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Как мозг человека решает сложные задачи

Эволюция разных видов протекает своим путем, делая повороты в сторону той или иной физиологической особенности, тем самым выделяя ее на фоне других и развивая ее до максимальной эффективности. Кто-то прекрасно видит в темноте, кто-то способен находится подо водой длительное время, а кто-то получил самый сильный эволюционный дар. Дар, способный созидать и разрушать, понимать и осуждать, спорить, где спор уместен, и где ему места нет. Дар этот — интеллект, а получателем его является человек. Одним из проявлений интеллекта является умение решать задачи, от легких до сложных, задействующих не только накопленные знания и опыт, но и учитывающих новые условия. Определить, как именно человек решает сложные задачи довольно сложно, но ученым из Массачусетского технологического института это удалось. Какие методы были задействованы, что они показали, и какой же механизм использует мозг человека для решения сложных задач? Ответы на эти вопросы мы найдем в докладе ученых.

Основа исследования

Человеческий мозг находит решения сложных многоступенчатых проблем, которые гораздо более гибкие, чем те, которые изучаются искусственными системами. Когнитивные теории приписывают эту гибкость определенным алгоритмам, таким как иерархическая обработка информации и контрфактуальное рассуждение. Контрфактуальное рассуждение является важным строительным блоком нашего ментального ландшафта, позволяя нам представлять альтернативные описания нашего предыдущего опыта. Знакомый сценарий — это когда мы чувствуем необходимость пересмотреть наши предположения из-за неожиданного поворота событий, например, неожиданной развилки на дороге во время вождения, резкой эмоциональной реакции друга или поворота сюжетной линии книги или фильма. Эти ситуации заставляют нас пересматривать прошлые события и предположения и искать альтернативные интерпретации, которые могли бы предоставить правдоподобное объяснение наших наблюдений. Учитывая центральную роль контрфактуальных рассуждений в познании, необходимо понять вычислительные основы этой стратегии.

Люди обычно полагаются на контрфактуальности, когда сталкиваются с деревьями решений с иерархией сценариев «если–то», приводящих к разным результатам. Однако озадачивает то, что деревья решений по своей сути не требуют вычисления контрфактуальностей. Напротив, оптимальная стратегия вывода для решения дерева решений заключается в том, чтобы полагаться на апостериорное убеждение по всем состояниям в дереве. Однако в сложных задачах вычисление апостериорной вероятности чрезвычайно сложно и иногда неразрешимо. Любопытно, что именно в этих условиях люди полагаются на контрфактуальности, что говорит о том, что контрфактуальные рассуждения могут быть опорой, когда невозможно вычислить апостериорную вероятность. Однако несколько важных вопросов о вычислительной основе контрфактуальных рассуждений остались без ответа. Какие вычислительные ограничения мотивируют опору на контрфактуальности? Принимают ли люди вычислительно рациональный подход к использованию контрфактуальностей? Вносят ли вычисления контрфактуальностей субоптимальности в поведение? Если да, то каковы они?

Авторы исследования разработали простую и интуитивно понятную задачу принятия решений, чтобы ответить на эти вопросы. Задача требовала от участников вывести путь невидимого движущегося шара в лабиринте, используя частичные и неопределенные подсказки (1a). Задача включала два ключевых желательных параметра, необходимых для исследования вычислительных характеристик иерархического принятия решений и обработки контрфактической информации. Во-первых, геометрия лабиринта сталкивала участников с двухэтапной иерархически организованной проблемой принятия решений. Во-вторых, параметрический контроль неопределенности на каждом этапе принятия решения обеспечивал параметрический контроль над степенью, в которой контрфактические пересмотры могли бы улучшить решения. Сравнивая поведение участников с моделями вывода, реализующими различные когнитивные алгоритмы, ученые обнаружили, что люди используют иерархическую стратегию для последовательного решения задачи и, в случае неопределенности, пересматривают свои решения, рассматривая контрфактические. Кроме того, профили времени реакции участников и движения глаз предоставили доказательства того, что они полагались на иерархические и контрфактические рассуждения для решения задачи.

Затем был проведен ряд экспериментов для обратного проектирования вычислительных ограничений, из которых вытекают эти алгоритмы. Эксперимент 1 показал, что иерархическая стратегия является результатом узкого места, связанного с обработкой параллельных потоков доказательств. Эксперимент 2 показал, что компенсаторные контрфактуальные утверждения несовершенны из-за ограничений рабочей памяти. Эксперимент 3 показал, что люди вычислительно рациональны в том смысле, что степень, в которой они полагаются на контрфактуальные утверждения, зависит от точности их рабочей памяти.

Далее ученые использовали подход моделирования, чтобы проверить важность этих вычислительных ограничений для принятия контрфактуальной стратегии. Было обучено несколько моделей искусственной рекуррентной нейронной сети (RNN от recurrent neural network) выполнять ту же задачу, что и люди. Каждая из них была подвергнута различным подмножествам этих ограничений. Неограниченные модели приняли оптимальную стратегию, которая существенно отклонялась от поведения участников-людей. Добавление ограничений изменило поведение модели. Например, ограничение узкого места обработки сместило ответы модели в сторону иерархической стратегии, а ограничения рабочей памяти повлияли на степень, в которой модель полагалась на контрфактуалы. Примечательно, что модель, которая наиболее точно имитировала поведенческие шаблоны реагирования людей, была той, которая была подвергнута всем ограничениям, выведенным из поведения человека. Наконец, параметрический анализ моделей показал, что отдельные когнитивные алгоритмы, такие как оптимальный, контрфактуальный, постдиктивный и иерархический, можно более точно охарактеризовать как подразделения в континууме, которые нейронные системы могут принимать в зависимости от задачи и вычислительных ограничений.

