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[Перевод] Могут ли KAN справляться с задачами компьютерного зрения?

Недавняя статья об новой архитектуре нейронных сетей на основе теоремы Колмогорова-Арнольда (KAN — Kolmogorov-Arnold Networks) вызвала большой ажиотаж: уже было представлено множество вариаций того, как правильно создавать такие сети, ведутся горячие дебаты, а рабочая ли схема и имеет ли право на жизнь и многое другое. Цель этой статьи постараться ответить на простой вопрос: могут ли KAN справляться с компьютерным зрением?

Исходный код всех экспериментов данной статьи можете найти по ссылке.

Пока ещё не ушли далеко, сразу же скажем, что у этой статьи два автора: Иван Дрокин, который написал оригинал на английском языке, проводил эксперименты и написал собственную библиотеку свёрток для KAN — torch-conv-kan. За вольный перевод для читателей Хабра, многочисленные ревью и правки оригинала статьи, а также часть глупых мемов отвечал Антон Клочков — автор телеграм-канала MLE шатает Produnction (нет, в названии нет опечатки) про нейронные сети, мемы, языки программирования и рассуждения об общих топиках в IT.
Все рассуждения в статье ведутся от лица Ивана.

Основы

Давайте начнем с самого фундаментального — математики. Если говорить кратко, то многослойные перцептроны (MLP — Multi-Layer Perceptron) представляют собой нелинейную функцию от взвешенной суммы входных данных, тогда как сети Колмогорова-Арнольда представляют собой сумму нелинейных унарных функций от входных данных.

Работоспособность MLP основывается на теореме Цыбенко или более известной в широких кругах, как универсальной теореме апроксимации. Если не вдаваться в детали, то она утверждает, что любую функцию можно апроксимировать с любой точностью с помощью одного достаточно широкого скрытого слоя с нелинейной функцией активации.

Чтобы не расписывать формулы в статье, скрин из Wikipedia с необходимым утверждением

С другой стороны, как уже было написано в начале статьи, работа KAN базируется на основе теоремы Колмогорова-Арнольда:

Чтобы не расписывать формулы в статье, скрин из Wikipedia с необходимым утверждением

Авторы статьи "KAN: Kolmogorov-Arnold Networks" разработали новый тип архитектуры нейронных сетей: обучаемые активации на рёбрах и суммирование результатов в узлах. В противовес этому, в MLP в узлах применяется фиксированная нелинейная функция, а на ребрах производится линейная проекция входов.

Наглядное представление разницы между двумя архитектурами. Картинка взята из статьи "KAN: Kolmogorov-Arnold Networks".

Что же это за "обучаемые активации" и как их обучать? В оригинальной статье было предложено использовать B-сплайны (с классными визуализациями можно глянуть следующую статью). Сплайн-функция степени представляет собой кусочно-полиномиальную функцию степени n-1 . Места, где отрезки соединяются, называются узлами. Ключевое свойство сплайн-функций заключается в том, что они и их производные могут быть непрерывными, в зависимости от кратности узлов.

Визуализация B-сплайна (синяя линия) и контролирующих её точек (красным цветом). Источник.

Плюсы и минусы KAN

Авторы выделяют следующие плюсы использование KAN относительно MLP:

Выше качество: KAN показали точность выше на большом множестве задач в сравнении с MLP. Первые могут более эффективно (в терминах качества) представлять сложные многомерные функции (спасибо теореме Колмогорова-Арнольда), что положительно сказывается на качестве.
Интерпретируемость: MLP — это чёрный ящик, сложно сказать, что происходит у них внутри, а KAN может предложить интересные возможности. Например, можно разложить сложную многомерную функцию на более простые компоненты, анализ которых может служить инсайтом о поведении модели, о работе на конкретных данных.
Гибкость и обобщаемость: за счёт обучаемости активаций можно лучше находить нелинейные зависимости в данных, что также ведёт к обобщаемости (но это не так просто).
Устойчивость к шумным данным и Adversarial Attacks: способность KAN улавливать более устойчивые представления данных с помощью адаптивных функций активации позволяют KAN быть более устойчивым к шумам и атакам.

Но есть и определённые сложности с KAN (No free lunch, помните?):

Чувствительность к гиперпараметрам: как и любая другая нейронная сеть, KAN чувствительна к множеству гиперпараметров, таких как learning rate, силу регуляризации, самой архитектуре. Проблема подбора правильных параметров остаётся актуальной и может в значительной степени влиять на сходимость. Тут стоит отметить, что на настоящий момент нет чётких рецептов того, как именно тюнить разного рода гиперпараметры (L1/L2 веса, параметры активаций, dropout коэффициенты и т.д.). Это чем-то напоминает времена, когда только начиналось развитие свёрточных нейронных сетей.
Высокие вычислительные затраты: адаптивные функции активации (например, B-сплайны) могут требовать больше ресурсов, чем классические MLP, что отражается на длительности и стоимости обучения и инференса;
Сложность моделей и масштабируемость: KAN масштабируемы в терминах гибкости модели, но при этом более глубокие сети ещё сильнее увеличивают вычислительные затраты. Масштабирование KAN на большие датасеты и сложные задачи, где вычислительная эффективность и интерпретируемость выходят на передний план, является пока сложной задачей.

