms, don't lose hope—FUNDSRETRIEVER can help. Contact them here: Email: [email protected] | WhatsApp: +16035121448 | Telegram: @Fundsretriever
24.06.26 01:28 Fraddy Pual

I never thought it would happen to me—but I lost $256,100 in Bitcoin through a shady investment deal. I was shattered, panicked, and convinced my savings were gone forever. Just when I was about to give up, I stumbled upon reviews for FUNDSRETRIEVER, a cyber recovery team with a solid reputation. I decided to give it a shot, and to my absolute shock, they recovered every single cent in record time. Working with them was a lifesaver. If you've been tricked by fake investment platforms, don't lose hope—FUNDSRETRIEVER can help. Contact them here: Email: [email protected] | WhatsApp: +16035121448 | Telegram: @Fundsretriever.
24.06.26 01:58 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 01:58 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 14:16 Universina da Mota

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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

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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

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25.06.26 21:25 Emilie Safi

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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

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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
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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
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02.07.26 01:22 Lieneke Bonnema

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04.07.26 15:32 Fraddy Pual

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06.07.26 16:20 Olga Ognjanović

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06.07.26 16:31 Joseph Weigl

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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

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13.07.26 23:49 [email protected]

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16.07.26 21:38 patricialovick86

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16.07.26 21:38 patricialovick86

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17.07.26 20:12 martinsjude080

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18.07.26 17:12 Malthe Larsen

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18.07.26 23:51 bernalzenaida

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19.07.26 04:10 Fraddy Pual

I can't thank Fundsretriever enough for everything they did for me. My name is Vanessa Conway, and I'm here to tell you my story of how I recovered money I never thought I'd see again. A few months ago, I put a significant amount of money into what looked like a genuine online investment company. At first, it felt real—they showed me fake profits and convinced me to invest even more. But when I tried to cash out, they went quiet and started asking for extra fees. That's when it hit me—I had been scammed. I was heartbroken, frustrated, and didn't know where to turn. That money was my savings—months of hard work gone. Then I found Fundsretriever online. I reached out, hoping for a miracle. Right away, their team made me feel heard. They were responsive, knowledgeable, and walked me through everything. They didn't just take my case—they took it seriously and kept me in the loop every step of the way. I finally felt like I had real experts fighting for me. And guess what? They actually got my money back. It wasn't instant, and it took teamwork, but it happened. When I saw those funds returned, I cried with joy. I'm sharing this so that anyone else out there who's been scammed knows—don't lose hope. Do your research before investing, and stay far away from platforms that promise too much too fast. And if you've already been stung, don't wait—get professional help immediately. Thank you, Fundsretriever, from the bottom of my heart. You didn't just recover my money—you restored my faith. — Vanessa Conway 📧 [email protected] 📱 WhatsApp: +16035121448 💬 Telegram: @Fundsretriever
19.07.26 19:53 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] Call/Text Number: +1 (336) 390-6684
19.07.26 19:53 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] Call/Text Number: +1 (336) 390-6684
19.07.26 19:54 kimberlyhebertt6877

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30.07.26 00:04 Ahmed

A really cool analysis, thank you. I was especially struck by how strictly the order is defined: data processing and formatting come first, with color only at the very end. This really saves you from the typical mistake of "first a pretty palette, then we figure out what the chart is for." And the palette validator with OKLCH + colorblindness check is absolutely fantastic; you almost never see that in regular tools. By the way, while reading about rank-trajectory and the logarithmic scale, I immediately remembered how convenient it is to analyze dynamics on charts in ExpertOption—I've been trading there for quite some time now. When the data is well visualized, decisions are noticeably easier and more relaxed. I also liked the point about "no more than eight colors" and the dual-axis ban. Strict restrictions sometimes actually produce better results than complete freedom. I'll try this approach myself.
30.07.26 17:27 wendytaylor015

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30.07.26 17:27 wendytaylor015

