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Н Новости

Математика прекрасного. Как создать красивую картинку, если ты дилетант, художник или нейросеть?

Привет, Хабр, я Павел Бузин, работаю аналитиком в компании Cloud.ru и занимаюсь решением задач, требующих применения различных математических методов, в том числе используемых для машинного обучения.

С появлением нейронных сетей почти каждый может попробовать себя в роли художника или дизайнера. Уверен, что будет неплохо максимально простым языком рассказать, каких правил стоит придерживаться, чтобы ваши работы получались на профессиональном уровне. В основе этих правил лежат закономерности, которые описаны на языке математики. Надеюсь, что понимание сути методов поможет вам найти новые и интересные дизайнерские решения.

В этой статье обсудим общие закономерности, так что если вы дизайнер, промпт-инженер или просто неравнодушны к прекрасному, вас ждет путешествие от Древней Греции до современных компьютеров с CAD и генеративными моделями. Математики и технари, добро пожаловать под кат, здесь вы будете чувствовать себя как дома. Гуманитарии, не пугайтесь, всё будет страшно только на первый взгляд.

5172234667eb4387e4de8c638c02468d.png

Это база

Создавая красивый кадр, картину или макет, профессиональные фотографы, художники и дизайнеры пользуются правилами композиции, которые имеют в своей основе красивые закономерности, описываемые простыми формулами. Кто-то делает это осознанно, кто-то просто мотивирует свой выбор «Ну так же красивее!». Давайте взглянем, что это за правила делают композицию гармоничной и какие формулы их описывают.

Правило третей

Первое правило композиции, с которого начинаются уроки в любой художке — никому не рассказывай о композиции делим план изображения на девять равных частей параллельными линиями, двумя вертикальными и двумя горизонтальными. Важные элементы изображения располагаем вдоль этих линий или на их пересечениях. Это правило настолько популярно и хорошо работает, что линии сетки есть даже у камер в сотовых телефонах.

Источник: https://habrastorage.org/r/w1560/getpro/habr/upload_files/ef2/295/b51/ef2295b5125d5608771549c17802ce9e.jpg

Правило третей является эмпирическим, то есть сформулированным по результатам человеческого опыта. Его создание приписывают английскому художнику 18 века Джошуа Рейнольдсу. И хотя в основе этого метода нет сложных обоснований, в правиле третей появляются соотношения 1:2 и 2:3 — а это первые числа последовательности Фибоначчи. Кстати о ней…

Золотое сечение и числа Фибоначчи

Золотое сечение — это такое деление отрезка, при котором отношение большей части к меньшей равно отношению всей длины отрезка к его большей части. Мы можем записать это следующим образом. Мы делим отрезок длины c на части длиной a и b. Тогда a и b будут связаны соотношением:

57eb585ae6f41cfa9f572801ea904706.png

Отношение a к b является решением квадратного уравнения вида x^2 – x -1 = 0. Положительное решение, получившее название «Золотое число» и обозначение Φ (буква древнегреческого алфавита, читается как «фи»).

Обратное число, обозначаемое строчной буквой 𝜑, имеет интересное свойство

41e4864e9ed76d3cac604b97c4831879.png3b1273efe3a9c260e083007e94c64d84.pngeb6e2bb31259cafb3d8efcd8659c7c94.png

На практике это выглядит так, что объект сохраняет гармоничные пропорции и «на боку».

ff04dfd8ad42717baac274d1a8b8775f.jpeg

Золотое сечение было известно и активно применялось строителями уже в Древней Греции. Спустя много сотен лет в 12 веке Леонардо Пизанский, также известный под именем Фибоначчи, изучал большое количество практических задач, которые в дальнейшем легли в основу теории чисел и исследования рядов.

Фибоначчи исследовал последовательность чисел, формируемых по следующим правилам:

  • первые два числа последовательности — это 0 и 1,

  • каждое следующее число последовательности образуется сложением двух предыдущих чисел.

Эта последовательность знакома очень многим, ее значения — 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, и т. д.

У чисел Фибоначчи много интересных свойств. Например, если сложить друг с другом квадраты со сторонами, равными числам Фибоначчи, они образуют спираль:

Источник: https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.zimerka.ru%2Fpage%2Fustroystva-aktualizatsii-bytiya%3Flang%3Dru&psig=AOvVaw3Guqr7SIVKVXgN846vnKIT&ust=1723734139581000&source=images&cd=vfe&opi=89978449&ved=0CBcQjhxqFwoTCLiw0Jrg9IcDFQAAAAAdAAAAABAQ

Давайте сразу расставим точки над i: золотое сечение и последовательность Фибоначчи — не одно и то же. А они как-то связаны?! Да, вот так: золотое сечение — это специфическое иррациональное число с уникальными свойствами пропорций, в то время как числа Фибоначчи — это бесконечная последовательность целых чисел, которые через свое соотношение приближаются к этому числу, но все-таки не равны ему.

Но поскольку разница эта скорее математическая, чем визуальная, оба понятия активно применяются в архитектуре, поскольку такие пропорции не просто приятны человеческому глазу, но еще и прочны и эффективны при строительстве, подтверждением чему являются сохранившиеся памятники древности.