Разновидности KAN

Некоторые из проблем, описанные выше, частично были решены в следующих модификациях.

В первую очередь, была представлена версия Fast KAN, в которой B-сплайны заменены радиальными базисными функциями (RBF). Это изменение помогает уменьшить вычислительные затраты на использование сплайнов.

Также появилось несколько Polynomial KAN: Лежандра, Чебышева, Якоби, Грама, Бернштейна, и Wavelet-based KAN. Про каждый из них можно узнать подробнее, перейдя по соответствующим ссылкам.

Свёртки для KAN

Для начала вспомним, что такое свёрточный слой? Наиболее распространенный тип свёрточного слоя — это слой двухмерной свёртки, обычно сокращаемый как Conv2D. В этом слое фильтр (или ядро) "скользит" по двухмерным входным данным (например, картинкам), выполняя поэлементное умножение. Результаты суммируются в одно число. Ядро выполняет ту же операцию для каждой позиции, по которой оно скользит, преобразуя двухмерную матрицу признаков в другую.

Хотя свёртки в одномерном и трёхмерном пространствах имеют тот же принцип, они используют разные ядра, размеры входных данных и выходных данных. Однако для упрощения мы сосредоточимся на двухмерной свёрточном слое. Если вы хотите углубиться в эту тему, прочитайте этот хороший пост.

Визуализация работы двухмерного свёрточного слоя. Пример взят из Wikimedia.

Как правило, после слоя свёртки применяются слой нормализации (например, BatchNorm, InstanceNorm и т.д.) и нелинейные активации (ReLU, LeakyReLU, SiLU и т.д.).

Более формально: предположим, что у нас есть входное изображение размером $N \times N$ . Для упрощения мы опустим ось канала (т.е. рассмотрим одноканальные изображения), она добавляет еще одно суммирование по оси канала. Итак, сначала нам нужно выполнить свертку с нашим ядром размером $m \times m$ :

$x_{ij} = \sum_{a=0}^{m-1} \sum_{b=0}^{m-1} \omega_{ab} y_{i+a,j+b}; \quad i, j = 1, N - m + 1$

Затем применяем батч нормализацию и нелинейность, например, ReLU:

Свёрточный слой в KAN будет работать иначе: ядро будет содержать не обучаемые веса (конкретные числа), а унарные, обучаемые нелинейные функции. В этом случае ядро "скользит" по двухмерным входным данным, выполняя поэлементное применение функций активации из этого фильтра. Результатом каждого из применений будет число, которые потом суммируются.

Опять же, более формально: давайте применим к нашему входному изображению свёрточный слой в терминах теоремы Колмогорова-Арнольда:

$x_{ij} = \sum_{a=0}^{m-1} \sum_{b=0}^{m-1} \phi_{ab}(y_{i+a,j+b}); \quad i, j = 1, N - m + 1$

Каждая $\phi_{ab}$ является унарной нелинейной обучаемой функцией со своими обучаемыми параметрами. В оригинальной статье авторы предлагают использовать функцию следующего вида:

$\phi(x) = \omega_{b}b(x) + w_{s}spline(x)$

где $w_{b}$ и $w_{s}$ — обучаемые параметры, spline(x) — B-сплайн. — это $\omega_b b(x)$ esidual activation functions, похожие на residual connctions из ResNet сетей. В оригинальной статье авторы предлагают выбрать в качестве b(x) функцию SiLU:

$b(x) = SiLU(x) = \frac {x}{1 + e^{-x}}$

Как было уже упомянуто выше, недавно было предложено использовать вместо сплайнов полиномиальные функции или RBF.

Подытожим вышесказанное: в классических свёрточных слоях ядра содержат просто веса (числа), тогда как KAN-свёртки содержат унарные функции:

$K = \begin{bmatrix} w_{1,1} & w_{1,2} & w_{1,3} \\ w_{2,1} & w_{2,2} & w_{2,3} \\ w_{3,1} & w_{3,2} & w_{3,3} \end{bmatrix}, \quad K_{\text{kan}} = \begin{bmatrix} \phi_{1,1} & \phi_{1,2} & \phi_{1,3} \\ \phi_{2,1} & \phi_{2,2} & \phi_{2,3} \\ \phi_{3,1} & \phi_{3,2} & \phi_{3,3} \end{bmatrix}$

Эксперименты

Реализацию различных типов KAN-свёрток, моделей, датасетов, сетапов экспериментов и многое другое можете найти моём репозитории torch-conv-kan.