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31.07.26 16:21 rssllhrnsb

I learned an important lesson after investing in what appeared to be a genuine opportunity. Unfortunately, I was unable to access my funds, which reinforced the importance of carrying out thorough due diligence, checking whether an investment is appropriately regulated, and seeking qualified professional advice rather than relying solely on online reviews or testimonials. During the process of addressing my case, I worked with Mrs. Doris Ashley, who communicated clearly, provided regular updates, and handled the matter in a professional manner. According to my experience, I have recovered $50,000 so far, while efforts to resolve the remaining balance are still in progress. If you wish to contact her, the details I used are: Mrs. Tatiana Sorina TEXT : (tatianasorina06 at G.Ma IL ..c 0 m ) Before committing money to any investment, take time to verify the legitimacy of the platform, confirm any relevant regulatory authorisations, and avoid investing more than you can comfortably afford to lose.
01.08.26 15:05 keithwilson9899

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01.08.26 15:05 keithwilson9899

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03.08.26 20:05 Philip

I was a victim of a crypto theft involving a Pink Drainer, which resulted in the theft of my Wrapped Bitcoin (WBTC) from my Polygon network. The experience was incredibly frustrating and distressing, as I had no idea how to recover my funds. Unfortunately, by the time I noticed the theft, the funds had already been drained to an address that I had no control over, making it seem like an irreversible situation.The attack happened when I clicked on what appeared to be a legitimate link. I didn’t realize at the time that it was a phishing attempt designed to siphon off my private keys and access my wallet. The Pink Drainer, a type of malicious script used by attackers, is specifically designed to exploit such vulnerabilities in crypto wallets. The moment I realized that my WBTC had been drained from my Polygon network. I felt completely helpless, as I didn’t have direct access to the thief's address, and there was no way to reverse the transaction on my own at that point, I started searching for ways to recover my funds, but most resources only offered generic advice that wasn’t practical in this particular case. I quickly realized that if I wanted to have any hope of getting my assets back, I would need professional assistance. After some research, I came across a reliable and trusted recovery team called Aspen Recovery Experts. Their expertise in cryptocurrency recovery, especially in cases like mine, seemed promising.I decided to reach out to Aspen Recovery Experts, and I’m incredibly grateful that I did. Their team of crypto recovery experts was able to help me trace the stolen funds and identify the path the funds took after they left my wallet. Using advanced tools and techniques, they were able to track the transactions on the blockchain, helping me understand where my WBTC had been sent. More importantly, they worked tirelessly to assist me in contacting the necessary parties and even interfaced with blockchain analysts to help facilitate the recovery process.Thanks to their efforts, I was able to successfully recover my stolen funds. The entire process took some time, but the Aspen Recovery Experts dedicated team provided regular updates and kept me informed throughout the process, which gave me a sense of hope and relief during an otherwise stressful time. If you’re ever in a similar situation, I highly recommend reaching out to a trusted recovery team like Aspen Recovery Expertshhh . Their professionalism, knowledge, and expertise were critical in helping me recover my funds and regain control of my crypto assets. Whatsapp : +1 747 231 9036 Telegram : @ prohackerspy Email : [email protected]
03.08.26 20:06 Philip

I was a victim of a crypto theft involving a Pink Drainer, which resulted in the theft of my Wrapped Bitcoin (WBTC) from my Polygon network. The experience was incredibly frustrating and distressing, as I had no idea how to recover my funds. Unfortunately, by the time I noticed the theft, the funds had already been drained to an address that I had no control over, making it seem like an irreversible situation.The attack happened when I clicked on what appeared to be a legitimate link. I didn’t realize at the time that it was a phishing attempt designed to siphon off my private keys and access my wallet. The Pink Drainer, a type of malicious script used by attackers, is specifically designed to exploit such vulnerabilities in crypto wallets. The moment I realized that my WBTC had been drained from my Polygon network. I felt completely helpless, as I didn’t have direct access to the thief's address, and there was no way to reverse the transaction on my own at that point, I started searching for ways to recover my funds, but most resources only offered generic advice that wasn’t practical in this particular case. I quickly realized that if I wanted to have any hope of getting my assets back, I would need professional assistance. After some research, I came across a reliable and trusted recovery team called Aspen Recovery Experts. Their expertise in cryptocurrency recovery, especially in cases like mine, seemed promising.I decided to reach out to Aspen Recovery Experts, and I’m incredibly grateful that I did. Their team of crypto recovery experts was able to help me trace the stolen funds and identify the path the funds took after they left my wallet. Using advanced tools and techniques, they were able to track the transactions on the blockchain, helping me understand where my WBTC had been sent. More importantly, they worked tirelessly to assist me in contacting the necessary parties and even interfaced with blockchain analysts to help facilitate the recovery process.Thanks to their efforts, I was able to successfully recover my stolen funds. The entire process took some time, but the Aspen Recovery Experts dedicated team provided regular updates and kept me informed throughout the process, which gave me a sense of hope and relief during an otherwise stressful time. If you’re ever in a similar situation, I highly recommend reaching out to a trusted recovery team like Aspen Recovery Expertshhh . Their professionalism, knowledge, and expertise were critical in helping me recover my funds and regain control of my crypto assets. Whatsapp : +1 747 231 9036 Telegram : @ prohackerspy Email : [email protected]
04.08.26 11:05 Kisnoles

