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Ищем Арнольда Шварценеггера среди мужчин, женщин и детей с помощью нейросети на С++

Привет, Хабр! Меня зовут Кирилл Колодяжный, я ведущий инженер-программист в YADRO. Помимо основных рабочих задач, включающих исследование проблем производительности СХД, я увлекаюсь машинным обучением. Участвовал в коммерческих проектах, связанных с техническим зрением, 3D-сканерами и обработкой фотографий. В задачах часто использовал С++, хотя машинное обучение традиционно ассоциируется с Python. Этот язык программирования буквально захватил сферу, его используют повсюду — от обучающих курсов до серьезных ML-проектов.

Однако Python — не единственный язык, на котором можно решать задачи машинного обучения. Так, альтернативой может стать С++. Если последний вам ближе, вам будет интересен и полезен этот текст.

Под катом разберемся:

  • как организовать работу с данными и загрузку обучающего датасета,

  • как описать структуру нейронной сети,

  • как использовать уже готовые алгоритмы машинного обучения из доступных библиотек и фреймворков,

  • как организовать конвейер обучения сети,

  • как использовать предобученные глубокие сети для решения задач.

Изображение сгенерировала нейросеть
Изображение сгенерировала нейросеть

Где в машинном обучении применяется С++

Реализация базовых вычислительных алгоритмов

C++ часто используется в машинном обучении для реализации сложных алгоритмов. Он широко применяется в бэкенде популярных фреймворков, таких как PyTorch, TensorFlow и scikit-learn. Они, в свою очередь, основаны на математических библиотеках, реализующих стандарт BLAS — например, OpenBLAS или cuBLAS. Это позволяет строить высокоуровневые математические библиотеки, к которым относятся Eigen, Armadillo и ATen. NumPy, популярная библиотека Python для работы с математическими операциями, также использует C++ для реализации внутренних функций, обеспечивая быструю и эффективную работу с тензорами и матрицами.

Кастомные функции для фреймворков

PyTorch и TensorFlow предоставляют специальный API для расширения функционала. Допустим, вам нужно реализовать тензорную операцию, которая не представлена в фреймворке и у вас есть достаточно удобный механизм для ее реализации на C++. Почему на C++? Потому что, скорее всего, вам потребуется использовать CUDA или OpenCL для эффективной реализации, а они тоже используются в связке с С++.

Машинное обучение на конечных устройствах

Наиболее массово C++ для машинного обучения применяется, когда готовый продукт деплоится, например, на устройство видеоаналитики. Чаще всего там нет смысла разворачивать Python-среду и ставить интерпретатор — достаточно выполнить алгоритм в режиме вывода (inference). Поэтому существует достаточно большой спектр фреймворков, заточенных на адаптацию под микроконтроллеры и embedded-платформы.

Допустим, есть проект OpenVINO. Он специализируется на деплое машинного обучения на Intel-платформы. TensorRT — это платформа для конвертации нейронных сетей от NVIDIA, достаточно массово используются на платформах типа Jetson, с архитектурами Xavier или Orin. PyTorch и TensorFlow — популярные фреймворки — тоже предоставляют свои механизмы для запуска этих алгоритмов в рамках C++ на устройствах. Это TorchScript, torch.jit, и TensorFlow Lite, tflite micro.

Хотите узнать, какие еще задачи решают разработчики на С++? Регистрируйтесь на бесплатный онлайн-митап YADRO по С++, который состоится 20 марта. Программа встречи — по ссылке.

Решаем задачу поиска лиц с помощью С++ и его библиотек

Мы поговорим о том, как использовать C++ на самом высоком уровне и решить задачи, где обычно используют Python или технологии Julia и R.

Задачу по поиску лиц можно разделить на два шага:

  1. Поиск регионов с лицами людей. Здесь воспользуемся готовым алгоритмом, доступным в библиотеке для машинного обучения: скользящим окном пройдемся по фотографии и классифицируем регионы как лицо или не лицо.

  2. Сравнение региона с лицом с искомым лицом. Для сравнения лиц реализуем свою нейронную сеть.

Этап 1. Ищем регионы с лицами людей

В поиске лица на фото с использованием метода скользящего окна есть нюанс: лица на фотографии могут быть разного масштаба, а у окна — фиксированный размер. Чтобы найти нужное лицо, мы построим пирамиду масштабируемых изображений: изменим размеры исходного фото, чтобы маленькие лица стали больше и попадали в фиксированное скользящее окно. Чтобы определить, является регион лицом или нет, опишем его математическим представлением (вектором). Для этого используем гистограмму направленных градиентов. Далее эти векторы можно будет разделить на два класса: лицо и не лицо.

Рассмотрим на примере, что такое пирамида масштабированных изображений. На следующей фотографии есть несколько людей.

Лицо на переднем плане достаточно большое, оно попадет в скользящее окно. На заднем плане лица маленькие — мы не сможем корректно описать и классифицировать их. Для решения проблемы построим несколько масштабов входного изображения.

Чтобы описать регион на фотографии для классификации, сделаем фото черно-белым — теперь каждый пиксель содержит только интенсивность цвета. Скользящее окно нужно разбить на прямоугольные подобласти и вычислить в них направления изменений от светлого к темному.

Скользящее окно
Скользящее окно

Таких направлений может быть много. Мы ограничимся определенными: вверх, вниз, вправо, влево и по диагонали.

Направления изменения цвета. Гистограмма частоты встречаемости.
Направления изменения цвета. Гистограмма частоты встречаемости.

Из полученных направлений сформируем гистограмму по частоте встречаемости. Эта гистограмма представляет собой одномерный вектор чисел, который мы сможем использовать для тренировки классификатора и оценивать, находится в этом регионе изображения лицо или нет.

Библиотека Dlib

Загрузка изображений

Для решения задачи нужна библиотека с ограниченным набором функций, простой установкой и без лишних зависимостей. Будем использовать Dlib — известную библиотеку, которая предоставляет алгоритмы для компьютерного зрения и машинного обучения. Она легковесная, собирается и импортируется проще, чем ее аналоги — например, OpenCV.

Для использования детекции лиц на фотографии достаточно использовать два заголовочных файла. Это image/io/h и frontal/fact/detector.h, которые будут отвечать за предоставление функций загрузки изображений и детекции лиц.

#include <dlib/image/io.h>
#include <dlib/image/processing/frontal/face/detector.h>
...
using namespace dlib;

Изображения могут быть представлены двумя типами данных: двумерным массивом или матрицей. Для работы с цветными изображениями или с изображениями в оттенках серого нам достаточно специализировать шаблон array2d нужным типом. В коде ниже мы видим тип rgb_pixel. На самом деле это 32-битный integer, он позволяет описывать пространство цветов в схеме RGB. А использование типа unsigned char позволит работать с оттенками серого.

using image_t = array2d<unsigned char>;
using rgb_image_t = array2d<rgb_pixel>;
using matrix_t = matrix<float>;

Также нам потребуется матрица. Это математический примитив, класс которого может специализироваться нужным типом данных. Мы используем float. Тип matrix предоставляет больше специализированной функциональности, которая пригодится на этапе тренировки нейронной сети.