MNIST

Итак, давайте начнём эксперименты со всем знакомого MNISTа.

Бейзлайн модели — простая нейронная сеть, состоящая из четырёх свёрточных слоёв. Для уменьшения размерности во втором и третьем свёрточных слоях используется параметр dilation=2.

Количество каналов в свёрточных слоях одинаково для всех моделей: 32, 64, 128, 256. После свёрток применяется Global Average Pooling, за которым следует линейный выходной слой. Кроме того, для регуляризиции используется Dropout слой: с параметром p = 0.25 в свёрточных слоях и p = 0.5 перед выходным слоем.

Пример реализации с использованием Pytorch и torch-conv-kan

import torch
import torch.nn as nn

from kan_convs import KANConv2DLayer


class SimpleConvKAN(nn.Module):
    def __init__(
            self,
            layer_sizes,
            num_classes: int = 10,
            input_channels: int = 1,
            spline_order: int = 3,
            groups: int = 1):
        super(SimpleConvKAN, self).__init__()
        self.layers = nn.Sequential(
            KANConv2DLayer(input_channels, layer_sizes[0], spline_order, kernel_size=3, groups=1, padding=1, stride=1,
                           dilation=1),
            KANConv2DLayer(layer_sizes[0], layer_sizes[1], spline_order, kernel_size=3, groups=groups, padding=1,
                           stride=2, dilation=1),
            KANConv2DLayer(layer_sizes[1], layer_sizes[2], spline_order, kernel_size=3, groups=groups, padding=1,
                           stride=2, dilation=1),
            KANConv2DLayer(layer_sizes[2], layer_sizes[3], spline_order, kernel_size=3, groups=groups, padding=1,
                           stride=1, dilation=1),
            nn.AdaptiveAvgPool2d((1, 1))
        )
        self.output = nn.Linear(layer_sizes[3], num_classes)
        self.drop = nn.Dropout(p=0.25)

    def forward(self, x):
        x = self.layers(x)
        x = torch.flatten(x, 1)
        x = self.drop(x)
        x = self.output(x)
        return x

Заметьте, что в случае классических свёрточных слоев, структура слоёв была бы примерно следующей: Conv2D -> Batch Normalization -> ReLU.

Для проведения экспериментов используются аугментации, которые вы можете посмотреть под катом.

Пример аугментаций с использованием torchvision

from torchvision.transforms import v2

transform_train = v2.Compose([
    v2.RandomAffine(degrees=20, translate=(0.1, 0.1), scale=(0.9, 1.1)),
    v2.ColorJitter(brightness=0.2, contrast=0.2),
    v2.ToTensor(),
    v2.Normalize((0.5,), (0.5,))
])

Кроме того, нам также необходимо исследовать влияние различных слоёв нормализации внутри свёрток KAN и влияние L1 регуляризации. В столбце Norm Layer во всех таблицах указывается, какой слой нормализации использовался во время эксперимента, а в столбце Affine указывается, был ли параметр affine слоя нормализации BatchNorm2d установлен как True или False.

Все эксперименты были выполнены с использованием NVIDIA RTX 3090 с идентичными параметрами.

Model	Accuracy	Parameters	Eval Time, s	Norm Layer	Affine	L1
SimpleConv, 4 layers	99.42	101066	0.7008	BatchNorm2D	False	0
SimpleKANConv, 4 layers	96.80	3488814	2.8306	InstanceNorm2D	False	0
SimpleKANConv, 4 layers	99.41	3489774	2.6362	InstanceNorm2D	True	0
SimpleKANConv, 4 layers	99.00	3489774	2.6401	BatchNorm2D	True	0
SimpleKANConv, 4 layers	98.89	3489774	2.4138	BatchNorm2D	True	1e-05

Модель на основе классических свёрток работает куда лучше нейронной сети с KAN-свёртами, которая к тому же имеет в 34 раза больше параметров и требует куда большего времени исполнения. Кажется, это не та "революция" в нейронных сетях, которую мы ожидали.

Давайте попробуем воспользоваться подходом Fast KAN и заменим сплайны на RBF:

Model	Accuracy	Parameters	Eval Time, s	Norm Layer	Affine	L1
SimpleConv, 4 layers	99.42	101066	0.7008	BatchNorm2D	True	0
SimpleFastKANConv, 4 layers	99.26	3488810	1.5636	InstanceNorm2D	False	0
SimpleFastKANConv, 4 layers	99.01	3489260	1.7406	InstanceNorm2D	True	0
SimpleFastKANConv, 4 layers	97.65	3489260	1.5999	BatchNorm2D	True	0
SimpleFastKANConv, 4 layers	95.62	3489260	1.6158	BatchNorm2D	True	1e-05

По времени стало получше, но при этом сами результаты неоднозначные: где-то стало лучше, где-то хуже.