Excellent analysis, thank you. I was particularly struck by how rigidly the skill sets the order: data processing and form come first, with color coming last. This really cures the habit of "first a pretty palette, then we'll figure it out." A palette validator using OKLCH + color blindness + WCAG is something most chart generators lack. And regarding the boundaries of competence, it's very clear. Where there's a self-checking loop (color), you delegate freely. Where there's a heuristic (form, data interpretation), you remain the final filter. This is a universal principle, not just for /dataviz. By the way, when you look at trading dashboards (including those of decent platforms like ExpertOption), it's immediately clear who thought about readability and who just threw in rainbow lines. Tools like this skill could greatly improve the quality of analytics. Thanks again for the detailed analysis – saved.
04.08.26 12:37 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] Call/Text Number: +1 (336) 390-6684
04.08.26 12:37 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] Call/Text Number: +1 (336) 390-6684
06.08.26 08:11 ROMMYHENDERSON344

All you need is to hire an expert to help you accomplish that. If there's any need to spy on your partner's phone. From my experience I lacked evidence to confront my husband on my suspicion on his infidelity, until I came across REALCYBERHACKERS which many commend him of assisting them in their spying mission. So I contacted him and he provided me with access into his phone to view all text messages, call logs, WhatsApp messages and even her location. This evidence helped me move him off my life . I recommend you consult REALCYBERHACKERS AT gmail com or whatsapp +14106350697 if you need access to your partner's phone or any kind of hacking, they carry out all kinds of hacking job
06.08.26 13:56 lydiassmith567

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06.08.26 13:56 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
11.08.26 03:43 raymont0714

I recommend a trusted cybersecurity PRO with experience in authorized device access, security testing, and data recovery. SHE work only with the owner's consent and follow all legal and privacy rules on meta data. With permission, this specialist can recover lost files, check device security offline & online, and review texts, call records, or hidden data (spy or lurk around a cheating partner or colleuge). Strict confidentiality agreements protect the information, and client details remain private. The work is careful, efficient, and suited to complex cases. For help securing or recovering information from a phone or another electronic device, use the details below 2 consult [email protected] +44 7476618364 I trust her secrecy a living witness. Her discretion is unmatched, ensuring your privacy is always maintained
12.08.26 16:37 rssllhrnsb

I learned an important lesson after investing in what appeared to be a genuine opportunity. Unfortunately, I was unable to access my funds, which reinforced the importance of carrying out thorough due diligence, checking whether an investment is appropriately regulated, and seeking qualified professional advice rather than relying solely on online reviews or testimonials. During the process of addressing my case, I worked with Mrs. Tatiana Sorina , who communicated clearly, provided regular updates, and handled the matter in a professional manner. According to my experience, I have recovered $50,000 so far, while efforts to resolve the remaining balance are still in progress. If you wish to contact her, the details I used are: Mrs. Tatiana Sorina TEXT : (tatianasorina06 at G_Ma IL dot ..c 0 m)…. Before committing money to any investment, take time to verify the legitimacy of the platform, confirm any relevant regulatory authorisations, and avoid investing more than you can comfortably afford to lose.
16.08.26 01:44 Matt Kegan

CapitalNode Analytics. They help to investigate and recover stolen digital assets from fake trading platforms. Great firm i must say.
18.08.26 04:59 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 WhatsApp/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.08.26 04:59 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 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

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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
15.09.26 03:35 elioduncan

I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]
15.09.26 15:45 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
15.09.26 15:45 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