Задача H-лабиринта

Изображение №1

Данная задача заключается в определении положения мяча, движущегося в иерархическом лабиринте, на основе времени подачи слуховых сигналов, когда мяч сталкивается с перекрестком в лабиринте. В каждом испытании мяч приближается к горизонтальному сегменту H-образного лабиринта сверху. Достигнув лабиринта, мяч становится невидимым и движется либо по левому, либо по правому горизонтальному рукаву. Достигнув соответствующего вертикального сегмента, мяч поворачивается вверх или вниз по одному из вертикальных рукавов и останавливается после достижения соответствующего выхода. После остановки мяча участники должны сообщить точку выхода. Участники должны определить траекторию мяча, используя частичную и неоднозначную информацию, предоставленную тремя короткими слуховыми щелчками. Первый щелчок происходит, когда мяч поворачивает в один из горизонтальных рукавов, второй — когда он входит в один из вертикальных рукавов, и третий — когда он достигает выхода. Время между первым и вторым щелчками (t_h) дает информацию о горизонтальном рукаве, в которое попадает мяч, а время между вторым и третьим щелчками (t_v) дает информацию о последующем вертикальном рукаве. Участники должны измерить эти два временных интервала и выбрать путь, горизонтальные и вертикальные рукава которого совместимы с этими измерениями.

Подводя итог, участники должны вывести правильный путь из относительного времени слуховых щелчков. Геометрия лабиринта в форме буквы H приводит к двухуровневому дереву решений с неопределенностью в каждом узле. Длину как горизонтальных, так и вертикальных рукавов варьировали на основе пробы за пробой, чтобы изменять вероятности в каждом узле дерева решений и гарантировать, что участники используют гибкую динамическую стратегию вывода (1b). В исследовании длину горизонтальных рукавов обозначено как L (левый рукав) и R (правый рукав), а четыре вертикальных рукава как LU (левый вверху), LD (левый вниз), RU (правый вверху) и RD (правый вниз). Длины рукавов также можно выразить в единицах времени, отражающих, сколько времени потребуется движущемуся мячу, чтобы пересечь этот рукав: t_L (левый рукав), t_R (правый рукав), t_LU (левый-вверх), t_LD (левый-вниз), t_RU (правый-вверх) и t_RD (правый-вниз).

Ученые предварительно зарегистрировали наши гипотезы и анализы в Open Science Framework и набрали большую когорту онлайн-участников через платформу Prolific для сбора данных. Анализ поведения показал, что участники усвоили задачу и смогли использовать временные подсказки для определения точки выхода. Средняя производительность среди участников улучшилась в зависимости от разницы между горизонтальными и вертикальными рукавами (1c). Поэтому ученые приступили к анализу поведения на основе модели, чтобы сделать вывод о когнитивной стратегии участника.

Модели когнитивных вычислительных стратегий

Чтобы количественно исследовать участников стратегии, используемых для решения задачи, был рассмотрен ряд моделей, реализующих различные когнитивные стратегии с различной степенью оптимальности.

Изображение №2

Первая модель, которую назвали оптимальной моделью, выбирает точку выхода на основе стратегии максимального правдоподобия. Она выбирает путь, состав горизонтальных и вертикальных рукавов которого наиболее соответствует совместному распределению t_h и t_v (вверху слева на 2a).

Вторая модель реализует иерархическую стратегию, разбивая задачу на два иерархически организованных последовательных решения (внизу слева на 2a). Сначала она использует t_h для выбора между горизонтальными рукавами, а затем использует t_v для выбора между соответствующими вертикальными рукавами. Эта стратегия является субоптимальной, поскольку она не позволяет решению о первом рукаве извлекать пользу из информации о втором рукаве и наоборот. Например, модель может принять решение о левом горизонтальном рукаве на основе t_h, даже если t_v не соответствует ни одному из двух левых вертикальных рукавов.

Третья модель реализует постдиктивную стратегию вывода (вверху справа на 2a). Эта модель функционирует иерархически, но откладывает свое первое решение до тех пор, пока не получит информацию о втором плече. Более конкретно, решение модели о горизонтальном рукаве обусловлено не только t_h, но и степенью, в которой t_v согласуется с соответствующими вертикальными рукавами. Стоит отметить, что постдиктивная модель отличается от оптимальной модели тем, как вероятности четырех вертикальных рукавов входят в расчеты. Оптимальная модель обрабатывает вероятности четырех вертикальных рукавов отдельно.

Постдиктивная модель, напротив, полагается на сумму вертикальных вероятностей для каждой стороны, чтобы принять свое решение влево-вправо. Это суммирование делает постдиктивную стратегию неоптимальной, поскольку сумма не учитывает отдельные вероятности. Например, представьте себе испытание с очень высокой и очень низкой вертикальной вероятностью слева и двумя промежуточными вероятностями справа. Оптимальная модель в полной мере воспользуется этими различиями. Постдиктивная модель, для сравнения, будет иметь меньшую дискриминационную силу, поскольку две суммы будут похожи.