Источник: https://www.google.com/url?sa=i&url=https%3A%2F%2Fdzen.ru%2Fa%2FXwTBGFKQgFj6vSzv&psig=AOvVaw2XCF0OyOHZC7QBkLB3gb8d&ust=1723736346613000&source=images&cd=vfe&opi=89978449&ved=0CBcQjhxqFwoTCIj7wbjo9IcDFQAAAAAdAAAAABAY

Немного элегантной математики

Теперь, когда основы позади, перейдем к более хардкорным вещам, которые лежат в основе современных систем автоматизированного проектирования. Каждый дизайнер, архитектор, 3D-художник использует их в своей практике, иногда даже сам того не подозревая.

Гладкие функции и поверхности

Гладкие кривые и поверхности являются важной частью окружающего нас комфорта — посмотрите на ваши мышку и iPhone.

Чтобы понять, что такое гладкость с математической точки зрения и каким законам подчиняется гармония гладкости, нам придется обратиться либо к функции одного аргумента на плоскости (привычная нам со школы кривая осях х и y), либо к функции нескольких аргументов, которые задают поверхность в пространстве.

Итак, функцию называют гладкой k-порядка если, сама функция и k ее производных являются непрерывными. Если рука гуманитария на этой строчке потянулась за пистолетом валокардином, спокойно, я сейчас всё объясню! Вы точно помните, как выглядит график линейной функции, вот так:

b8edd719152e8a9a4ea0e804a4dc280e.png

Производная функции — это то, насколько круто (с какой скоростью) меняется функция в любой конкретной точке. Для прямой этот показатель будет одинаковым в любой точке графика и будет равен угловому коэффициенту — k. А теперь давайте усложним задачу и возьмем любую кривую, как определить, гладкая она или нет?

e53a6c3f4384324adfbee0107fa3af09.png

Проверить, можно ли взять производную от ее производной в любой точке графика. С графиком слева, например, этот фокус не пройдет по очевидной причине — он не является непрерывным в точке 0. А вот с правой вполне прокатит. Если получилось так сделать один раз — это будет гладкая кривая 1-го порядка. Если можно брать производную от производной в любой точке графика, а потом от нее еще k раз (дифференцировать) — гладкой кривой k-порядка.

На практике человек очень плохо различает разрывы третьей и последующих производных: это относится и к визуальному, и к тактильному восприятию. Но при этом человек очень хорошо различает линии и поверхности разной кривизны. Короче, чтобы понять насколько гладкая ваша кривая, посмотрите на нее, если она примерно как на правой картинке выше — она гладкая, а если как на левой — она только притворяется и ее неплохо бы побрить. Ну или нет. Тут зависит от того, гармонии или дисгармонии вы хотите добиться. В общем, если кривые в вашем творении такой формы, что от них можно взять производную и не раз, а два или даже три — будьте уверены, вы создали шедевр.

О производных наглядно от пользователей Pikabu
О производных наглядно от пользователей Pikabu

Кстати, о кривизне. Математическое понятие кривизны ввел Эйлер в 18 веке. Кривизна определяется в каждой конкретной точке и вычисляется как величина, обратная радиусу окружности, касающейся этой кривой k = 1/R. В общем случае методы вычисления радиуса окружности требуют применения методов дифференциального исчисления, но можно ограничиться приближением, как показано на рисунке.

edf368e3829dbc97b5bb38a098c7290e.png

Сказанное выше справедливо для плоскости, а для поверхности в трехмерном пространстве радиусы будут определяться в двух перпендикулярных плоскостях.

Для наших целей применения в 3D-графике и дизайне важно одно: если поверхность будет «накрывать» одну сферу, мы получим фигуру типа половинки яйца (эллиптический параболоид), а если «накроет» сразу две сферы — получится седло (гиперболический параболоид).

Какими бывают кривые поверхности. Источник: https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%B2%D1%82%D0%BE%D1%80%D0%BE%D0%B3%D0%BE_%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%B0
Какими бывают кривые поверхности. Источник: https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%B2%D1%82%D0%BE%D1%80%D0%BE%D0%B3%D0%BE_%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%B0

Кстати, плоскость у нас определяется как гладкая поверхность нулевой кривизны. А теперь достаем двойные листочки и описываем функцию, задающую такую фигуру:

659607a09f61f31dedfe72fd44580d54.png

Ладно-ладно, я пошутил! Но я не просто так вспомнил слона Экзюпери: как раз для того чтобы описывать такие сложные кривые и поверхности, существует такое математическое ухищрение как кусочно-определяемая функция. Это когда, чтобы описать сложную форму, мы берем эту дольку от ежа (красивой, гладкой гиперболы), эту дольку от чижа (элегантной параболы), а в месте их стыка просто обеспечиваем непрерывность.

Это как если бы у нас было много фотографий совершенно идеальных женщин и мы пытались бы из отдельных их частей собрать фоторобот вашей новой знакомой: брови как у Анджелины Джоли, улыбка Киры Найтли. Вот этот кусочек фотки условного идеала (непрерывной функции), взятый от одного места стыка до другого называется сплайном.

3be3bb228b7868b3b0b68e7a1807a9c1.png

Кривые и поверхности Безье

Чего общего у автомобиля Citroën DS, Adobe Photoshop и CSS-анимации? Да, они: кривые Безье.