Тогда попробуем ещё одну функцию вместо сплайнов: дискретные полиномы Чебышева. Сам факт что полиномы дискретны в теории должно дать неплохие результаты для обработки дискретных данных — изображений и текстов. Давайте узнаем, так ли это:

Model	Accuracy	Parameters	Eval Time, s	Norm Layer	Affine	L1
SimpleConv, 4 layers	99.42	101066	0.7008	BatchNorm2D	True	0
SimpleKAGNConv, 4 layers	98.21	487866	1.8506	InstanceNorm2D	False	0
SimpleKAGNConv, 4 layers	99.46	488826	1.8813	InstanceNorm2D	True	0
SimpleKAGNConv, 4 layers	99.49	488826	1.7253	BatchNorm2D	True	0
SimpleKAGNConv, 4 layers	99.44	488826	1.8979	BatchNorm2D	True	1e-05

Новые KAN-свёртки выдают качество чуть лучше традиционной модели, но работают в 2.5 раза медленнее и имеют почти в пять раз больше параметров. L1 регуляризация немного снижает производительность модели, но это область для дальнейших улучшений.

CIFAR 100

Бейзлайн модели здесь меняется. Теперь у нас будет восемь свёрточных слоёв . Для уменьшения размерности во втором, третьем и шестом свёрточных слоях используется параметр dilation=2. Для каждого слоя число каналов равно соответвующе 16, 32, 64, 128, 256, 256, 512, 512. Всё остальное в модели остается без изменений.

Аугментации, которые используются в экспериментах с CIFAR 100 можете посмотреть под катом.

Пример аугментаций с использованием torchvision

from torchvision.transforms import v2
from torchvision.transforms.autoaugment import AutoAugmentPolicy

transform_train = v2.Compose([
    v2.RandomHorizontalFlip(p=0.5),
    v2.RandomChoice([v2.AutoAugment(AutoAugmentPolicy.CIFAR10),
        v2.AutoAugment(AutoAugmentPolicy.IMAGENET),
        v2.AutoAugment(AutoAugmentPolicy.SVHN),
        v2.TrivialAugmentWide()]),
    v2.ToTensor(),
    v2.Normalize((0.5,), (0.5,))
])

Model	Accuracy	Parameters	Eval Time, s	Norm Layer	Affine	L1
SimpleConv, 8 layers	57.52	1187172	1.8265	BatchNorm2D	True	0
SimpleKAGNConv, 8 layers	29.39	22655732	2.5358	InstanceNorm2D	False	0
SimpleKAGNConv, 8 layers	48.56	22659284	2.0454	InstanceNorm2D	True	0
SimpleKAGNConv, 8 layers	59.27	22659284	2.6460	BatchNorm2D	True	0
SimpleKAGNConv, 8 layers	58.07	22659284	2.2583	BatchNorm2D	True	1e-05

KAN-свёртки на основе дискретных полиномов Чебышева показывают лучшее качество, хотя и с бОльшими временными затратами и существенно бОльшим количеством параметров (более чем в 20 раз больше). BatchNorm2D, по-видимому, является лучшим вариантом для нормализации внутренних признаков в KAN-свёртках на дискретных полиномов Чебышева.

Использование последних кажется многообещающим для дальнейших экспериментов на ImageNet1k и других "реальных" наборах данных.

Заключение

Итак, могут ли KAN справляться с компьютерным зрением? Кажется, что да! Смогут ли они заменить классические CNN? Это еще предстоит выяснить.

MLP используется уже много лет и нуждается в обновлении. Мы уже видели подобные изменения. Например, шесть лет назад сети Long Short-Term Memory (LSTM), которые долгое время были основой для моделирования последовательностей, были заменены трансформерами в качестве стандартного строительного блока для архитектуры языковых моделей. Похожий сдвиг для MLP был бы интригующим.

Свёрточные нейронные сети, которые доминировали в течение многих лет (и до сих пор являются основой для компьютерного зрения), в конечном итоге были частично заменены визуальными трансформерами (ViT). Возможно, пришло время для нового лидера в этой области?

Однако прежде чем это произойдет, сообществу необходимо найти эффективные методы для обучения сетей Колмогорова-Арнольда, свёрточных сетей Колмогорова-Арнольда (ConvKAN) и ViT-KAN, а также решить проблемы, которые связаны с этими моделями (например, скорость инференса, количество параметров).