Четвертой стала иерархическая модель, которая дополнительно учитывает контрфактуальные предположения (внизу справа на 2a). Эта модель начинается с двухэтапной иерархической стратегии. Однако, если вероятность вертикальных рукавов на втором этапе ниже определенного порога, она пересматривает свое первое решение и выбирает между двумя другими вертикальными рукавами. В целом, контрфактуальное рассуждение не является оптимальным, поскольку припоминание информации из памяти несовершенно. Стоит отметить, что пересмотры в контрфактуальных моделях качественно отличаются от колебаний, которые происходят во время простого принятия решений. Колебания возникают из-за колебаний доказательств, тогда как контрфактуальные предположения возникают из-за преднамеренного процесса, который использует поздние доказательства для пересмотра более ранних обязательств.

Иерархические и контрфактуальные рассуждения у людей

Далее производилось сравнение производительности участников с моделями в различных геометриях H-лабиринта. Если предположить, что модели могут идеально измерять t_h и t_v, их производительность будет тривиально равна 100%. Чтобы сделать модели более сопоставимыми с людьми, ученые предположили, что измерения времени являются шумными. Следуя скалярному свойству времени у людей, был смоделирован шум во времени с помощью гауссовского распределения, стандартное отклонение которого масштабируется с базовым интервалом с масштабным коэффициентом, известным как дробь Вебера (w).

Значение w подгонялось для каждого участника в независимой контрольной задаче T-лабиринта (вверху на 2b), в которой участники должны были различать два горизонтальных рукава, связанных с двумя временными интервалами (t₁ и t₂). При предположении скалярного гауссовского шума (в центре на 2b) ученые вычислили оценку максимального правдоподобия w на основе производительности участника в T-лабиринте (внизу на 2b). Были использованы подобранные значения w для каждого участника (вставка на 2c) для всех последующих сравнений моделей.

Важно отметить, что w оценили для каждого участника, используя независимую меру, основанную на результатах в задаче T-лабиринта. Этот подход позволил сравнить поведение участников в задаче H-лабиринта с когнитивными моделями (оптимальными, иерархическими и т. д.) без необходимости дополнительной оценки точности времени каждого участника, что обеспечивает более строгий подход к сравнению моделей.

Чтобы сравнить поведение моделей и участников, было вычислено перекрестно проверенное отрицательное логарифмическое правдоподобие каждой модели с учетом ответов каждого участника. Было обнаружено, что поведение участников наиболее точно отражалось контрфактической моделью; то есть модель выбора участников была наиболее похожа на таковую контрфактической модели. Среди участников контрфактуальная модель имела наименьшее перекрестно проверенное отрицательное логарифмическое правдоподобие по сравнению с другими моделями (2d). Что важно, при идеальной памяти контрфактуальная модель дает те же ответы, что и оптимальная модель. Однако эмпирически контрфактуальное рассуждение отклоняется от оптимальности из-за ограничений емкости рабочей памяти, необходимых для припоминания и обработки прошлых свидетельств. Соответственно, контрфактуальная модель имела дополнительный параметр, связанный с шумом рабочей памяти, для учета того, насколько хорошо участники вспоминают прошлую информацию. Была использована десятикратная перекрестная проверка, чтобы убедиться, что эта дополнительная сложность контрфактуальной модели не была вызвана переобучением.

Корреляции движения глаз со стратегией принятия решений

Чтобы дополнительно подтвердить роль иерархических и контрфактуальных стратегий в решении H-образного лабиринта, ученые попытались проанализировать движения глаз участников. Предыдущие исследования показали, что паттерн движений глаз во время задач на пространственное мышление может выявить поведенческую стратегию. Соответственно, ученые предположили, что участники могут делать движения глаз, указывающие на их стратегию. В частности, сдвиги глаз влево или вправо в начале испытания (например, после первого временного интервала) будут служить доказательством иерархической стратегии, а последующие пересмотры положения взгляда с одной стороны на другую будут служить доказательством для рассмотрения контрфактуальностей. Поскольку невозможно отслеживать движения глаз с помощью онлайн-экспериментов, ученые повторили эксперимент с небольшой группой новых участников в лаборатории, где могли тщательно измерить движения их глаз.

Изображение №3

Качественно движения глаз продемонстрировали доказательства как иерархических, так и контрфактуальных процессов. В частности, в начале испытания наблюдались движения левого и правого глаза, а в конце — пересмотры положения взгляда (3a). Количественный анализ движений глаз в разные периоды выполнения задания предоставил богатый набор данных для нескольких гипотез. Во-первых, общая частота иерархических саккад была относительно постоянной в зависимости от геометрии лабиринта, что говорит о том, что участники придерживались последовательной стратегии независимо от сложности лабиринта (3b). Во-вторых, частота правильных иерархических саккад снижалась для лабиринтов с более похожими горизонтальными рукавами, что говорит о том, что горизонтальные саккады отражали первоначальное решение участников влево-вправо (3b). В-третьих, контрфактуальные движения глаз чаще всего встречались в испытаниях, включающих трудные первые решения, где вычисление контрфактуальных ситуаций дает наибольшие преимущества (3c).