До того как все телевизоры стали плоскими, а автомобили начали выпускаться на единых платформах, французская компания Citroën выпускала Citroën DS. На этом чуде инженерной мысли катались президент Де Голль, Фантомас и менталист Патрик Джейн. Даже спустя почти 70 лет этот дизайн не оставляет равнодушным.

Очевидно, дело в красивых изгибах корпуса. Но как эти изгибы создавались, если никаких систем автоматизированного проектирования и тем более 3D-моделирования тогда и в помине не было? Придется начать эту историю издалека…

c8bce25f008ee95f28fed7eafcfd6e23.jpeg

Полиномы Бернштейна

В далеком 1912 году российский и советский математик Сергей Бернштейн изучал полиномы, которые в общем виде задаются следующими формулами:

deb267c926d97dac842d52ae39927d1f.png3a0043f4315e2331cf689401f1e69c40.png

В данном случае является биномиальным коэффициентом.

Что это за набор букв такой? Объясняю.

Представим, что у нас есть какая-то особенно хитровыдуманная кривая (поезд), которую нам нужно повторить. Чтобы ее повторить, нам нужно математически описать форму, но нет простой единой формулы, которая позволяет это сделать. Тогда мы разбираем кривую на «запчасти», каждая из которых описывается суммами отдельных многочленов Бернштейна (тележки, колесные пары, рессоры, сцепки, платформы, крепеж). В этом случае мы можем собрать кривую (поезд) очень или не очень похожую на интересующую нас модель.

У полиномов есть замечательное свойство: они все гладкие и непрерывные (как в предыдущей части статьи). Это значит, если мы зададим в пространстве n опорных точек P0, P1, … Pn, повторяющих исходную кривую, у нас будет возможность подобрать такую совокупность кривых, которая гармонично будет проходить через все интересующие нас точки.

Вот, например, вам очень хочется сникерс. Можно купить молочный шоколад, арахис, сварить нугу, карамель и замутить собственный батончик очень похожий на сникерс. Или можно взять спортивный протеин, намешать из него что-то, добавить орехов, покрыть шоколадом. Получится отдаленно похоже, только радости калорий будет меньше. Вот с полиномами Бернштейна примерно так же.

Вот некоторые базовые «запчасти», из которых можно собрать подавляющее большинство кривых:

6387b1aac3de4243816552f2aefa2b36.png

Вижу в ваших глазах немой вопрос: причем тут Citroën DS? А притом, что во второй половине 50-х математик из компании Citroën Поль де Кастельжо изобрел алгоритм построения кривых, где полиномы Бернштейна играют ключевую роль. Но поскольку разработки де Кастельжо защищались коммерческой тайной, более широкую известность этот алгоритм получил под именем другого француза — Пьера Безье. Безье работал на конкурирующий Renault и сумел первым опубликовать свои труды. Давайте разберемся, что это был за алгоритм такой?

Мы все со школьных времен привыкли записывать функции в виде y = f(x). Но при такой форме записи сложно нарисовать многозначные кривые, даже простую окружность. Для этого придется воспользоваться уравнением x2 + y2 = R2. Или y = √(R2 – x2) (верхняя половина) и y = -√(R2 – x2) (нижняя половина).

Но если мы введем третью переменную t, которая будет меняться от 0 до 1, то мы сможем записать наше уравнение в более лаконичном и приятном виде:

6cba11118395f6d084781fec95a44480.png

Теперь применим параметрическую запись к многочленам Бернштейна на плоскости.

Вернемся к написанию координат в виде x1, x2, …, xm для того чтобы в дальнейшем нам было легко масштабировать наши вычисления на трехмерное и многомерное пространства.

Тогда каждая нужная нам кривая будет задаваться как множество точек B(t), координаты x1 и x2, которых удовлетворяют условиям:

786a9ebddf1d6d5e4f3c2ab9437a60e2.png

или в общем виде:

ae651a889662f6b82707354e7786badc.png

Вот примерно по такой формуле все графические редакторы мира рисуют кривые Безье. У меня, к сожалению, не было возможности подглядеть исходный код таких программ как MS Paint, Adobe Illustrator, CorelDraw и GIMP, но по всем признакам для построения криволинейных форм там используются кривые, составленные из кусочков кубических кривых Безье (сплайны кривых Безье).

Если ни разу не доводилось с ними работать, давайте попрактикуемся. Зададим наши точки P0 и P3 (эти точки P называют опорными точками) в виде векторов, т. е. P0 болд = (x0, y0), а P3 болд = (x3, y3). Аналогично и для других опорных точек. Мы возьмем 4 точки с номерами 0, 1, 2 и 3, для иллюстрации этого достаточно, но желающие могут взять и больше:

89766831e85e8f21ced3f5149ccbed6b.png

Следом добавим точку P1, визуально проведя перпендикулярные прямые вниз от точки P1 и вправо от точки P0:

0467e247e7641e832afb1b5ce3363d21.png

Теперь через точки P0 и P3 проведем 2 прямые так, чтобы они пересекались под углом 90°, и на этом пересечении добавим точку P2:

46bcee48576ddf18d32b67b93b4c84e0.png

Итого у нас получится S-образная кривая на плоскости, построенная с помощью 2 контрольных точек и 2 опорных. В данном случае точки будут расположены на углах квадрата:

b40f704c8b8cdeb3c37f3f81e4b16136.png

Но создавать кривые Безье можно не только на плоскости, но и в пространстве! Если точки P0 и P3 не лежат в одной плоскости, мы получим такое изображение:

Источник: https://youtu.be/_4_GNXiXETM?t=1194

Кривая Безье для одной точки P0 есть сама точка P0

Если n=1, то двум точкам P0 и P1 соответствует отрезок, соединяющий эти точки. Кривая задается уравнением

5a333dc138d063a0c2f14d6f4bbf3c9f.png

и называется линейной кривой Безье.