Для загрузки изображений нам достаточно использовать функцию load_image из библиотеки Dlib. Организовано все просто: функция принимает путь к файлу изображения и сама определяет тип изображения — png, jpeg или bmp.

std::string image_file_path;
...
image_t gray_scale_image;
load_image(gray_scale_image, image_file_path);
 
rgb_image_t rgb_img;
load_image(rgb_img, image_file_path);

Пирамида масштабированных изображений

Следующий этап — построение пирамиды масштабированных изображений с помощью функции pyramid_up. 

image_t gray_scale_image;
...
pyramid_up(gray_scale_image);

Существует и функция pyramid_down: можно построить пирамиду для уменьшения картинки. Мы видим, что функция принимает на вход один объект — изображение, которое нужно отмасштабировать. Остальные уровни масштабирования помещаются в то же изображение и присоединяются к основному друг за другом. Это сделано так, потому что вся остальная функциональность библиотеки понимает формат и использует его автоматически.

Детектор лиц

Для детекции лиц мы создаем объект типа face_detector с помощью функции get_frontal_face_detector. 

auto face_detector = get_frontal_face_detector();
...
auto face_rects = face_detector(gray_scale_image);

У формата есть перегруженный оператор функции, который принимает на вход изображение. Результатом является контейнер, который содержит прямоугольники — регионы с лицами.

Использование get_frontal_face_detector накладывает ограничение: система работает только с лицами, снятыми в анфас. Однако библиотека предоставляет и функциональность, основанную на глубоких нейронных сетях, для детекции лиц в других положениях.

Постобработка регионов с лицами

С помощью функции face_detector мы определили прямоугольники с лицами. Их необходимо вырезать, чтобы получить отдельные изображения. К сожалению, тип array2d не позволяет работать с частями изображения — для этого его нужно преобразовать в матрицу с помощью функции mat. 

image_t image;
rectange roi;
...
auto image_as_matrix = mat(image);
matrix<image_t::type> face_mat = subm(image_as_matrix, roi);

Если мы передадим двумерный массив, получим матрицу. А с помощью функции subm (submatrix) получим регион с лицом. Эта функция принимает два параметра: объект матрицы и размер прямоугольника, который нас интересует.

Отложенные вычисления в C++

Зачастую в математических библиотеках для C++ и фреймворках машинного обучения некоторые операции, например, обрезка матрицы или умножение матрицы, не выполняются сразу. Вместо этого возвращается объект, описывающий данную операцию. Этот подход называется отложенным вычислением (lazy calculation). Результат операции вычисляется только тогда, когда он действительно нужен. Это позволяет библиотеке оптимизировать вычисления или вообще их не проводить, если результат не используется. Если требуется получить результат операции сразу, необходимо указать тип объекта результата, например, matrix<image_t::type>. При таком вызове выделится память для копирования изображения.

После того как мы вырезали прямоугольники с лицами, нужно привести их к стандартному размеру и формату. Для этого используем функцию resize_image. Она принимает объект исходного изображения и объект изображения нужного размера, куда будет записан результат масштабирования. Эта функция имеет дополнительные параметры, которые влияют на интерполяцию при увеличении (upsampling) или уменьшении (downsampling) изображения. Эти параметры определяют способ обработки и вычисления новых пикселей. В нашем случае используются параметры по умолчанию.

image_t image;
 
...
 
image_t scaled_image(FACE_SIZE, FACE_SIZE);
resize_image(image, scaled_image);

Далее нам нужно преобразовать целочисленные значения пикселей изображения в вещественные. Сначала используем функцию matrix_cast и приведем внутренний тип матрицы изображения к типу float. Также нужно, чтобы все значения пикселей были нормализованы — приведены к одному масштабу. Поскольку наша картинка в оттенках серого, пиксели принимают значения от 0 до 255. Чтобы привести их к общему масштабу от 0 до 1, делим на 255.

return matrix_cast<float>(mat(scaled_image))/255.0f;

Эти действия важны для следующего этапа — обучения нейронной сети.

Объединение всех частей кода для детекции лиц

auto face_detector = get_frontal_face_detector();
image_t img;
load_image(img, image_file_path);
pyramid_up(img);
auto face_rects = face_detector(img);
for (auto& face_rect : face_rects) {
  matrix<image_t::type> face_mat = subm(mat(img), face_rect);
  image_t scaled_face(FACE_SIZE, FACE_SIZE);
  resize_image(face_mat, scaled_face);
  auto face_imge = matrix_cast<float>(mat(scaled_face))/255.0f;
  ...
  // обработка изображения
}

Этих функций достаточно для реализации нашего первого этапа, который включает загрузку изображения, нахождение в нем лиц, получение изображений лиц, приведение их к нужному масштабу и формату.

Код получится компактным и выразительным, похожим на аналоги на Python.

Пример работы кода
Пример работы кода

Этап 2. Сравниваем регион с целевым лицом

Сиамские сети

Один из самых распространенных способов обучить нейронную сеть поиску похожих объектов — сиамские сети, тренированные с разными целевыми функциями, например, с функциями потерь Contrastive Loss или Triplet Loss. Такой подход также называют «изучением метрик» (metric learning), потому что сравнивать можно не только изображения, но и объекты из разных предметных областей.

Сеть с двумя входами
Сеть с двумя входами

На входы подаются изображения разных людей. Наша задача — обучить нейронную сеть так, чтобы она выдавала векторы, схожие для одного человека и разные для нескольких людей. Подход к тренировке будет отличаться в зависимости от выбранной функции потерь.

Contrastive Loss

Функция потерь Contrastive Loss основана на том, что мы максимизируем расстояние между разными классами векторов и минимизируем между одинаковыми. В формуле ниже d — это расстояние, а y принимает значения 0 или 1 в зависимости от того, одинаковые изображения или нет.

888458037dd01a5d003d2e42e9f1cc1a.png

Здесь d вычисляется как квадрат расстояния, что соответствует минимизации евклидового расстояния, описывающего два объекта.

Triplet Loss

Подход с другой целевой функцией Triplet Loss чем-то похож: мы снова будем вычислять расстояние. У нас есть три сети с одной архитектурой и весами, через них проходит три изображения: якорное и два примера — позитивный и негативный.