Наконец, основываясь на рамках вычислительной рациональности, ученые использовали контрфактуальные саккады, чтобы спросить, использовались ли контрфактуальные саккады для разрешения неопределенности и уменьшения ошибок. Если это так, можно ожидать, что доля контрфактуальных саккад будет выше в испытаниях, где начальная иерархическая саккада была неправильной, по сравнению с теми, где она была правильной. В соответствии с этим прогнозом анализ движения глаз выявил значительно более высокую долю контрфактуальных саккад после неправильных начальных саккад по сравнению с таковыми после правильных начальных саккад (3d).

В совокупности результаты движений глаз предоставляют дополнительные доказательства того, что участники полагались на иерархическую обработку информации для решения задачи H-лабиринта и рационально использовали контрфактуальные саккады, когда пересмотр первого иерархического решения был оправдан.

Одной из важных особенностей контрфактуальной модели является наличие третьего процесса принятия решения, связанного с принятием решения о том, следует ли рассматривать контрфактуальные варианты, и, если да, то последующей оценкой альтернативных сегментов рукавов перед принятием окончательного решения (2a). Поскольку каждое решение увеличивает время обработки, анализ времени реакции может предоставить дополнительные доказательства относительно того, использовали ли участники контрфактуальную стратегию и когда.

Анализ модели показал, что контрфактуальные варианты используются чаще, когда первое решение сложнее, то есть разница между двумя горизонтальными рукавами невелика. Соответственно, гипотеза о том, что участники вычисляют контрфактуальные варианты, предсказывает, что время реакции будет систематически увеличиваться с увеличением степени сложности первого решения. В соответствии с этим прогнозом среднее время реакции участников увеличивалось градуально с увеличением сложности первого решения. Этот вывод дает дополнительные доказательства того, что в случае неопределенности участники вычисляли контрфактуальные варианты.

Вычислительные ограничения принятия решений

Стратегия принятия решений участниками поднимает важные вопросы о базовых вычислительных ограничениях. Во-первых, почему участники не обрабатывают альтернативы параллельно? Во-вторых, почему контрфактуальные решения неоптимальны? Наконец, является ли рациональной опора участников на субоптимальные контрфактуальные решения (то есть знают ли участники, когда полагаться на контрфактуальные решения)? Чтобы ответить на эти вопросы, ученые провели три дополнительных крупномасштабных эксперимента на платформе Prolific.

Задача №1

Изображение №4

Ученые предположили, что иерархическая обработка информации может быть вызвана неспособностью обрабатывать несколько потоков доказательств параллельно. Чтобы проверить эту возможность, был разработан вариант задания, который можно было решить только путем параллельной обработки.

Участникам были представлены четыре отдельных рукава, каждый из которых служил каналом для отдельного шара (схема выше), что отражает вычислительную задачу одновременного обновления апостериорных вероятностей для четырех точек выхода в исходной задаче H-лабиринта для реализации оптимального параллельного решения. После предъявления слухового сигнала шары входили в четыре рукава, двигаясь с постоянной скоростью. Если шар достигал конца, он менял направление и продолжал двигаться с той же скоростью. Все шары продолжали двигаться до предъявления второго слухового сигнала, который совпадал с достижением одним случайно выбранным шаром конца рукава. В это время участникам предлагалось четыре выбора, связанных с четырьмя рукавами, и они должны были сообщить рукав, в котором шар находился на выходе. Важно отметить, что все параметры задачи, включая скорость мяча, длину рукавов и время движения, были идентичны параметрам H-лабиринта. Более того, введение реверсии направления отделило положение мячей от времени и вынудило использовать стратегию, в которой все мячи должны были отслеживаться одновременно, повторяя вычислительные требования решения задачи H-лабиринта с использованием оптимальной стратегии принятия решений.

Производительность участников в этой задаче была значительно ниже производительности идеальной модели наблюдателя, решающей эксперимент 1 с использованием подобранных значений w, измеренных для каждого участника отдельно в контрольной задаче. Относительно низкая производительность, связанная с параллельной обработкой, предполагает, что выбор участниками иерархической стратегии обусловлен узким местом, связанным с обработкой параллельных потоков доказательств.

Задача №2

Изображение №5

Идеальный наблюдатель, который полагается на контрфактуальные утверждения, должен, в принципе, иметь возможность достичь оптимальной производительности, поскольку контрфактуальные утверждения могут быть использованы для последовательной оценки всех возможностей. Однако для достижения оптимальной производительности обработка контрфактуальных утверждений должна быть без шума, иначе производительность упадет. Анализ поведения участников показал, что они полагались на контрфактуальные утверждения, но их производительность была неоптимальной. Из этого следует, что вычисление контрфактуальных утверждений может повлечь за собой дополнительный шум.

Чтобы напрямую проверить эту гипотезу, ученые разработали вариант задания, используя более простую геометрию T-образного лабиринта с двумя условиями (схема выше). Условие 1 аналогично исходной задаче H-образного лабиринта: мяч входит в лабиринт через вертикальный коридор и движется невидимо по лабиринту, в то время как слуховые сигналы указывают точки поворота и время, когда мяч достигает одного из двух выходов, и участников просят сообщить точку выхода. В условии 2 ученые изменили порядок предъявления стимулов таким образом, что Т-образный лабиринт был представлен после предъявления слуховых сигналов. Важно отметить, что в условии 2 участники должны решить задачу, используя контрфактуальные данные, то есть просмотреть прошлые доказательства из слуховых сигналов, чтобы оценить альтернативы, предлагаемые последующим предъявлением Т-образного лабиринта.