Квадратичная кривая Безье для n = 2 задается тремя опорными точками: P0, P1 и P2.

Иллюстрация квадратичной кривой Безье
Иллюстрация квадратичной кривой Безье

Кубическая кривая Безье задается параметрическим уравнением:

86ca781522e2f4d075e92d976f1f015b.png

При этом точки P1 и P2 могут быть в одной плоскости с P0 и P3, так и в разных плоскостях, что позволяет строить трехмерные объемные кривые.

Пример кубической кривой Безье приведен выше, а вот так иллюстрируется построение кривой Безье на анимации из вики:

79495852b936f76521dcb460ae55b453.pngИсточник: https://upload.wikimedia.org/wikipedia/commons/d/db/B%C3%A9zier_3_big.gif
Источник: https://upload.wikimedia.org/wikipedia/commons/d/db/B%C3%A9zier_3_big.gif

Как видите, достижения математики находят широкое применение в дизайне, и этот процесс приобрел новые импульсы для развития после появления цифровой фотографии и компьютерной графики.

Анатомия генеративных моделей

Многие имели опыт работы с такими генеративными сетями как MidJourney, DALL-E, Kandinsky и другими. К сожалению, в силу достаточно высокой сложности применяемых методов и алгоритмов большинство пользователей вынуждены воспринимать эти сети как черный ящик. Попробую описать процесс их работы более понятно, а применение — более осмысленным для читателя. Основываться буду на документации и статьях разработчиков данных моделей, а также собственном опыте работы в проектах по машинному обучению. Давайте сначала коротко пробежимся по основополагающим понятиям.

Эмбеддинги, метрики, расстояния

Эмбеддинг в переводе с английского означает «встраивание». Так называют процесс (и результат) сопоставления интересующих нас объектов — слов, фраз, картинок с векторами, соответствующим этим объектам в многомерном пространстве.

Почему для сопоставления и генерации изображений и слов используются именно векторы? У них есть свойства, которые очень удобны для анализа таких сложных явлений, как естественные языки и визуальные образы:

  • близким понятиям соответствуют близкие векторы в многомерном пространстве, например «кошка» и «кот» будут где-то рядом;

  • с векторами легко производить математические операции, например, примерно (подчеркну: ПРИМЕРНО) выполняются следующие равенства: «нога + мяч = футбол», «конь - мужчина + женщина = лошадь»;

  • векторы — это направленные отрезки, мы всегда знаем, где у них начало, а где конец, соответственно, даже если некоторые «точки маршрута», через которые проходит вектор, повторяются, при анализе мы не спутаем «масть» и «месть», «карету» и «корыто» и даже омографы и омофоны будут представлены немного разными векторами;

  • поскольку мы имеем дело с векторами в многомерном пространстве, нам становится доступен анализ схожести и различия понятий по разным критериям: например, «маленький синий резиновый кубик» и «маленький желтый резиновый кубик» будут отличаться только в пространстве, определяющем яркость красного и синего цветов в RGB-палитре, а во всех остальных направлениях их векторы будут совпадать.

Вот несколько известных моделей, которые работают с эмбеддингами: Word2Vec, GloVe, BERT, GPT, CLIP.

Расстояние необходимо нам для численной оценки разницы между двумя векторами. Казалось бы: проведи прямую между двумя объектами и дело в шляпе. Но что делать, когда мы оперируем в n-мерном пространстве? Для таких случаев часто используют так называемое «манхэттенское расстояние» или «расстояние городских кварталов» — это расстояние между двумя точками, измеренное вдоль осей, расположенных под прямым углом друг к другу (как городские кварталы). Его вычисляют путем нахождения суммы абсолютных разностей соответствующих координат векторов. Так для векторов A = (x1, y1, z1) и B = (x2, y2, z2) манхэттенское расстояние рассчитывается так: |x1 - x2| + |y1 - y2| + |z1 - z2|.

7c0c51d130328f2d42ee066ce85def6c.png

Расстояние городских кварталов удобно в машинном обучении еще и потому, что менее подвержено погрешностям в многомерном пространстве. Приведу пример: вы смотрите телевизор в своей квартире: формально расстояние до соседа сверху и через стенку в эвклидовом пространстве между вами незначительно — 3 метра. Только, чтобы дойти до соседа сверху, вам понадобится пройти по коридору, выйти на лестницу, подняться на этаж выше и постучать в дверь. А сосед через стену может оказаться как ближе, так и дальше, в зависимости от того, живет он в вашем подъезде или в соседнем. Но если мы вообще не учитываем такое измерение как «подъезд», то вы и ваш сосед через стену для товарища сверху примерно одно и то же.