Позитивный пример — это тот же самый объект, представленный иначе. В нашем случае сфотографированный под другим углом. Негативный пример — это пример другого объекта.
Позитивный пример — это тот же самый объект, представленный иначе. В нашем случае сфотографированный под другим углом. Негативный пример — это пример другого объекта.

Для примеров мы получаем три характеристических вектора (embbedings vectors), которые поступают на вход функции Triplet Loss. Здесь вычисляется два евклидовых расстояния между якорным изображением, позитивным и негативным примерами.

0d4115fb3638e2f9e04872045d0a2731.png

Функция должна обучить сеть так, чтобы расстояние между якорным и позитивным примером было минимальное, а между якорным и негативным — максимальное.

Результат обучения
Результат обучения

Датасет

Для обучения нейронных сетей нужны тренировочные данные — датасет. Мы используем доступный датасет Facial Recognition Dataset collected from Pinterest. Это набор из 105 фотографий знаменитостей с приблизительно одинаковым масштабом, но разным ракурсом и освещением.

Датасет Facial Recognition Dataset collected from Pinterest
Датасет Facial Recognition Dataset collected from Pinterest

Обратим внимание, что наш модуль для определения лиц реализован только для лиц, снятых в фас. Значит, на некоторых фото найти лица не получится. Это приведет к несбалансированности датасета, и в последствии может стать одной из причин низкого качества сравнения лиц. В реальных задачах уделяйте достаточно внимания подготовке тренировочных и проверочных данных.

Применение библиотеки PyTorch для работы с тренировочными данными

Для реализации нашей задумки воспользуемся библиотекой PyTorch, которая представляет собой набор инструментов для машинного обучения. Важно отметить, что для C++ также существует LibTorch — библиотека, которая предоставляет С++ интерфейс для ядра PyTorch. LibTorch включает практически всю функциональность Python-версии и имеет схожий синтаксис. Если вы уже работали с PyTorch на Python, освоить LibTorch на C++ будет достаточно просто.

Для начала работы с LibTorch нам достаточно подключить один заголовочный файл, вся функциональность помещена в пространство имен torch. 

#include <torch/torch.h>
...
using namespace torch;

Начнем с построения конвейера обучения (training pipeline) нейронной сети. Первый шаг — работа с данными:

  • загрузка фотографий,

  • приведение их к нужному размеру и формату,

  • следование стратегии, которую предписывает фреймворк PyTorch.

Для этого достаточно унаследоваться от класса Dataset и реализовать два метода:

  • get возвращает один экземпляр данных для обучения,

  • size возвращает, сколько всего у нас таких данных существует. 

class FaceDataset : public torch::data::datasets::Dataset<FaceDataset> {
  using Example = torch::data::Example<>;
 
 public:
 
  Example get(size_t index) override;
 
  torch::optional<size_t> size() const override;
};

Интерфейс для работы с тренировочными данными

Мы уже знаем, как загрузить изображение с помощью библиотеки Dlib и функции load_image. Дальше нам необходимо преобразовать загруженную матрицу в тензор — тип данных в библиотеке PyTorch. Для создания тензора из матрицы Dlib используется функция from_blob, которая принимает на вход адрес в памяти, размер тензора и тип внутренних данных. 

std::vector<Tensor> face_tensors;
...
image_t img;
dlib::load_image(img, path);
auto face_rects = face_detector(img);
...
matrix_t face_mat = crop_scale_cast_face(img, face_rects[i]);
 
auto face_tensor = from_blob(&face_mat(0, 0),              
                             {1, face_mat.nr(), face_mat.nc()}, 
                             torch::kFloat);               
 
face_tensors.push_back(face_tensor.clone())

В приведенном примере используется функция crop_scale_cast_face. Она реализует ранее описанную нами функциональность для вырезания региона с лицом и его преобразование в нужный для обучения сети формат.

Чтобы выделить память под наш тензор и скопировать данные, мы вызываем метод clone у объекта face_tensor с типом torch::Tensor.

Затем нужно реализовать проход по директории с фотографиями, их загрузку и преобразование в тензоры. А потом — доступ по индексу к каждому тензору, который представляет лицо в методе get. Следуя API Pytorch в реализации метода get нам нужно вернуть вернуть объект обучаемых данных класса Dataset::Example, так как наше класс унаследован от Dataset то в коде представленном ниже это FaceDataset::Example.

FaceDataset::Example FaceDataset::get(size_t index) {
  size_t positive_index;                    	
  size_t negative_index;                    	
  ...       	
  // объединение трех тензоров изображений в один тензор
  return {cat({
          	face_tensors[index],
          	face_tensors[positive_index],
          	face_tensors[negative_index]}),
          tensor({1.f, 1.f, 0.f},           	
               	torch::kFloat)
     	};
}

Чтобы использовать Triplet Loss в нашей функции обучения, необходимо объединить три изображения лиц в один тензор. Обычно объект Dataset::Example представляет собой пару тензоров — обучающие данные и их метки. Однако для Triplet Loss нам нужно объединить три тензора лиц. Используя функцию cat, мы объединяем их последовательно, добавляя одно дополнительное измерение к тензору. Также в качестве меток передаем тензор 1, 1, 0. Инициализация всех объектов довольно проста и напоминает использование функциональности в Python. Затем мы создаем объект типа FaceDataset, в конструктор которого передаем путь к директории с изображениями датасета.

std::string path;
...
// батчи будут организованы в vector<Tensor>
auto dataset = FaceDataset(path);
...
// батчи будут организованы в один Tensor
auto dataset = FaceDataset(path).map(data::transforms::Stack<>());

Здесь обратим внимание, как мы используем библиотеку PyTorch для реализации эффективного обучения нейронных сетей. Мы будем работать не с одним экземпляром обучаемых данных, а с набором (batch) — например, из 8, 32, 16 экземпляров. Это необходимо для эффективной утилизации вычислительных ресурсов и эффективной передачи данных из «оперативки» в память видеокарты. Поэтому PyTorch предоставляет для объектов типа Dataset метод map, который описывает, каким образом можно конкатенировать (объединять) экземпляры обучаемых данных.

В данном случае в методе map используется объект типа Stack — он обозначает, что батч наших данных будет объединен в один объект типа torch::Tensor. Если это не сделать, он будет представлен стандартным вектором в C++. Это не очень удобно, потому что потом придется вручную создавать тензор.

Объекты типа Dataset используются совместно с объектами типа DataLoader. DataLoader реализует определенную стратегию работы с наборами данных для обучения.