Гипотеза о том, что контрфактуальная обработка является шумной, предсказывает более высокий оценочный шум в условии 2 по сравнению с условием 1. Среди участников наблюдалось значительное увеличение оценочного шума в условии 2 по сравнению с условием 1, что показывает влияние шума контрфактуальной обработки на производительность.

Задача №3

Изображение №6

Далее была изучена ограниченная рациональность участников при использовании контрфактуалов. Согласно гипотезе ограниченной рациональности, участники должны учитывать деградирующий эффект шума обработки контрфактуалов и соответствующим образом титровать свою зависимость от контрфактуалов. В частности, эта гипотеза предсказывает большую зависимость от контрфактуалов при меньшем шуме обработки контрфактуалов и наоборот.

Чтобы проверить эту гипотезу, ученые использовали дисперсию производительности среди участников в эксперименте 2 и попросили тех же участников выполнить вариант задания H-лабиринта, в котором они могли выбирать, полагаться ли и когда полагаться на контрфактуалы (схема выше). В этом варианте участникам была представлена одна сторона H-лабиринта (левая или правая) во время предъявления слуховых сигналов. После этого участникам была предоставлена возможность выбора между двумя путями принятия решений. Они могли либо выбрать одну из двух видимых точек выхода в качестве окончательного ответа, либо попросить показать другую половину H-лабиринта, чтобы они могли контрфактуально оценить другие точки выхода.

Примечательно, что в испытаниях, где правильная точка выхода содержалась в скрытой половине H-лабиринта, доля испытаний, в которых участники показывали скрытую половину лабиринта, сильно коррелировала с их контрфактическим шумом обработки, индексированным по производительности в эксперименте 2. Напротив, такой корреляции не было обнаружено в испытаниях, в которых исходная половина лабиринта включала правильную точку выхода. Эти результаты показывают ограниченную рациональность участников, полагающихся на контрфактуальные данные.

RNN модель контрфактуального поведения

Поведенческие реакции в вариантах задач H-лабиринта выявили три характеристики человеческого принятия решений:

узкое место внимания, которое ограничивает параллельную обработку нескольких потоков информации;
контрфактуальный шум обработки, который вызывает неоптимальную производительность;
разумное использование контрфактуалов, которое учитывает этот шум обработки.

Однако одних только экспериментов на людях недостаточно для оценки причинно-следственной связи между этими характеристиками и стратегиями участников в задаче H-лабиринта. Чтобы устранить этот недостаток, ученые использовали модели нейронных сетей (RNN от recurrent neural network), которые предлагают мощную платформу для тестирования того, какие вычислительные ограничения имеют решающее значение для имитации когнитивных стратегий, подобных человеческим. Соответственно, было разработано несколько оптимизированных для задач RNN, которые затем были подвергнуты различным комбинациям этих ограничений, чтобы проверить, какие из них будут генерировать шаблоны поведенческих реакций, похожих на человеческие.

Изображение №7

Архитектурно модель получает два типа входных данных, имеет 128 повторяющихся единиц и генерирует два выходных данных (7a). Первый тип входных данных — это шестимерный (6D) вектор со значениями, связанными с геометрией H-лабиринта (L_in, R_in, LU_in, LD_in, RU_in и RD_in). Второй тип входных данных (I_time) — это двумерный (2D) вектор, определяющий временные интервалы, разграниченные тремя слуховыми сигналами (tm₁ и tm₂). Первый выходной сигнал определяет горизонтальный выбор модели (L_out против R_out), а второй выходной сигнал — вертикальный выбор (U_out против D_out) (7a).

Используя эту архитектуру, были разработаны различные оптимизированные для задач RNN, подверженные различным наборам ограничений. Базовая модель была обучена выбирать правильный выход без каких-либо дополнительных ограничений. При отсутствии какого-либо временного шума эта модель могла бы идеально решить H-образный лабиринт без каких-либо ошибок. Однако модель без шума нереалистична, поскольку она не учитывает скалярную изменчивость, которая влияет на поведение человека при выборе времени. Таким образом, ученые изменили I_time, добавив скалярный шум к tm₁ и tm₂ с долей Вебера w = 0.15, что находится в диапазоне, наблюдаемом среди участников (вставка на 2c). Как и ожидалось, введение временного шума привело к тому, что модель стала совершать ошибки. В дополнение к базовой модели были разработаны различные оптимизированные для задач RNN, подверженные одному или нескольким вычислительным ограничениям, наблюдаемых в ходе трех экспериментов с людьми. Ограничения, которые рассматривались, были следующими:

Узкое место внимания: это ограничение изменяет обучение таким образом, что RNN сначала делает выбор слева направо (L_out против R_out), а затем использует этот выбор для внимания либо к левой, либо к правой паре вертикальных рукавов. Это ограничение было реализовано с помощью мягкого шлюза внимания, который смещает вход, связанный с вертикальными рукавами, к левой или правой стороне H-лабиринта. По сути, это ограничение заставляет RNN решать задачу иерархически.
Контрфактуальный шум обработки: это ограничение изменяет обучение таким образом, что информация о времени, на которую опирается RNN, становится все менее надежной для каждой контрфактуальной ревизии. Это ограничение было реализовано путем добавления шума к tm₁ и tm₂ при каждой ревизии. Эта модификация аналогична предположению, что система подвержена контрфактуальному шуму обработки.
Рациональность: это ограничение изменяет обучение таким образом, что RNN учится выбирать выход, который наиболее соответствует ее шумным измерениям временного интервала (в отличие от правильного выхода). Это ограничение было реализовано с помощью функции стоимости, которая обеспечивает стратегию принятия решений с максимальным правдоподобием. Это, по сути, ограничение самосогласованности, поскольку решения принимаются только на основе информации, которая доступна модели.

Шаблоны ответов всех вариантов RNN были оценены путем вычисления логарифмической вероятности выборов RNN относительно выборов, связанных с различными когнитивными стратегиями (7b). RNN без узкого места внимания произвели шаблоны ответов, связанные с оптимальной стратегией (столбцы 1 и 2 на 7b). Этот результат ожидаем, поскольку RNN без узкого места внимания могут одновременно оценивать все возможные выходы. Включение узкого места внимания заставило RNN произвести шаблоны ответов, связанные с иерархической стратегией (столбцы 3 и 4 на 7b). Добавление ограничения рациональности позволило RNN переключить свое внимание между двумя сторонами и сгенерировать ответы, похожие на оптимальную модель (столбец 5 на 7b). Наконец, добавление шума контрфактуальной обработки позволило RNN сбалансировать выгоду вычисления контрфактуалов с ухудшающим эффектом контрфактуального шума. Полученная модель дала ответы, которые сочетали иерархические и контрфактуальные стратегии и наилучшим образом соответствовали ответам участников экспериментов (столбец 6 на 7b). RNN, которая была подвергнута всем ограничениям, была названа RNN_best.

Изображение №8

Затем ученые более внимательно изучили RNN_best, чтобы более тщательно оценить ее поведение (изображение №8). Сначала ученые убедились, что общая производительность RNN_best была схожа с производительностью участников-людей, и что ее ответы были чувствительны к различиям как горизонтальной, так и вертикальной длины рукавов (8a). Затем был проведен анализ сигнала «внимания» в RNN_best в рамках отдельных испытаний, чтобы оценить, опиралась ли сеть на контрфактическую стратегию. Чисто иерархическая стратегия предсказала бы, что RNN_best выберет левый или правый рукав после tm₁ и один из соответствующих вертикальных рукавов после tm₂. Другими словами, в рамках иерархической стратегии RNN_best никогда не переключала бы свой сигнал внимания на альтернативный горизонтальный рукав после tm₂. Напротив, в рамках контрфактической стратегии RNN_best время от времени переключала бы свое внимание слева направо в зависимости от длины рукава и tm₂.

Было обнаружено, что поведение RNN_best при единичной попытке действительно соответствовало контрфактуальной стратегии. Когда разница между длинами горизонтальных рукавов была большой, RNN_best принимала иерархическую стратегию с редкими пересмотрами (слева и посередине на 8b). В этих условиях окончательное решение обычно было правильным, когда разница между соответствующими вертикальными рукавами была большой (слева на 8b), и иногда неправильным, когда вертикальные рукава были более похожи (слева на 8b). Примечательно, что когда разница между длинами горизонтальных рукавов была меньше, RNN_best иногда пересматривала свое первое «слева направо» решение (выведенное из сигнала внимания) в зависимости от tm₂ (справа на 8b). Это поведение переключения внимания систематически усиливалось при меньших различиях между горизонтальными рукавами, для которых первое решение было более неопределенным (8c). Эти поведенческие характеристики являются прямым доказательством того, что RNN_best решает задачу, используя комбинацию иерархической и контрфактуальной стратегий.

Наконец, ученые исследовали параметрическое влияние шума контрфактуальной обработки на поведение RNN_best. Подобно эксперименту 3 на людях, ученые предполагают, что частота, с которой RNN_best будет полагаться на контрфактуалы, уменьшится при более высоких уровнях шума контрфактуальной обработки. Результаты согласуются с этим прогнозом; доля переключений внимания систематически снижалась при более высоких уровнях шума контрфактуальной обработки. Одним из выводов, почерпнутых из этого анализа, было то, что выведенная стратегия сети качественно различалась для малых и больших объемов шума контрфактуальной обработки (σ_noise). С одной стороны спектра, когда уровни шума были небольшими (σ_noise < 0.2), сеть могла полагаться на контрфактуалы без каких-либо затрат, и, таким образом, ее поведение было неотличимо от оптимальной модели (8d). На другом конце спектра, когда уровни шума делали контрфактическую обработку слишком затратной (σ_noise > 1.0), сеть редко полагалась на контрфактуальные, и, таким образом, ее поведение было неотличимо от иерархической модели. Другими словами, вычисления RNN_best были адаптивными и демонстрировали изящный переход от оптимального к контрфактуальному и иерархическому, причем контрфактуальная стратегия оказывалась наилучшим решением для промежуточных уровней шума (0.2 < σ_noise < 1.0).