Хотя меня очень вдохновляет эта новая архитектура и начальные эксперименты показывают обнадеживающие результаты, я остаюсь несколько скептичен. Необходимы ещё эксперименты. Оставайтесь с нами, мы собираемся углубиться в эту тему.

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11 июн. 2024 г.

07.09.23 16:24 CherryTeam

Cherry Team atlyginimų skaičiavimo programa yra labai naudingas įrankis įmonėms, kai reikia efektyviai valdyti ir skaičiuoti darbuotojų atlyginimus. Ši programinė įranga, turinti išsamias funkcijas ir patogią naudotojo sąsają, suteikia daug privalumų, kurie padeda supaprastinti darbo užmokesčio skaičiavimo procesus ir pagerinti finansų valdymą. Štai keletas pagrindinių priežasčių, kodėl Cherry Team atlyginimų skaičiavimo programa yra naudinga įmonėms: Automatizuoti ir tikslūs skaičiavimai: Atlyginimų skaičiavimai rankiniu būdu gali būti klaidingi ir reikalauti daug laiko. Programinė įranga Cherry Team automatizuoja visą atlyginimų skaičiavimo procesą, todėl nebereikia atlikti skaičiavimų rankiniu būdu ir sumažėja klaidų rizika. Tiksliai apskaičiuodama atlyginimus, įskaitant tokius veiksnius, kaip pagrindinis atlyginimas, viršvalandžiai, premijos, išskaitos ir mokesčiai, programa užtikrina tikslius ir be klaidų darbo užmokesčio skaičiavimo rezultatus. Sutaupoma laiko ir išlaidų: Darbo užmokesčio valdymas gali būti daug darbo jėgos reikalaujanti užduotis, reikalaujanti daug laiko ir išteklių. Programa Cherry Team supaprastina ir pagreitina darbo užmokesčio skaičiavimo procesą, nes automatizuoja skaičiavimus, generuoja darbo užmokesčio žiniaraščius ir tvarko išskaičiuojamus mokesčius. Šis automatizavimas padeda įmonėms sutaupyti daug laiko ir pastangų, todėl žmogiškųjų išteklių ir finansų komandos gali sutelkti dėmesį į strategiškai svarbesnę veiklą. Be to, racionalizuodamos darbo užmokesčio operacijas, įmonės gali sumažinti administracines išlaidas, susijusias su rankiniu darbo užmokesčio tvarkymu. Mokesčių ir darbo teisės aktų laikymasis: Įmonėms labai svarbu laikytis mokesčių ir darbo teisės aktų, kad išvengtų baudų ir teisinių problemų. Programinė įranga Cherry Team seka besikeičiančius mokesčių įstatymus ir darbo reglamentus, užtikrindama tikslius skaičiavimus ir teisinių reikalavimų laikymąsi. Programa gali dirbti su sudėtingais mokesčių scenarijais, pavyzdžiui, keliomis mokesčių grupėmis ir įvairių rūšių atskaitymais, todėl užtikrina atitiktį reikalavimams ir kartu sumažina klaidų riziką. Ataskaitų rengimas ir analizė: Programa Cherry Team siūlo patikimas ataskaitų teikimo ir analizės galimybes, suteikiančias įmonėms vertingų įžvalgų apie darbo užmokesčio duomenis. Ji gali generuoti ataskaitas apie įvairius aspektus, pavyzdžiui, darbo užmokesčio paskirstymą, išskaičiuojamus mokesčius ir darbo sąnaudas. Šios ataskaitos leidžia įmonėms analizuoti darbo užmokesčio tendencijas, nustatyti tobulintinas sritis ir priimti pagrįstus finansinius sprendimus. Pasinaudodamos duomenimis pagrįstomis įžvalgomis, įmonės gali optimizuoti savo darbo užmokesčio strategijas ir veiksmingai kontroliuoti išlaidas. Integracija su kitomis sistemomis: Cherry Team programinė įranga dažnai sklandžiai integruojama su kitomis personalo ir apskaitos sistemomis. Tokia integracija leidžia automatiškai perkelti atitinkamus duomenis, pavyzdžiui, informaciją apie darbuotojus ir finansinius įrašus, todėl nebereikia dubliuoti duomenų. Supaprastintas duomenų srautas tarp sistemų padidina bendrą efektyvumą ir sumažina duomenų klaidų ar neatitikimų riziką. Cherry Team atlyginimų apskaičiavimo programa įmonėms teikia didelę naudą - automatiniai ir tikslūs skaičiavimai, laiko ir sąnaudų taupymas, atitiktis mokesčių ir darbo teisės aktų reikalavimams, ataskaitų teikimo ir analizės galimybės bei integracija su kitomis sistemomis. Naudodamos šią programinę įrangą įmonės gali supaprastinti darbo užmokesčio skaičiavimo procesus, užtikrinti tikslumą ir atitiktį reikalavimams, padidinti darbuotojų pasitenkinimą ir gauti vertingų įžvalgų apie savo finansinius duomenis. Programa Cherry Team pasirodo esanti nepakeičiamas įrankis įmonėms, siekiančioms efektyviai ir veiksmingai valdyti darbo užmokestį. https://cherryteam.lt/lt/
08.10.23 01:30 davec8080