Каким образом создается объект DataLoder? В данном случае используем функцию make_data_loader, специализированную типом RandomSampler. Это значит, что данные из датасета будут выбираться случайным образом, с помощью равномерного распределения. Это важно для нормального обучения нейронных сетей и других алгоритмов машинного обучения. 

auto train_loader = data::make_data_loader<data::samplers::RandomSampler>(
                               	std::move(face_dataset),
                               	data::DataLoaderOptions()
                               	   	.batch_size(batch_size)
                               	   	.workers(num_workers)
                	);

Дальше функция принимает на вход объект датасета и дополнительные опции для работы с ним. Этими опциями выступают batch_size и workers. Workers — это количество потоков, которые будут использованы для формирования батчей тренировочных данных. Это важно, потому что датасеты — это обычно очень большие наборы данных, для их эффективной обработки используют много вычислительных ресурсов. Даже если датасет помещается в оперативную память, использование нескольких потоков workers позволяет распараллелить их предобработку. Такая предобработка включает в себя масштабирование, нормализацию, приведение к формату данных и так далее.

После того как мы создали датасет и завернули его в DataLoader, его использование становится тривиальным:

  1. С помощью обычного range-based for цикла проходимся по батчам.

  2. На каждой итерации цикла получаем ссылку на конкретный батч.

  3. С помощью полей батча получаем значения data и target.

data — это наши тренировочные данные, один экземпляр которых представлен одним вектором. Но там может быть несколько векторов наших тренировочных данных, каждый вектор — это тройка объединенных изображений. Количество векторов мы описывали с помощью batch_size. A target — это тензоры с нашей разметкой, их количество тоже равно batch_size. 

for (auto& batch : *train_loader) {
  	auto merged_img = batch.data.to(device);
  	auto targets = batch.target.to(device);
 
  	// Разделяем изображение на 3 части
  	auto anchor_img = merged_img.narrow(1, 0, 1);
  	auto positive_img = merged_img.narrow(1, 1, 1);
  	auto negative_img = merged_img.narrow(1, 2, 1);
  	...
}

Если вспомним, когда мы реализовывали функцию get, мы объединили наши три фотографии в один тензор. Далее нам их нужно развернуть. Для этого понадобится функция narrow: мы используем индекс в первой размерности, для получения среза тензора, представляющего нужное изображение. Функциональность полностью совпадает с интерфейсом на Python.

Архитектура нейронной сети

После того, как мы научили программу работать с данными, загружать их, предоставлять в формате, необходимом для тренировки, мы можем описать архитектуру нейронной сети для решения задачи. Для примера реализуем достаточно простой подход: три сверточных слоя, за которыми следует три линейных полносвязных слоя.

Схема архитектуры сети. Число 128 в конце означает, что сеть будет выдавать одномерный вектор размерностью 128, который и будет характеризовать изображение.
Схема архитектуры сети. Число 128 в конце означает, что сеть будет выдавать одномерный вектор размерностью 128, который и будет характеризовать изображение.

Схема архитектуры сети. Число 128 в конце означает, что сеть будет выдавать одномерный вектор размерностью 128, который и будет характеризовать изображениеЧтобы реализовать какой-то элемент нейронной сети или другого алгоритма машинного обучения в фреймворке библиотеки PyTorch, необходимо унаследоваться от класса Module — точно так же, как в Python. 

class FaceEmbeddingNetworkImpl : public torch::nn::Module {
 public:
  FaceEmbeddingNetworkImpl();
  torch::Tensor forward(torch::Tensor x);
 
 private:
  torch::nn::Sequential cnn_;
  torch::nn::Sequential fc_;
};
 
TORCH_MODULE(FaceEmbeddingNetwork);

Здесь важно использовать макрос TORCH_MODULE — он зарегистрирует этот модуль в системе автоградиента библиотеки PyTorch — и реализовать метод, который будет осуществлять прямой проход по нейронной сети или другому алгоритму. Кстати, forward в данном случае — это просто соглашение, а не виртуальная функция. Вместо него может быть любое другое название.

Сверточные и полносвязные слои

Мы разделим нейронную сеть на сверточные и полносвязные (линейные) слои и объединим их в контейнер Sequential. Sequential реализует набор методов, похожий на вектор C++, у него есть векторы push_back, которые последовательно заполняются слоями. 

cnn_ = Sequential();
 
cnn_->push_back(Conv2d(Conv2dOptions(1, 96, 11).stride(4)));
cnn_->push_back(Functional(torch::relu));
cnn_->push_back(MaxPool2d(MaxPool2dOptions(3).stride(2)));
 
cnn_->push_back(Conv2d(Conv2dOptions(96, 256, 5).stride(1)));
cnn_->push_back(Functional(torch::relu));
cnn_->push_back(MaxPool2d(MaxPool2dOptions(2).stride(2)));
 
cnn_->push_back(Conv2d(Conv2dOptions(256, 384, 3).stride(1)));
cnn_->push_back(Functional(torch::relu));
 
register_module("cnn", cnn_);

Сверточные слои

Мы добавляем в контейнер объект типа Conv2d для двумерной свертки, за которым следует объект, реализующий функцию активации ReLU, а затем операции пулинга. Этот процесс повторяется три раза, создавая слои с различными параметрами: размеры каналов и ядер свертки, операции пулинга, размер страйда. Мы используем контейнер Sequential для эффективного фьюзинга слоев в библиотеке PyTorch

Регистрация Sequential-контейнера с использованием метода register_module важна для автоградиентов.

fc_ = Sequential();
	
fc_->push_back(Linear(LinearOptions(384, 1024)));
fc_->push_back(Functional(torch::relu)); 
  
fc_->push_back(Linear(LinearOptions(1024, 256)));
fc_->push_back(Functional(torch::relu));
 
fc_->push_back(Linear(LinearOptions(256, EMBEDDIGS_SIZE)));
  
register_module("fc", fc_);

Полносвязные слои

Аналогично для линейных полносвязных слоев, мы также помещаем их в Sequential-контейнер с помощью методов pushback.

Хотя все это можно было сделать в одном контейнере Sequential, мы их разделили для наглядности. Создав слои, из которых состоит нейронная сеть, мы можем реализовать метод forward. 

Tensor FaceEmbeddingNetworkImpl::forward(Tensor x) {
  x = cnn_->forward(x);
  x = x.view({x.size(0), -1}); // Разворачиваем 3D тензор в 1D
  x = fc_->forward(x);
  return x;
}

В этом методе реализован прямой проход сети: мы программируем то, как входные данные проходят через слои в нужном нам порядке. Переход от сверточных слоев к полносвязным требует развертывания 3D-тензора в одномерный. Это достигается операцией view без дополнительного выделения памяти или копирования данных.

И этот метод возвращает уже преобразованные данные, в нашем случае — вектор, который характеризует входное изображение.