Есть у такого способа измерения расстояний и интересные свойства. Допустим, у нас есть два близких объекта A и B, между которыми расстояние R. С одной стороны очевидно, что они не равны друг другу. Но если мы немного увеличим расстояние между этими объектами (на небольшую величину r), в область между R и R+r попадет большое число не сильно связанных с ними объектов. В конце статьи расскажу, как это использовать.

Метрика тоже очень важная величина: она используется для измерения ошибки предсказания нашей модели в сравнении с желаемым результатом.

Обычно чем меньше значение метрики, тем лучше, но это не обязательно. Отметим, что одной из метрик является расстояние, о котором я уже рассказал выше.

Какие метрики мы можем использовать, чтобы сравнить два изображения, одно из которых является целевым?

Французский математик Рене Фреше (эх, любят же французы кривые!) предложил сравнивать сходство двух кривых A(t) и B(t) с помощью выражения:

87a69e012f35dfe9aba25734499b1d32.png

Дышите, понимаю, выглядит страшно. Смысл этого жуткого нагромождения скобок в следующем: мы берем все доступные нам точки на этих кривых A(t) и B(t), которые могут зависеть от набора параметров α и β соответственно, измеряем расстояние между этими точками для равных значений t, находим максимальное значение этого расстояния в зависимости от параметров α и β. Минимальное значение (нижняя граница) функции F(A(α), B(β)) и есть искомое расстояние. Короче, мы ищем минимум максимума.

Для наглядности давайте посмотрим на более приятном примере: например, человек гуляет с корги. Хозяин идет своим путем, обходя лужи, корж бодро трусит где-то рядом по своей собственной траектории и со своей скоростью. Путь каждого в отдельности — кривая, а расстоянием Фреше между ними будет минимальная длина поводка, которая потребуется, чтобы и пес, и хозяин, полностью прошли свой путь.

04d50986fb4f17e6243f22b68876f78f.png

Как расстояние Фреше поможет нам сравнить картинки? А вот как: представим, что у нас есть нейронная сеть-классификатор, которая определяет вероятности того, что изображено на нашей картинке. Обычно ответ выглядит так:

Собака – 25%

Волк – 15%

Лиса – 5%

Сова – 3%

Если мы пойдем дальше и вместо функций будем вычислять расстояние между вероятностями нашей и эталонной картинки и считать для них расстояние Фреше — мы получаем метрику Frechet inception distance (FID), что можно перевести как начальное расстояние по Фреше. Такой метод значительно эффективное попиксельного сравнения картинок, ведь если мы сфотографируем один и тот же объект с немного разных ракурсов, расстояние между пикселями изменится, а вот расстояние Фреше останется примерно тем же.

Такой метод оказался значительно эффективнее попиксельного сравнения картинок, который сразу выдает большую ошибку при небольших сдвигах и поворотах изображений и имеет и другие недостатки.

Проиллюстрируем это на примере.

Возьмем две последовательности A и B пикселей красного цвета, у которых меняется яркость. Одна последовательность отличается от другой только на 1 единицу яркости.

В цветовой гамме RGB (для простоты иллюстации мы выделяем только R) сдвиг на 1 пиксель выглядит так:

Иллюстрация почему сдвиг при попиксельном сравнении дает большую ошибку
Иллюстрация почему сдвиг при попиксельном сравнении дает большую ошибку

Значения яркости, приведенные в каждом пикселе и выделенные желтым, меняются в диапазоне от 0 до 255. В табличном виде это выглядит так:

d7b2dd28ec5e93bd81a3e50f6a317e39.png

Разница между A и B — 8.

Разница между A и B при сдвиге B на 1 пиксель — 236.

Расстояние Фреше между A и B при сдвиге на 1 пиксель (с округлением до целого) — 2.

Генерация: GAN против диффузии

Третий закон Кларка гласит, что любая достаточно развитая технология неотличима от магии. При первом появлении работа генеративных сетей воспринималась как настоящая магия. Но за этой магией стоят математические алгоритмы, понять работу которых сможет каждый.

Широкое распространение сегодня получили два метода генерации изображений: генеративные состязательные сети (GAN) и диффузионные модели. Результат их работы для пользователя очень похож, но технологии под капотом совершенно разные. Оба подхода могут генерировать высококачественные данные, но диффузионные модели часто показывают лучшее качество и большее разнообразие результатов, особенно в задачах, связанных с генерацией изображений.

GAN — это алгоритм который сталкивает 2 нейросети: одна из которых генерирует образцы чего-либо, а другая пытается установить их подлинность. Проще говоря, одна нейросеть изображает что-нибудь, а вторая кричит «не верю» до тех пор, пока предложения первой не станут похожи на что-то настоящее: портрет, пейзаж или дизайнерскую сумочку.

С диффузией же всё намного сложнее. Возможно, некоторые из читателей имели возможность наблюдать работу художников, особенно если они рисуют пейзажи на холсте. Художник наносит последовательно грунт, основу фона, контуры основных элементов, отрисовывает сначала крупные, а потом мелкие детали. Работа художника и процесс генерации изображения диффузионной моделью имеют очень много общего.

Представим, что у нас есть набор изображений.