The "Shibarium for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH. The Plot Thickens. Someone posted the actual transactions!!!! https://bscscan.com/tx/0xa846ea0367c89c3f0bbfcc221cceea4c90d8f56ead2eb479d4cee41c75e02c97 It seems the article is true!!!! And it's also FUD. Let me explain. Check this link: https://bscscan.com/token/0x5a752c9fe3520522ea88f37a41c3ddd97c022c2f So there really is a "Shibarium" token. And somebody did a rug pull with it. CONFIRMED. But the "Shibarium" token for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH.
24.06.24 04:31 tashandiarisha

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26.06.24 18:46 Jacobethannn098

LEGAL RECOUP FOR CRYPTO THEFT BY ADRIAN LAMO HACKER
26.06.24 18:46 Jacobethannn098

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04.07.24 04:49 ZionNaomi

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13.07.24 21:13 michaelharrell825

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17.07.24 02:26 thompsonrickey

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18.07.24 20:13 austinagastya

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27.08.24 12:50 James889900

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27.08.24 13:06 James889900

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02.09.24 20:24 [email protected]

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06.09.24 01:35 Celinagarcia

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06.09.24 01:44 Celinagarcia

HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.
16.09.24 00:10 marcusaustin

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16.09.24 00:11 marcusaustin

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23.09.24 18:56 matthewshimself

At first, I was admittedly skeptical about Worldcoin (ref: https://worldcoin.org/blog/worldcoin/this-is-worldcoin-video-explainer-series), particularly around the use of biometric data and the WLD token as a reward mechanism for it. However, after following the project closer, I’ve come to appreciate the broader vision and see the value in the underlying tech behind it. The concept of Proof of Personhood (ref: https://worldcoin.org/blog/worldcoin/proof-of-personhood-what-it-is-why-its-needed) has definitely caught my attention, and does seem like a crucial step towards tackling growing issues like bots, deepfakes, and identity fraud. Sam Altman’s vision is nothing short of ambitious, but I do think he & Alex Blania have the chops to realize it as mainstay in the global economy.
01.10.24 14:54 Sinewclaudia

I lost about $876k few months ago trading on a fake binary option investment websites. I didn't knew they were fake until I tried to withdraw. Immediately, I realized these guys were fake. I contacted Sinew Claudia world recovery, my friend who has such experience before and was able to recover them, recommended me to contact them. I'm a living testimony of a successful recovery now. You can contact the legitimate recovery company below for help and assistance. [email protected] [email protected] WhatsApp: 6262645164
02.10.24 22:27 Emily Hunter

Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.
18.10.24 09:34 freidatollerud

The growth of WIN44 in Brazil is very interesting! If you're looking for more options for online betting and casino games, I recommend checking out Casinos in Brazil. It's a reliable platform that offers a wide variety of games and provides a safe and enjoyable experience for users. It's worth checking out! https://win44.vip
31.10.24 00:13 ytre89

Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.
02.11.24 14:44 diannamendoza732

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12.11.24 00:50 TERESA

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17.11.24 09:31 Vivianlocke223

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19.11.24 03:06 [email protected]

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19.11.24 03:07 [email protected]

My entire existence fell apart when a malevolent hacker recently gained access to my online accounts. I felt violated and extremely uneasy after discovering that the digital platforms I depended on for communication, employment, and finances had been compromised. Regaining control and restoring my digital security was an overwhelming task in the immediate aftermath. To help me navigate the difficult process of recovering my accounts and getting my peace of mind back, TRUST GEEKS HACK EXPERT came into my life as a ray of hope. They immediately put their highly skilled professionals to work, thoroughly examining the vulnerability and methodically preventing unwanted access. They guided me through each stage soothingly, explaining what was occurring and why, so I never felt lost or alone. They communicated with service providers to restore my legitimate access while skillfully navigating the complex labyrinth of account recovery procedures. My digital footprint was cleaned and strengthened against future attacks thanks to their equally amazing ability to remove any remaining evidence of the hacker's presence. However, TRUST GEEKS HACK EXPERT actual worth went beyond its technical aspects. They offered constant emotional support during the ordeal, understanding my fragility and sense of violation. My tense nerves were calmed by their comforting presence and kind comments, which served as a reminder that I wasn't alone in this struggle. With their help, I was able to reestablish my sense of security and control, which enabled me to return my attention to the significant areas of my life that had been upended. Ultimately, TRUST GEEKS HACK EXPERT all-encompassing strategy not only recovered my online accounts but also my general peace of mind, which is a priceless result for which I am incredibly appreciative of their knowledge and kindness. Make the approach and send a message to TRUST GEEKS HACK EXPERT Via Web site <> www://trustgeekshackexpert.com/-- E>mail: Trustgeekshackexpert(At)fastservice..com -- TeleGram,<> Trustgeekshackexpert
21.11.24 04:14 ronaldandre617