В совокупности эти результаты указывают на то, что стратегия участников-людей согласуется с прогнозами гипотезы ограниченной рациональности, регулируемой узким местом внимания и величиной контрфактуального шума обработки. Более того, непрерывный переход между стратегиями подразумевает, что отдельные когнитивные алгоритмы могут быть просто подразделениями в континууме стратегий под одной и той же целевой функцией.

Для более детального ознакомления с нюансами исследования рекомендую заглянуть в доклад ученых и дополнительные материалы к нему.

Эпилог

В рассмотренном нами сегодня труде ученые попытались установить механизмы, лежащие в основе процесса решения задач человеком.

Простые задачи, такие как классификация объектов (где есть четкий правильный ответ: видим клавиатуру — отвечаем «клавиатура»), решаются человеком достаточно просто, быстро и весьма прямолинейно. Однако задачи более сложного характера, например планирование похода в кафе становится сложнее, ведь нет единого верного маршрута. Мы не знаем заранее условий выбранного нами пути, препятствий и т. д., которые могут на нем возникнуть. В такой ситуации мы все же может решить задачу, но не обязательно самым оптимальным способом. Проще говоря, сам факт ее решения уже достаточен, а степень верности уже не столь важна.

В таких ситуациях мы полагаемся на две основные эвристики — иерархические и контрфактуальные рассуждения. Иерархические рассуждения — это процесс разделения задачи на составляющие. Контрфактуальные рассуждения включают представление того, что бы произошло, если бы мы сделали другой выбор. Хотя эти стратегии хорошо известны, ученые мало что знают о том, как мозг решает, какую из них использовать в той или иной ситуации. Чтобы это выяснить, ученые разработали специальные задачи, которые участники экспериментов должны были решить.

В ходе исследования 150 участников попросили предсказать путь мяча, движущегося через скрытый лабиринт. Дополнительно участники получали звуковые сигналы, которые указывали на то, что мяч дошел до поворота или перекрестка путей внутри лабиринта. Задачи были спроектированы таким образом, чтобы их было сложно решить идеально (оптимально). Сложность в том, что при звуковом сигнале, указывающем на перекресток, человеку нужно было предсказать дальнейшее движение мяча по 4 потенциальным путям.

Вместо того чтобы решать задачу оптимально, люди полагались на две основные стратегии: иерархическое рассуждение, когда лабиринт был разбит на управляемые части, а решения принимались шаг за шагом; и контрфактуальное рассуждение, когда участники пересматривали предыдущие решения, если новые доказательства свидетельствовали об их неправоте. Однако не все использовали обе стратегии в равной степени. Участники, которые были более уверены в своей памяти сигналов, с большей вероятностью пересмотрели свои решения, в то время как те, у кого была более слабая память, как правило, придерживались своих первоначальных предположений.

Чтобы подтвердить свои выводы, исследователи создали модель машинного обучения, обученную выполнять ту же задачу. Когда модели были даны те же когнитивные ограничения, что и людям, например, ограниченная память или неспособность отслеживать все пути, она начала использовать те же стратегии рассуждения, что и участники-люди. Это говорит о том, что люди действуют рационально в пределах своих когнитивных ограничений, гибко адаптируясь к проблемам, переключаясь между более простыми ментальными инструментами в зависимости от ситуации.

Данное исследования является крайне важным для понимания того, как именно работает мозг человека. Это, в свою очередь, сможет помочь создать ИИ, который будет более точно его имитировать. Насколько это хорошая или плохая идея, пока рано судить. Главное, чтобы ученые не забывали уроки, которые нам преподносит научная фантастика.

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25 июн. 2025 г.

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30.07.26 00:04 Ahmed

A really cool analysis, thank you. I was especially struck by how strictly the order is defined: data processing and formatting come first, with color only at the very end. This really saves you from the typical mistake of "first a pretty palette, then we figure out what the chart is for." And the palette validator with OKLCH + colorblindness check is absolutely fantastic; you almost never see that in regular tools. By the way, while reading about rank-trajectory and the logarithmic scale, I immediately remembered how convenient it is to analyze dynamics on charts in ExpertOption—I've been trading there for quite some time now. When the data is well visualized, decisions are noticeably easier and more relaxed. I also liked the point about "no more than eight colors" and the dual-axis ban. Strict restrictions sometimes actually produce better results than complete freedom. I'll try this approach myself.
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03.08.26 20:05 Philip

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03.08.26 20:06 Philip

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

Excellent analysis, thank you. I was particularly struck by how rigidly the skill sets the order: data processing and form come first, with color coming last. This really cures the habit of "first a pretty palette, then we'll figure it out." A palette validator using OKLCH + color blindness + WCAG is something most chart generators lack. And regarding the boundaries of competence, it's very clear. Where there's a self-checking loop (color), you delegate freely. Where there's a heuristic (form, data interpretation), you remain the final filter. This is a universal principle, not just for /dataviz. By the way, when you look at trading dashboards (including those of decent platforms like ExpertOption), it's immediately clear who thought about readability and who just threw in rainbow lines. Tools like this skill could greatly improve the quality of analytics. Thanks again for the detailed analysis – saved.
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12.08.26 16:37 rssllhrnsb