Этап 1. Сделаем картинки для обучения моделей (таких картинок нужно много). Последовательно для каждой картинки будем проводить набор следующих операций:

  • добавим случайным образом немного пятен;

  • повторим процесс много раз до тех пор, пока от исходное изображение не пропадет совсем.

Компьютер позволяет нам очень быстро выделить разницу между картинками на каждом этапе и проделать тот же набор действий в обратном порядке. Провернем этот фарш назад — и картина будет словно появляться на холсте, пока пятна последовательно исчезают. Эти искажения, которые добавляют на картинки называются шумом (noise), а процесс их удаления — denoising.

Этап 2. Используем пары последовательно изменяемых картинок для обучения нейросети. Так как компьютер может сравнить два изображения с использованием метрик, о которых мы говорили ранее, и определить, какое изображение ближе к оригинальному, у нас появляется возможность последовательно отделять искажения от оригинального изображения как показано на рисунке ниже.

Источник: https://www.assemblyai.com/blog/minimagen-build-your-own-imagen-text-to-image-model/

Так как модель не знает, какое должно получиться восстановленное изображение, она использует специальные модули — сэмплеры, а помогают им промпты. В процессе восстановления сэмплер после каждого шага уточняет: картина на шаге n+1 больше похожа на промпт, нежели картинка на шаге n? И так шаг за шагом наша модель, словно художник, очень большим количеством мазков кистью рисует картину от крупных деталей к мелким. Эта часть, процесс восстановления изображения, получила название обратной диффузии (backward diffusion).

А теперь, собственно, магия: если машина может нарисовать обратно то, что есть, то может нарисовать и то, чего нет. Можно сгенерировать шум и шаг за шагом подсказывать, где нужно стереть шум, чтобы получить что-то похожее на то, что хочет пользователь.

Как думает модель?

Теперь у нас есть все необходимое, чтобы понять основные принципы работы генеративных нейронных сетей. Воспользуюсь материалами о модели, выложенными в репозитории.

Посмотрим на внутреннее устройство модели Kandinsky. Как и другие мультимодальные модели, Kandinsky умеет работать с текстом и изображениями, а с версии 3.0 — даже с видео.

Используя модель Kandinsky, мы можем создавать изображения на основе текстового описания сюжета, создавать изображения по мотивам других изображений и объединять сюжеты двух изображений в одно.

Kandinsky в разрезе
Kandinsky в разрезе

Как видно из иллюстрации, при каждом сценарии работы на первом этапе Kandinsky с помощью нейросети CLIP-ViT-G осуществляет преобразование изображений и текстов в эмбеддинги. На следующем шаге мы производим операции с эмбеддингами-векторами. При этом мы можем их не только складывать, но и вычитать. Это необходимо для исключения каких-либо нежелательных элементов в итоговом изображении, а сам процесс получил название negative prompting или «негативная подсказка».

На следующем этапе с помощью модели U-Net производится восстановление изображения, используя механизм диффузии и эмбеддинги как подсказки для кристаллизации.

На заключительном этапе модель MOVQ улучшает изображение.

«Ну и для чего я всё это прочитал?»

А теперь перейдем к итогам. Как повлиять на то, какой получится ваша картинка?

Если вы никогда не учились в художке и не читали книг по основам дизайна и композиции, чтобы сделать красивые фотографии или получить удачный опыт рисования картин, стоит учитывать базу: располагать значимые элементы на пересечении линий горизонтальных и вертикальных третей, а также руководствоваться пропорциями Фибоначчи при построении композиций, пространств или декора.

Если вы профессиональный художник, дизайнер или 3D-артист, то раздел про элегантную математику поможет вам понять, как менять радиусы закругления углов, где поставить опорные точки для получения нужной формы кривой и какие параметры поверхностей задавать для достижения нужного вам эффекта. Теперь, если вам нужно создать какой-нибудь предмет обтекаемых форм, вы сможете понять, насколько гармонична его гладкость: непритязательные могут на глазок прикинуть, не намешаны ли там гладкие кривые разного порядка, а дотошные возьмут производную и будут уверены наверняка.

Если вы создаете картинки с помощью нейросетей, помните, что самое главное — промпты-подсказки. В роли промптов могут выступать и текст, и базовые изображения. Тут я вам, конечно, Америку не открыл, но если вы не первый день знакомы с нейросетями, то наверняка знаете: в них всё очень быстро меняется, и конкретные слова, которые вчера давали один результат, послезавтра могут дать другой. Медленнее всего изменениям подвержен математический фундамент генеративных моделей, именно поэтому его понимание помогает стабильно воспроизводить желаемые результаты.

Как мы выяснили сегодня, то, какими именно будут промпты, и как они повлияют на результат, зависит от количества параметров (измерений) в модели, того, какие значения окажутся рядом с искомыми в многомерном пространстве, того, что получается при сложении значений и даже от…языка запроса! Ведь некоторые слова могут являться омографами или синонимами в одном языке, и не иметь таких свойств в другом, а, соответственно, их векторное представление для разных языков будет отличаться. Например, на заре разработки многих text-to-image моделей, когда цензурой еще не успели озаботиться, разработчики сетовали, что слишком много пользователей хотят генерить…синичек. Пары больших синичек, если вы понимаете о чем я.