Being a parent is great until your toddler figures out how to use your devices. One afternoon, I left my phone unattended for just a few minutes rookie mistake of the century. I thought I’d take a quick break, but little did I know that my curious little genius was about to embark on a digital adventure. By the time I came back, I was greeted by two shocking revelations: my toddler had somehow managed to buy a $5 dinosaur toy online and, even more alarmingly, had locked me out of my cryptocurrency wallet holding a hefty $75,000. Yes, you heard that right a dinosaur toy was the least of my worries! At first, I laughed it off. I mean, what toddler doesn’t have a penchant for expensive toys? But then reality set in. I stared at my phone in disbelief, desperately trying to guess whatever random string of gibberish my toddler had typed as a new password. Was it “dinosaur”? Or perhaps “sippy cup”? I felt like I was in a bizarre game of Password Gone Wrong. Every attempt led to failure, and soon the laughter faded, replaced by sheer panic. I was in way over my head, and my heart raced as the countdown of time ticked away. That’s when I decided to take action and turned to Digital Tech Guard Recovery, hoping they could solve the mystery that was my toddler’s handiwork. I explained my predicament, half-expecting them to chuckle at my misfortune, but they were incredibly professional and empathetic. Their confidence put me at ease, and I knew I was in good hands. Contact With WhatsApp: +1 (443) 859 - 2886 Email digital tech guard . com Telegram: digital tech guard recovery . com website link :: https : // digital tech guard . com Their team took on the challenge like pros, employing their advanced techniques to unlock my wallet with a level of skill I can only describe as magical. As I paced around, anxiously waiting for updates, I imagined my toddler inadvertently locking away my life savings forever. But lo and behold, it didn’t take long for Digital Tech Guard Recovery to work their magic. Not only did they recover the $75,000, but they also gave me invaluable tips on securing my wallet better like not leaving it accessible to tiny fingers! Who knew parenting could lead to such dramatic situations? Crisis averted, and I learned my lesson: always keep my devices out of reach of little explorers. If you ever find yourself in a similar predicament whether it’s tech-savvy toddlers or other digital disasters don’t hesitate to reach out to Digital Tech Guard Recovery. They saved my funds and my sanity, proving that no challenge is too great, even when it involves a toddler’s mischievous fingers!
21.11.24 08:02 Emily Hunter

If I hadn't found a review online and filed a complaint via email to support@deftrecoup. com , the people behind this unregulated scheme would have gotten away with leaving me in financial ruins. It was truly the most difficult period of my life.
22.11.24 04:41 [email protected]

I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT
22.11.24 15:26 cliftonhandyman

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22.11.24 23:43 teresaborja

all thanks to Tech Cyber Force Recovery expert assistance. As a novice in cryptocurrency, I had been carefully accumulating a modest amount of Bitcoin, meticulously safeguarding my digital wallet and private keys. However, as the adage goes, the best-laid plans can often go awry, and that's precisely what happened to me. Due to a series of technical mishaps and human errors, I found myself locked out of my Bitcoin wallet, unable to access the fruits of my digital labors. Panic set in as I frantically searched for a solution, scouring the internet for any glimmer of hope. That's when I stumbled upon the Tech Cyber Force Recovery team, a group of seasoned cryptocurrency specialists who had built a reputation for their ability to recover lost or inaccessible digital assets. Skeptical at first, I reached out, desperate for a miracle. To my utter amazement, the Tech Cyber Force Recovery experts quickly assessed my situation and devised a meticulous plan of attack. Through their deep technical knowledge, unwavering determination, and a keen eye for detail, they were able to navigate the complex labyrinth of blockchain technology, ultimately recovering my entire Bitcoin portfolio. What had once seemed like a hopeless endeavor was now a reality, and I found myself once again in possession of my digital wealth, all thanks to the incredible efforts of the Tech Cyber Force Recovery team. This experience has not only restored my faith in the cryptocurrency ecosystem. Still, it has also instilled in me a profound appreciation for the critical role that expert recovery services can play in safeguarding one's digital assets. ENAIL < Tech cybers force recovery @ cyber services. com > WEBSITE < ht tps : // tech cyber force recovery. info > TEXT < +1. 561. 726. 3697 >
24.11.24 02:21 [email protected]