Создание конвейера для обучения нейронной сети

Описав структуру нейронной сети, мы можем создать конвейер для ее обучения. Для этого сначала надо создать объект модели: 

FaceEmbeddingNetwork model_;

Так как класс модели унаследован от класса Module, у нас уже есть методы для переключения в различные режимы. Переключаем модель в режим тренировки с помощью метода train. Далее создаем объект оптимизатора для нейронной сети, в данном случае Adam. Обратите внимание: конструктор Adam принимает на вход model все параметры (веса) нашей сети

model_->train();
 
optim::Adam optimizer(model_->parameters());
 
nn::TripletMarginLoss triplet_loss(
                      	nn::TripletMarginLossOptions().margin(3.f));
 
for (size_t epoch = 0; epoch < num_epochs; ++epoch) {
  for (auto& batch : *train_loader) {
 
	// Подготовка батча данных
	
	// Вызов функций прямого распространения
 
	// Вычисление значения функции потерь 
 
	// Вызов функций обратного распространения ошибки
 
	// Обновление значений параметров
  }
}
save(model_, "weights.dat");

Теперь описываем нашу целевую функцию (функцию потерь) triplet_loss. Обычно целевые функции принимают дополнительные параметры, которые разработчик подбирает вручную или с использования автоматических техник.

Тренировка состоит из двух циклов: первый проходит по эпохам, второй, «вложенный», — по батчам. Прохождение одной эпохи означает прохождение по всему датасету. Что включает в себя цикл:

  1. Подготовку батча: разбиение изображения на три части.

  2. Пропуск изображений через нейронную сеть для получения трех характеристических векторов.

  3. Передачу векторов в функцию triplet_loss для вычисления значения функции потерь.

  4. Использование значения функции потерь и механизма автоградиента для вычисления всех градиентов.

  5. Обновление параметров сети с использованием оптимизатора.

После такой тренировки с помощью функции save, которая принимает имя файла и объект нейронной сети, мы можем сохранить снимок (snapshot) модели в файл.

Чтобы пропустить эти изображения через нейронную сеть, мы вызываем метод forward, в который передаем объект тензора изображения. Делаем это для якорного, позитивного и негативного примеров, получаем три характеристических вектора и подаем их в метод forward функции потерь.

auto anchor = model_->forward(anchor_img);
auto positive = model_->forward(positive_img
auto negative = model_->forward(negative_img);
 
auto loss_value = triplet_loss->forward(anchor, positive, negative);

После этого достаточно вызвать метод backward, который автоматически вычислит значение всех производных — результаты пригодятся для обновления параметров сети в методе step объекта optimizer. Также важно не забывать использовать метод zero_grad, чтобы очистить значения производных от предыдущих значений.

optimizer.zero_grad(); // Обнуление значений градиентов
loss_value.backward(); // Обратное распространение ошибки
optimizer.step();  	// Обновление параметров

Пример использования нейронной сети

Представим, что у нас есть метод get_embeddings, который принимает на вход изображение и выдает его характеристический вектор (embedding). По сути он подает его на вход нашей нейронной сети и получает как результат 128-размерный вектор. 

image_t target_face_img;
...
auto target_embeddings = get_embeddings(target_face_img);
...
image_t img;
...
auto face_rects = face_detector(img);
for (auto& face_rect : face_rects) {
  auto face_mat = crop_scale_cast_face(img, face_rect);
  auto face_embeddings = get_embeddings(face_mat);
  auto distance = length(target_embeddings - face_embeddings);
  if (distance < search_threshold) {
	// целевое лицо найдено 
  }
}

Как использовать эту функцию:

  1. При работе с объектом face_detector на целевом изображении с несколькими людьми мы получаем положение лиц в виде прямоугольников.

  2. Затем в цикле масштабируем их, приводим к нужному формату.

  3. Для каждого лица используем функцию get_embeddings, чтобы получить характеристический вектор.

  4. Вычисляем разницу между этими векторами и характеристическим вектором лица и находим норму этого вектора с помощью функции length из библиотеки Dlib, что, по сути, является евклидовым расстоянием между векторами.

  5. Сравниваем это значение с пороговым значением search_treshhold.

Если значение расстояния меньше порогового значения, мы считаем, что лица похожи.

При использовании моделей важно учитывать их состояния. Например, модель может находиться в состоянии тренировки (train), когда мы обучаем ее, или в состоянии вывода (inference или evaluation), которое мы получаем с помощью вызова метода eval.

Когда мы переводим модель в состояние eval, необходимо также указать PyTorch, что мы не хотим использовать автоградиент. Для этого создается объект типа NoGradGard, который действует в рамках текущего скоупа на C++. Это важно для оптимизации производительности, так как система автоградиента требовательна к ресурсам — как вычислительным, так и памяти.

Функция get_embeddings принимает на вход матрицу изображения из библиотеки Dlib. Эта матрица представляет собой результат загрузки изображения и преобразования его в матрицу с типом float для дальнейшей обработки.

embeddigs_t get_embeddings(matrix_t& face_img) {
  model_->eval();
  torch::NoGradGuard no_grad;
 
  auto face_tensor = matrix_to_tensor(face_img);
  face_tensor = face_tensor.to(kGPU);
 
  auto output = model_->forward(face_tensor);
  output = output.to(kCPU);
  const auto* data_ptr = output.const_data_ptr<float>();
 
  return dlib::mat(data_ptr, EMBEDDIGS_SIZE, 1);
}

Дальше мы преобразуем объект матрицы в формате PyTorch с помощью метода matrix_to_float, используя тот же подход, что и при создании класса FaceDataset. Затем перемещаем тензор в графический процессор (GPU) с помощью функции to, указывая тип устройства, куда нужно перенести данные. После этого передаем загруженный вектор в метод forward и получаем характеристический вектор. Мы можем перенести этот вектор на устройство CPU с помощью функции to, вернув его обратно в оперативную память. Наконец, мы преобразуем тензор библиотеки PyTorch обратно в тип данных матрицы Dlib, используя функцию mat, которая принимает указатель на память и размерность вектора.

Результаты обучения нейронной сети

Мы сравнивали лицо Арнольда Шварценеггера с лицами людей на фото. На картинке видно, что значение расстояния на мужских лицах находятся в одном диапазоне, а на женских и детских — в другом. Это значит, что нейросеть не научилась определять целевое лицо, но смогла отличить мужчин от женщин и детей.

Результаты обучения нейронной сети с помощью подхода, который я описал
Результаты обучения нейронной сети с помощью подхода, который я описал

Большую задачу, которую мы ставили в начале статьи — научить нейросеть искать лицо Арнольда на фото, мы не решили. Это связано с тем, что мы использовали маленький датасет, у нас была небольшая и простая по архитектуре нейросеть, мы не использовали специальные твики для обучения.

Мы рассмотрели общий подход к использованию библиотеки PyTorch, в частности С++ API, реализованный в LibTorch. Мы создали нейронную сеть и настроили конвейер обучения. Этот подход можно применять не только для простых моделей, но и для более сложных и масштабных решений.