Иногда синички — это просто синички
Иногда синички — это просто синички

Для закрепления материала давайте проиллюстрирую на примере запросов к нейросети Kandinsky, как меняется результат в зависимости от промпта. По запросу «голубое небо» он почти всегда (по крайней мере, по состоянию на июль 2024) генерирует небо над морем или полем с линией горизонта:

Результат по запросу «голубое небо»
Результат по запросу «голубое небо»

При этом по запросу «светло-голубое небо» всегда выдается небо без посторонних примесей:

Результат по запросу «светло-голубое небо»
Результат по запросу «светло-голубое небо»

Текстовых промптов можно задать несколько, перечислив их через запятую, например «черное море, звездное небо»:

Результат по запросу «черное море, звездное небо»
Результат по запросу «черное море, звездное небо»

Чтобы избежать попадания на картинку назойливых «соседей» по векторному пространству, о которых мы говорили в части про манхэттенское расстояние, можно использовать негативный промпт. Он предназначен для избегания появления указанных объектов на изображении. Пример: «черное море» + негативный промпт «звездное небо».

Так меняет картинку добавление негативного промпта «звездное небо»
Так меняет картинку добавление негативного промпта «звездное небо»

Опытные промпт-инженеры, конечно, уже знают про использование негативных промптов и прочий файн-тюнинг, но готов поспорить, немногие думали о том, почему это работает именно так с математической точки зрения.

Надеюсь, мне, как автору статьи, удалось доступно рассказать о сути математических методов, которые в том или ином виде используются всеми, кто рисует красивое. По крайней мере, я очень старался и буду рад вопросам и комментариям. Про отбор полученных результатов, файн-тюнинг, развертывание собственных сервисов генерации изображений и прочее, расскажу уже для тех, кто более углубленно работает с text-to-image моделями и как-нибудь в другой раз. Спасибо, что осилили столько букв!


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  • 14.09.25 12:44 robertalfred175

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    Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.

  • 19.09.25 15:27 tonykith01477

    There are not many reviews about free crypto recovery fixed but the ones that exist are mostly positive. I have no idea how that is possible, but it is clear that they are fabricated. However, there are also negative reviews – and I highly recommend paying attention to them. These are real people describing their unfortunate experiences with this scam. It’s the same story as always – fraudsters create a fake website to con people out of money. Nothing new but look no more and contact FASTRECOVERYAGENT These types of scams are everywhere. If you have already lost money to scammers i mean any type be it sending to scammers account , or if you have a case about stolen bitcoin , usdt, or any type of cryptocurrency whatsoever just reach out to www.fastrecoveryagent.com, i really owe this group of recovery expert because they saved me after bad investment with a fake broker, i literally owe them my life as they saved me from some bunch of scammers, but see how life is , i got every cent of my investment back with the profit , reach out to to them today and tell them from Mary because i promise them i will tell the whole world when the recovery is complete, and here i go after i got my recovered assets thats why im doing what i promised. do not fall for another scam. contact the,m today!!!!

  • 19.09.25 17:12 wendytaylor015

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

  • 19.09.25 17:12 wendytaylor015

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

  • 20.09.25 15:05 faithlawrence

    I can’t recommend Sylvester Bryant enough. He successfully recovered €210,000 in Ethereum for me after I had lost hope. His expertise in tracing and reclaiming funds from scams is truly remarkable. What stood out most was his calm, professional approach and deep technical knowledge, which gave me complete confidence throughout the process. If you’ve lost money to a scam, I strongly encourage you to reach out to him. You can contact him via email at [[email protected] ] or on WhatsApp at +1 512 577 7957. He is genuinely dedicated to helping people recover what they’ve lost, and his support has been invaluable to me.

  • 20.09.25 15:53 blessing1198

    It is distressing to lose USDT due to a bitcoin wallet hack. Although it is challenging, stolen USDT can be recovered. Taking prompt, wise action increases your chances. Marie can help you with reporting the theft, what to do right away, and USDT recovery. Contact her on WhatsApp at +1 7127594675, or email [email protected].

  • 21.09.25 12:05 star1121

    Consider this: In cryptocurrency, you see what appears to be a fantastic opportunity. After investing your hard-earned money, you see it disappear into the wallet of a con artist. Your bank account seems empty as rage and regret merge in this stomach punch. These days, cryptocurrency frauds are very common, however recovering your cryptocurrency from scammers is still possible. You can track down and possibly recover what you lost with shrewd actions. Marie can help; contact her at [email protected] and on WhatsApp at +1 7127594675.

  • 23.09.25 03:23 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

  • 23.09.25 03:23 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

  • 23.09.25 03:23 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

  • 23.09.25 03:54 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

  • 23.09.25 14:45 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 23.09.25 19:27 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.

  • 23.09.25 22:38 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 12:22 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.

  • 24.09.25 15:50 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 15:50 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 15:50 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 19:08 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 19:50 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 19:55 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 20:52 elizabethrush89

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

  • 24.09.25 20:52 elizabethrush89

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

  • 26.09.25 12:29 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider (recoveryfundprovider @ gmail. com WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.

  • 26.09.25 15:42 elizabethrush89

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

  • 26.09.25 15:42 elizabethrush89

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

  • 26.09.25 16:40 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 16:40 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 19:08 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( [email protected]. WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.