I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT
25.11.24 02:19 briankennedy

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25.11.24 02:20 briankennedy

After countless hours of research and desperate attempts to find a solution, I stumbled upon FASTFUND RECOVERY. It was like finding an oasis in the middle of a desert. Their website promised to help victims of scams reclaim what was rightfully theirs, and I instantly knew I had to give them a shot. Before diving headfirst into the recovery process, I wanted to make sure that FASTFUND RECOVERY was the real deal. So, I did my due diligence and looked into their expertise and reputation. To my relief, I found that they had an impeccable track record, successfully assisting countless individuals in recovering their lost funds. Their team consisted of experts in cybersecurity and financial fraud, armed with the knowledge and tools needed to tackle even the most intricate scams. With their reputation preceding them, I felt a renewed sense of hope. FASTFUND RECOVERY successfully came to my aid and got back the amount I lost to these scammers and for this, I am sending this article for clarification. The info of FASTFUND RECOVERY is email: Fastfundrecovery8 (@)Gmail (.) com. Web fastfundrecovery(.)com. (W/A 1 807/500/7554)
26.11.24 21:59 [email protected]

In a world brimming with enticing investment opportunities, it is crucial to tread carefully. The rise of digital currencies has attracted many eager investors, but along with this excitement lurk deceitful characters ready to exploit the unsuspecting. I learned this lesson the hard way, and I want to share my story in the hopes that it can save someone from making the same mistakes I did. It all began innocently enough when I came across an engaging individual on Facebook. Lured in by promises of high returns in the cryptocurrency market, I felt the electric thrill of potential wealth coursing through me. Initial investments returned some profits, and that exhilarating taste of success fueled my ambition. Encouraged by a meager withdrawal, I decided to commit even more funds. This was the moment I let my guard down, blinded by greed. As time went on, the red flags started to multiply. The moment I tried to withdraw my earnings, a cascade of unreasonable fees appeared like a thick mist, obscuring the truth. “Just a little more,” they said, “Just until the next phase.” I watched my hard-earned money slip through my fingers as I scraped together every last cent to pay those relentless fees. My trust had become my downfall. In the end, I lost not just a significant amount of cash, but my peace of mind about $1.1 million vanished into the abyss of false promises and hollow guarantees. But despair birthed hope. After a cascade of letdowns, I enlisted the help of KAY-NINE CYBER SERVICES, a team that specializes in reclaiming lost funds from scams. Amazingly, they worked tirelessly to piece together what had been ripped away, providing me with honest guidance when I felt utterly defeated. Their expertise in navigating the treacherous waters of crypto recovery was a lifeline I desperately needed. To anyone reading this, please let my story serve as a warning. High returns often come wrapped in the guise of deception. Protect your investments, scrutinize every opportunity, and trust your instincts. Remember, the allure of quick riches can lead you straight to heartbreak, but with cautious determination and support, it is possible to begin healing from such devastating loss. Stay informed, stay vigilant, and may you choose your investment paths wisely. Email: kaynine @ cyberservices . com
26.11.24 23:12 rickrobinson8

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26.11.24 23:12 rickrobinson8

Although recovering from the terrible effects of investment fraud can seem like an impossible task, it is possible to regain financial stability and go on with the correct assistance and tools. In my own experience with Wizard Web Recovery, a specialized company that assisted me in navigating the difficulties of recouping my losses following my fall prey to a sophisticated online fraud, that was undoubtedly the case. My life money had disappeared in an instant, leaving me in a state of shock when I first contacted Spartan Tech Group Retrieval through this Email: spartantechretrieval (@) g r o u p m a i l .c o m The compassionate and knowledgeable team there quickly put my mind at ease, outlining a clear and comprehensive plan of action. They painstakingly examined every aspect of my case, using their broad business contacts and knowledge to track the movement of my pilfered money. They empowered me to make knowledgeable decisions regarding the rehabilitation process by keeping me updated and involved at every stage. But what I valued most was their unrelenting commitment and perseverance; they persisted in trying every option until a sizable amount of my lost money had been successfully restored. It was a long and arduous journey, filled with ups and downs, but having Spartan Tech Group Retrieval in my corner made all the difference. Thanks to their tireless efforts, I was eventually able to rebuild my financial foundation and reclaim a sense of security and control over my life. While the emotional scars of investment fraud may never fully heal, working with this remarkable organization played a crucial role in my ability to move forward and recover. For proper talks, contact on WhatsApp:+1 (971) 4 8 7 - 3 5 3 8 and Telegram:+1 (581) 2 8 6 - 8 0 9 2 Thank you for your time reading as it will be of help.
27.11.24 00:39 [email protected]

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27.11.24 09:10 Michal Novotny

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