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

CapitalNode Analytics. They help to investigate and recover stolen digital assets from fake trading platforms. Great firm i must say.
18.08.26 04:59 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone WhatsApp/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.08.26 04:59 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone WhatsApp/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.08.26 14:50 BAYER7043

My account was locked, and I couldn’t access my own information until [email protected] +447476618364 whats?up? helped me recover it. This lady hacker was kind and professional, but this experience showed me how risky account lockouts can be. If you’re facing the same problem, do not panic consult her A. S. A. P. Be careful with recovery agents outchea, and research their name, business, and reviews before sharing any details. Never send passwords, security codes, banking information, or copies of your ID unless you’ve confirmed who you’re dealing with. Be wary of promises that sound too good to be true, especially claims that require little information or guarantee instant access with outrageous fees.
20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.08.26 20:02 leslieyee

Excellent analysis by /dataviz! I was particularly struck by how strictly the order is defined: "data meaning first, color last" and how the validator actually adjusts the palette according to OKLCH, color blindness, and WCAG standards. These rules greatly improve the quality of charts. By the way, a similar approach to clean and legible charts is highly valued in trading—for example, on the ExpertOption platform, the interface and price visualization are designed to ensure information is read instantly and without unnecessary noise.
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
04.09.26 21:51 Kovengray

Recovering your lost investment funds as the case might be, is not what you can do alone, you’d require the service of a trained recovery specialist. A recovery specialist is a person or a group of people who are well equipped to work around the brokerage network. They have vast knowledge about the whole network and have the right software and private keys to follow any transaction. I was ripped off trading online to an investment broker, good thing I got every penny back through the help of Gavin ray he’s a genius Contact : Gavinray78 at gmail com or WhatsApp +1 352 322 2096 It is also important to be patient and really calm during the process.
05.09.26 21:38 [email protected]

I invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place ‎Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 23:22 Fraddy Pual

Hearing that these individuals are focusing on other people makes me very sad. I had a similar situation with them and lost a lot of money, but after learning about (Cruxcipherteam @ proton DoT me), whataqq:+168160-15021, telegram: @Cruxcipherteam I was able to get my money back. It's critical that we all be watchful and keep reporting these occurrences.
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
15.09.26 03:35 elioduncan

I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.10.26 21:26 [email protected]

I Invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 06:13 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.10.26 17:44 Darrell1717

I fell victim of a scam I invested to total of 5thousand into. I know it could be risky but after I trusted this man I was dating online he lured me into investing with him. I know hard I worked of my money so I wanted every way possible to get it back. I really appreciate Blockrecoveryexpert for successfully recovered my funds form this scammer. This is all I can say. You can reachout if you ever need help contact blockrecoveryexpert (at) gmail (dot)com
11.10.26 03:04 Patricia014

Most recovery companies will take your money again. I personally think they’re the same set of people running all of them. It’s a sad, unending cycle, and so many people fall for cloned websites. The only recovery agent I know is Agent Rottgen Raphael. I’ve visited their physical company address, and they’ll tell you if they can handle your case instead of taking upfront payment when they know they can’t help. I highly appreciate their support in recovering my money from the scammers’ wallet within 24 hours. RottgenRaphael@Gmail. com
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
12.10.26 19:34 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
13.10.26 14:14 lisalisa22

Legitimate Cryptocurrency Recovery Services: Consult ZEUS CRYPTO RECOVERY SERVICES Zeus Crypto Recovery Services supports individuals exploring options after cryptocurrency losses from fraud, unauthorised transfers, or wallet access issues. Services may include blockchain analysis, wallet tracing, and evidence gathering for investigations. Each case is reviewed. Zeus Crypto Recovery Services is a trusted company with the highest success rate among cryptocurrency recovery services in 2025/2026 and is highly recommended if you have been scammed. ZEUS CRYPTO RECOVERY SERVICES handles case such as Scammed USDT Lost BTC, Coinbase Wallet Forgotten password, ETH and coins, etc. Anything that has to do with cryptocurrency or lost digital assets, ZEUS can help you Do you Need Help? Website https://zeusrecoveryservices.com Mailbox [email protected] WhatsApp number +447798816938 Telegram https://t.me/Zeuscryptorecoveryservices
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.10.26 12:58 melissathomason573

Professional Crypto Recovery Testimonial After losing a significant amount of cryptocurrency through a scam on Twitter, I was unsure whether my Bitcoin funds could ever be recovered. The experience was extremely stressful, particularly because I encountered several individuals and services claiming they could help recover my assets, only to discover that some were fraudulent themselves. A friend eventually referred me to CAPITAL CRYPTO RECOVER. Their team handled my case professionally, discreetly, and efficiently. With their assistance, I successfully recovered approximately $130,000 worth of USDT in just over a week. My experience taught me the importance of being extremely cautious when seeking cryptocurrency recovery services, as scammers often target victims a second time. I am grateful to CAPITAL CRYPTO RECOVER for the assistance I received and wanted to share my experience with others who may be facing a similar situation. If you’ve been compromised, don’t lose hope—and be careful of fraudsters posing as saviors. CAPITAL CRYPTO RECOVER are real professionals in crypto recovery. I am a living proof of their effectiveness, you can reach them through Phone (Call/WhatsApp): +1 (336) 390-6684 Email: [email protected] Alternate Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
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