  • 26.09.25 19:53 carolinehudso83

    You are one step away from recovering your lost crypto funds. CAPITAL REDEMPTION WIZARD is the solution. Without them, I would have lost everything. I was scammed through a compromised email, lured by a fake Elon Musk Bitcoin investment. After applying and completing KYC, I was credited with 2.5 Bitcoin. When I tried to withdraw, I was hit with fees, and my wallet was emptied of $103,000.00. Their support team was hostile. I researched and found CAPITAL REDEMPTION WIZARD. They recovered my hacked Bitcoin. I learned the Bitcoin offer was a scam. CAPITAL REDEMPTION WIZARD guided me through this. Email: ( [email protected] ) Whats app or text +1 518 468 2985 Website https://bestrecoveryagent.com/

  • 26.09.25 22:25 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 22:59 elizabethrush89

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

  • 26.09.25 22:59 elizabethrush89

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

  • 27.09.25 03:07 Angela_Moore

    I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.

  • 28.09.25 00:42 Anitastar

    Wizard Hilton Cyber Tech's strategic approach to Bitcoin recovery represents a mutually beneficial collaboration that offers valuable advantages for all involved. At the core of this innovative partnership is a shared commitment to leveraging cutting-edge technology and expertise to tackle the increasingly complex challenges of cryptocurrency theft and loss. By combining Wizard Hilton's world-class cybersecurity capabilities with the deep industry insights and recovery methodologies of Cyber Tech, this alliance is poised to revolutionize the way individuals and organizations safeguard their digital assets. Through a meticulous, multi-layered process, the team meticulously analyzes each case, employing advanced forensic techniques to trace the flow of stolen funds and identify potential recovery avenues. This rigorous approach not only maximizes the chances of successful Bitcoin retrieval, but also provides invaluable intelligence to enhance future security measures and prevention strategies. Importantly, the collaboration is built on a foundation of trust, transparency, and a genuine concern for the well-being of clients, ensuring that the recovery process is handled with the utmost care and discretion. As the cryptocurrency landscape continues to evolve, this strategic alliance between Wizard Hilton Cyber Tech stands as a shining example of how industry leaders can come together to safeguard digital assets, protect victims of cybercrime, and pave the way for a more secure and resilient cryptocurrency ecosystem. Email : wizardhiltoncybertech ( @ ) gmail (. ) com     OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number  +18737715701 Thanks.

  • 28.09.25 01:48 marcushenderson624

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

  • 28.09.25 01:48 marcushenderson624

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

  • 28.09.25 01:49 marcushenderson624

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

  • 29.09.25 13:47 thomassankara

    USDT recovery expert / company I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.

  • 29.09.25 16:32 elizabethrush89

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

  • 29.09.25 16:32 elizabethrush89

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

  • 29.09.25 19:46 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( recoveryfundprovider@gmail. com WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.

  • 29.09.25 21:06 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 29.09.25 21:07 beverlyalex010

    I ended my marriage. My spouse was unfaithful. I found clear proof of her cheating. She hid her phone activity. Many secrets were on her phone. She used different apps. I hired a private investigator. I needed solid evidence first. I did not want to accuse her without proof. That could lead to legal trouble. They helped me access her phone. They linked her phone use to mine. I could then watch her phone without her knowing. This is how I learned about her affair. I also found out she planned to take my money. She intended to leave with her new partner. If you are in a similar situation, reach out to [email protected] WhatsApp at +44 736-644-5035. Get ahead of things.

  • 30.09.25 11:02 patricialovick86

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

  • 30.09.25 11:02 patricialovick86

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

  • 01.10.25 16:51 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( [email protected] WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.

  • 01.10.25 17:24 johnn

    Anthony davies, renowned for his expertise in recovering stolen cryptocurrency, especially specializing in USDT, provided invaluable assistance in a scenario where a significant sum of $571,000 was taken from me. I had the privilege of witnessing his exceptional skills firsthand and I am truly thankful for his prompt efforts, which led to the successful recovery of the entire amount in just a span of 72 hours. Mr Anthony davies swift reactions and efficient tactics not only resolved my financial troubles but also alleviated much of the stress on my mental well-being. You can reach out to him immediately and get connected with email at anthonydaviestech@gmail com also can be contacted on WhatsApp at +951 490-8435, he is an expert in the field most especially in recovering lost digital assets.

  • 01.10.25 17:25 johnn

    Anthony davies, renowned for his expertise in recovering stolen cryptocurrency, especially specializing in USDT, provided invaluable assistance in a scenario where a significant sum of $571,000 was taken from me. I had the privilege of witnessing his exceptional skills firsthand and I am truly thankful for his prompt efforts, which led to the successful recovery of the entire amount in just a span of 72 hours. Mr Anthony davies swift reactions and efficient tactics not only resolved my financial troubles but also alleviated much of the stress on my mental well-being. You can reach out to him immediately and get connected with email at anthonydaviestech@gmail com also can be contacted on WhatsApp at +951 490-8435, he is an expert in the field most especially in recovering lost digital assets.

  • 02.10.25 08:48 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 02.10.25 08:48 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 02.10.25 08:48 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 Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 03.10.25 17:26 dieter1121

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  • 04.10.25 10:13 elizabethrush89

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  • 04.10.25 10:13 elizabethrush89

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

  • 04.10.25 20:25 Tonerdomark

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