В следующем блоке расскажу, как решить такую же задачу и получить более выразительный результат — нам понадобятся предтренированные сети.

Та же задача, но другое решение: используем предтренированную нейронную сеть

Описание сети

Чтобы решить задачу поиска лиц, мы можем использовать нейросети, ранее обученные другими компаниями или инженерами. Мы воспользуемся сетью Inception Resnet (V1) — это большая сеть, натренированная на большем объеме данных, который называется VGGFace2.

У нее другая архитектура, она намного сложнее ранее использованной сети. Убедитесь сами:

На этой схеме представлена самая верхняя структура этой сети. Каждый такой блок — еще одна нейронная сеть, они связаны друг с другом последовательно.
На этой схеме представлена самая верхняя структура этой сети. Каждый такой блок — еще одна нейронная сеть, они связаны друг с другом последовательно.
Здесь мы видим схему реализации блока верхнего уровня Stem. Он состоит из набора сверток и пулинга, связанных последовательно.
Здесь мы видим схему реализации блока верхнего уровня Stem. Он состоит из набора сверток и пулинга, связанных последовательно.
Это схемы блоков верхнего уровня Inception. Они представлены уже более сложной структурой с параллельным (skip-connection) прохождением данных в сети.
Это схемы блоков верхнего уровня Inception. Они представлены уже более сложной структурой с параллельным (skip-connection) прохождением данных в сети.
Это схемы Reduction блоков верхнего уровня. Они также представлены сложной структурой с разными путями прохождения данных.
Это схемы Reduction блоков верхнего уровня. Они также представлены сложной структурой с разными путями прохождения данных.

Как использовать предтренированную сеть

Для использования этой нейронной сети сначала нам необходимо обратиться к Python. Мы экспортируем сеть в формат, доступный для использования в C++. Для этого можем создать объект типа InceptionResnetV1 в Python, передавая в конструктор дополнительные параметры, такие как имя датасета, на котором сеть была обучена. Библиотека предоставляет различные варианты инициализации сети в зависимости от использованного датасета. Мы также вызываем метод eval, чтобы переключить сеть в режим вывода, а затем создаем произвольный тензор, который будет использоваться как пример входных данных, как мы видели ранее в C++.

import torch
from facenet_pytorch import InceptionResnetV1
 
resnet = InceptionResnetV1(pretrained='vggface2').eval()
 
# Пример входных данных для трассировки
example = torch.rand(1, 3, 100, 100)
 
traced_script_module = torch.jit.trace(resnet, example)
 
traced_script_module.save("face_net.pt")

Тут важно только сохранить размерность. В коде мы видим 1, 3, 100, 100 — это значит, что создаются три канала размером 100х100 пикселей. Для экспорта воспользуемся трейсингом для нейронных сетей. Это механизм, который реализован в PyTorch. Передав на вход сети этот пример входных данных, механизм трейсинга последовательно сохранит все вызванные операции, которые происходили в нейронной сети: свертки, функции активации и так далее. Результат трейса можно сохранить в файл, который можно будет загрузить как в C++, так и в Python.

Загрузка в C++ делается достаточно просто. Функция load, которую предоставляет нам заголовочный файл script.h, будет находиться в пространстве имен torch::jit::script. Как результат мы получим объект типа jit::script::Module, который похож по функциональности на модули из PyTorch. Знакомым способом мы можем его перевести на GPU с помощью функции to.

#include <torch/script.h>
...
using namespace torch::jit::script;
...
Module script_model_ = load(model_path_str);
script_model_.to(kGPU);

Как его дальше использовать? Загрузив этот модуль, нам необходимо подать ему на вход наше изображение, чтобы получить характеристический вектор для сравнения. Рассмотрим реализацию функции get_embeddigs с использованием загруженного модуля сети.

embeddigs_t get_embeddings(matrix_t& face_img) {
  auto sch_face_tensor = matrix_to_tensor(face_img);
  auto face_tensor =
   	torch::cat({sch_face_tensor,
               	sch_face_tensor,
               	sch_face_tensor},
              	0);
  face_tensor.unsqueeze_(0);
  face_tensor = face_tensor.to(device);
  std::vector<torch::jit::IValue> inputs = {face_tensor};
  auto output = script_model_.forward(inputs).toTensor();
  ...
}

Функцию matrix_to_tensor мы разбирали, она преобразует матрицу Dlib в тензор библиотеки PyTorch. Далее воспользуемся функцией конкатенации, чтобы повторить тензор три раза.

Загруженная сеть обучалась на цветных изображениях. При анализе примера для трассировки мы создавали случайный тензор с тремя каналами — формат RGB. Поэтому, объединив три серых канала, мы превращаем их в с-формат. Для реального проекта нам следует переписать функциональность загрузки и предобработки изображений для использования RGB.

С помощью функции unsqueeze мы добавляем дополнительную размерность для батча. Эта сеть предназначена для работы не только с одной картинкой, но и с батчем изображений. Расчет характеристических векторов нескольких изображений одновременно повышает эффективность использования ресурсов.

После получения RGB-тензора face_tensor мы преобразуем его в значение torch::jit::IValue. Это соглашение фреймворка для трассировки в PyTorch. Передача этого значения в метод forward загруженного модуля — стандартный подход. Метод вернет объект типа torch::jit::IValue, который при необходимости можно преобразовать в тензор PyTorch и другие типы данных.

Результаты использования предтренированной сети

Применив уже тренированную глубокую нейронную сеть, мы увидим другие результаты. На этой фотографии мы видим, что сравнив Арнольда с Арнольдом, мы получаем значение порядка 0,6, для других двух лиц это значение уже больше единицы.

Результаты обучения предтренированной сети: значение для лица Аронольда — 0,6
Результаты обучения предтренированной сети: значение для лица Аронольда — 0,6

На следующей фотографии мы видим, что при сравнении характеристических векторов для людей, не похожих на Арнольда, мы получаем значение порядка единицы или выше. Вот этот подход уже можно использовать для сравнения лиц. Задав порог в 0,7, сеть может отличить Арнольда от лиц других людей.

Результаты сравнения целевого лица с остальными показали, что сеть сможет отличить Арнольда от других людей, если задать порог в 0,7
Результаты сравнения целевого лица с остальными показали, что сеть сможет отличить Арнольда от других людей, если задать порог в 0,7

Писать или не писать нейронную сеть на С++

Мое мнение — конечно, писать. В первую очередь я думаю о командах, которые хотят решать задачи, связанные с машинным обучением, но не имеют в штате Python-разработчика. Для них есть альтернатива. Еще мой способ может быть полезным для тех, кто уже написал код работы с данными на С++ и хочет использовать его в реализации или обучении нейросети — таким инженерам не придется переписывать код на Python или писать обертки.

Неважно, на каком языке решается задача — она в любом случае довольно сложная. Инженеры до сих пор проводят исследования и ищут лучшее решение для тренировки нейронных сетей и решения задач по поиску лиц. Кто знает — возможно, это будет С++.

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  • 07.09.23 16:24 CherryTeam

    Cherry Team atlyginimų skaičiavimo programa yra labai naudingas įrankis įmonėms, kai reikia efektyviai valdyti ir skaičiuoti darbuotojų atlyginimus. Ši programinė įranga, turinti išsamias funkcijas ir patogią naudotojo sąsają, suteikia daug privalumų, kurie padeda supaprastinti darbo užmokesčio skaičiavimo procesus ir pagerinti finansų valdymą. Štai keletas pagrindinių priežasčių, kodėl Cherry Team atlyginimų skaičiavimo programa yra naudinga įmonėms: Automatizuoti ir tikslūs skaičiavimai: Atlyginimų skaičiavimai rankiniu būdu gali būti klaidingi ir reikalauti daug laiko. Programinė įranga Cherry Team automatizuoja visą atlyginimų skaičiavimo procesą, todėl nebereikia atlikti skaičiavimų rankiniu būdu ir sumažėja klaidų rizika. Tiksliai apskaičiuodama atlyginimus, įskaitant tokius veiksnius, kaip pagrindinis atlyginimas, viršvalandžiai, premijos, išskaitos ir mokesčiai, programa užtikrina tikslius ir be klaidų darbo užmokesčio skaičiavimo rezultatus. Sutaupoma laiko ir išlaidų: Darbo užmokesčio valdymas gali būti daug darbo jėgos reikalaujanti užduotis, reikalaujanti daug laiko ir išteklių. Programa Cherry Team supaprastina ir pagreitina darbo užmokesčio skaičiavimo procesą, nes automatizuoja skaičiavimus, generuoja darbo užmokesčio žiniaraščius ir tvarko išskaičiuojamus mokesčius. Šis automatizavimas padeda įmonėms sutaupyti daug laiko ir pastangų, todėl žmogiškųjų išteklių ir finansų komandos gali sutelkti dėmesį į strategiškai svarbesnę veiklą. Be to, racionalizuodamos darbo užmokesčio operacijas, įmonės gali sumažinti administracines išlaidas, susijusias su rankiniu darbo užmokesčio tvarkymu. Mokesčių ir darbo teisės aktų laikymasis: Įmonėms labai svarbu laikytis mokesčių ir darbo teisės aktų, kad išvengtų baudų ir teisinių problemų. Programinė įranga Cherry Team seka besikeičiančius mokesčių įstatymus ir darbo reglamentus, užtikrindama tikslius skaičiavimus ir teisinių reikalavimų laikymąsi. Programa gali dirbti su sudėtingais mokesčių scenarijais, pavyzdžiui, keliomis mokesčių grupėmis ir įvairių rūšių atskaitymais, todėl užtikrina atitiktį reikalavimams ir kartu sumažina klaidų riziką. Ataskaitų rengimas ir analizė: Programa Cherry Team siūlo patikimas ataskaitų teikimo ir analizės galimybes, suteikiančias įmonėms vertingų įžvalgų apie darbo užmokesčio duomenis. Ji gali generuoti ataskaitas apie įvairius aspektus, pavyzdžiui, darbo užmokesčio paskirstymą, išskaičiuojamus mokesčius ir darbo sąnaudas. Šios ataskaitos leidžia įmonėms analizuoti darbo užmokesčio tendencijas, nustatyti tobulintinas sritis ir priimti pagrįstus finansinius sprendimus. Pasinaudodamos duomenimis pagrįstomis įžvalgomis, įmonės gali optimizuoti savo darbo užmokesčio strategijas ir veiksmingai kontroliuoti išlaidas. Integracija su kitomis sistemomis: Cherry Team programinė įranga dažnai sklandžiai integruojama su kitomis personalo ir apskaitos sistemomis. Tokia integracija leidžia automatiškai perkelti atitinkamus duomenis, pavyzdžiui, informaciją apie darbuotojus ir finansinius įrašus, todėl nebereikia dubliuoti duomenų. Supaprastintas duomenų srautas tarp sistemų padidina bendrą efektyvumą ir sumažina duomenų klaidų ar neatitikimų riziką. Cherry Team atlyginimų apskaičiavimo programa įmonėms teikia didelę naudą - automatiniai ir tikslūs skaičiavimai, laiko ir sąnaudų taupymas, atitiktis mokesčių ir darbo teisės aktų reikalavimams, ataskaitų teikimo ir analizės galimybės bei integracija su kitomis sistemomis. Naudodamos šią programinę įrangą įmonės gali supaprastinti darbo užmokesčio skaičiavimo procesus, užtikrinti tikslumą ir atitiktį reikalavimams, padidinti darbuotojų pasitenkinimą ir gauti vertingų įžvalgų apie savo finansinius duomenis. Programa Cherry Team pasirodo esanti nepakeičiamas įrankis įmonėms, siekiančioms efektyviai ir veiksmingai valdyti darbo užmokestį. https://cherryteam.lt/lt/

  • 08.10.23 01:30 davec8080

    The "Shibarium for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH. The Plot Thickens. Someone posted the actual transactions!!!! https://bscscan.com/tx/0xa846ea0367c89c3f0bbfcc221cceea4c90d8f56ead2eb479d4cee41c75e02c97 It seems the article is true!!!! And it's also FUD. Let me explain. Check this link: https://bscscan.com/token/0x5a752c9fe3520522ea88f37a41c3ddd97c022c2f So there really is a "Shibarium" token. And somebody did a rug pull with it. CONFIRMED. But the "Shibarium" token for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH.

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  • 26.11.24 21:59 [email protected]

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  • 27.11.24 00:39 [email protected]

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  • 27.11.24 09:10 Michal Novotny

    The biggest issue with cryptocurrency is that it is unregulated, wh ich is why different people can come up with different fake stories all the time, and it is unfortunate that platforms like Facebook and others only care about the money they make from them through ads. I saw an ad on Facebook for Cointiger and fell into the scam, losing over $30,000. I reported it to Facebook, but they did nothing until I discovered deftrecoup . c o m from a crypto community; they retrieved approximately 95% of the total amount I lost.

  • 01.12.24 17:21 KollanderMurdasanu

    REACH OUT TO THEM WhatsApp + 156 172 63 697 Telegram (@)Techcyberforc We were in quite a bit of distress. The thrill of our crypto investments, which had once sparked excitement in our lives, was slowly turning into anxiety when my husband pointed out unusual withdrawal issues. At first, we brushed it off as minor glitches, but the situation escalated when we found ourselves facing login re-validation requests that essentially locked us out of our crypto wallet—despite entering the correct credentials. Frustrated and anxious, we sought advice from a few friends, only to hit a wall of uncertainty. Turning to the vast expanse of the internet felt daunting, but in doing so, we stumbled upon TECH CYBER FORCE RECOVERY. I approached them with a mix of skepticism and hope; after all, my understanding of these technical matters was quite limited. Yet, from our very first interaction, it was clear that they were the experts we desperately needed. They walked us through the intricacies of the recovery process, patiently explaining each mechanism—even if some of it went over my head, their reassurance was calming. Our responsibility was simple: to provide the correct information to prove our ownership of the crypto account, and thankfully, we remained on point in our responses. in a timely fashion, TECH CYBER FORCE RECOVERY delivered on their promises, addressing all our withdrawal and access issues exactly when they said they would. The relief we felt was immense, and the integrity they displayed made me confident in fully recommending their services. If you ever find yourself in a similar predicament with your crypto investments, I wholeheartedly suggest reaching out to them. You can connect with TECH CYBER FORCE RECOVERY through their contact details for assistance and valuable guidance. Remember, hope is only a reach away!

  • 02.12.24 23:02 ytre89

    Online crypto investment can seem like a promising opportunity, but it's crucial to recognize that there are no guarantees. My experience serves as a stark reminder of this reality. I was drawn in by the allure of high returns and the persuasive marketing tactics employed by various brokers. Their polished presentations and testimonials made it seem easy to profit from cryptocurrency trading. Everything appeared to be legitimate. I received enticing messages about the potential for substantial gains, and the brokers seemed knowledgeable and professional. Driven by excitement and the fear of missing out, I invested a significant amount of my savings. The promise of quick profits overshadowed the red flags I should have noticed. I trusted these brokers without conducting proper research, which was a major mistake. As time went on, I realized that the promised returns were nothing but illusions. My attempts to withdraw funds were met with endless excuses and delays. It became painfully clear that I had fallen victim. The reality hit hard: my hard-earned money was gone, I lost my peace of mind and sanity. In my desperation, I sought help from a company called DEFTRECOUP. That was the turning point for me as I had a good conversation and eventually filed a complaint via DEFTRECOUP COM. They were quite delicate and ensured I got out of the most difficult situation of my life in one piece.

  • 04.12.24 22:24 andreygagloev

    When I first heard about Bitcoin back in 2018, I was skeptical. The idea of a decentralized, digital currency seemed too good to be true. But I was intrigued as I learned more about the technology behind it and its potential. I started small, investing just a few hundred dollars, dipping my toes into the cryptocurrency waters. At first, it was exhilarating to watch the value of my investment grow exponentially. I felt like I was part of the future, an early adopter of this revolutionary new asset. But that euphoria was short-lived. One day, I logged into my digital wallet only to find it empty - my Bitcoin had vanished without a trace. It turned out that the online exchange I had trusted had been hacked, and my funds were stolen. I was devastated, both financially and emotionally. All the potential I had seen in Bitcoin was tainted by the harsh reality that with decentralization came a lack of regulation and oversight. My hard-earned money was gone, lost to the ether of the digital world. This experience taught me a painful lesson about the price of trust in the uncharted territory of cryptocurrency. While the technology holds incredible promise, the risks can be catastrophic if you don't approach it with extreme caution. My Bitcoin investment gamble had failed, and I was left to pick up the pieces, wiser but poorer for having placed my faith in the wrong hands. My sincere appreciation goes to MUYERN TRUST HACKER. You are my hero in recovering my lost funds. Send a direct m a i l ( muyerntrusted ( @ ) mail-me ( . )c o m ) or message on whats app : + 1 ( 4-4-0 ) ( 3 -3 -5 ) ( 0-2-0-5 )

  • 12.12.24 00:35 amandagregory

    HOW TO HIRE A HACKER TO RECOVER STOLEN BITCOIN WITH FASTFUND RECOVERY

  • 12.12.24 00:35 amandagregory

    HOW TO HIRE A HACKER TO RECOVER STOLEN BITCOIN WITH FASTFUND RECOVERY... A few months ago, I made a huge mistake. I invested in what seemed like a legitimate crypto opportunity, only to find out I’d been scammed. I lost a significant amount of money, and the scam platform vanished overnight. I felt completely lost.I had heard of Fastfund Recovery and decided to reach out, even though I was skeptical. From the first conversation, they made me feel heard and understood. They explained the recovery process clearly and kept me updated every step of the way.Within weeks, Fastfund Recovery successfully to recovered my lost funds—something I honestly didn’t think was possible. Their team was professional, transparent, and genuinely caring. I can’t thank them enough for turning a nightmare into a hopeful outcome. If you’re in a similar situation, don’t hesitate to contact them. They truly deliver on their promises. Gmail::: fastfundrecovery8(@)gmail com .....Whatsapp ::: 1::807::::500::::7554

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  • 27.12.24 00:21 swiftdream

    I lost about $475,000.00 USD to a fake cryptocurrency trading platform a few weeks back after I got lured into the trading platform with the intent of earning a 15% profit daily trading on the platform. It was a hell of a time for me as I could hardly pay my bills and got me ruined financially. I had to confide in a close friend of mine who then introduced me to this crypto recovery team with the best recovery SWIFTDREAM i contacted them and they were able to completely recover my stolen digital assets with ease. Their service was superb, and my problems were solved in swift action, It only took them 48 hours to investigate and track down those scammers and my funds were returned to me. I strongly recommend this team to anyone going through a similar situation with their investment or fund theft to look up this team for the best appropriate solution to avoid losing huge funds to these scammers. Send complaint to Email: info [email protected]

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  • 04.01.25 04:56 florencestella

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  • 18.01.25 12:41 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] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected]

  • 18.01.25 12:41 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] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected]

  • 20.01.25 15:39 patricialovick86

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  • 22.01.25 21:43 DoraJaimes23

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

  • 23.01.25 02:36 [email protected]

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

  • 23.01.25 02:37 [email protected]

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

  • 23.01.25 14:20 nellymargaret

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  • 26.01.25 03:54 [email protected]

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

  • 28.01.25 21:48 [email protected]

    It’s unfortunate that many people have become victims of scams, and some are facing challenges accessing their Bitcoin wallets. However, there's excellent news! With Chris Wang, you can count on top-notch service that guarantees results in hacking. We have successfully helped both individuals and organizations recover lost files, passwords, funds, and more. If you need assistance, don’t hesitate—check out recoverypro247 on Google Mail! What specific methods does Chris Wang use to recover lost funds and passwords? Are there any guarantees regarding the success rate of the recovery services offered? What are the initial steps to begin the recovery process with recoverypro247? this things i tend to ask

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