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Эпизод 1. Трансформер идёт в Atari Frostbite

Какие информационные процессы протекают в нашем мозгу? Какие цели он преследует? Какой моделью данных и какой алгеброй можно передать его работу? Почему мы подвержены разным когнитивным искажениям? Зачем нам сон и можно ли без него? Как использовать наш мозг на полную катушку?

Меня зовут Михаил Кочеров и я хочу понять, как работает наш мозг. А что значит понять? Вот знание о морфологии мозга или о его развитии от момента зачатия до момента смерти — это понято или нет? Каждому своё. Для меня понять — значит, уметь воспроизвести пусть и в упрощённом виде. Постичь ключевые механизмы и знать, как из них собрать работающую систему, воспроизводящую интеллектуальные свойства мозга в целостном виде.

Люди, птицы, рыбы и т.д. — это автономные интеллектуальные субъекты с мозгом. Познают мир в меру своих возможностей, адаптируются к нему, вырабатывают оптимальное поведение на основе проб, ошибок и редких, но столь желанных наград. Это не что иное, как обучение с подкреплением, или Reinforcement Learning (RL). Отсюда идея: разрабатываем RL-агента для нетривиальной проблемы и по ходу сталкиваемся с теми же трудностями и задачами, с которыми столкнулась живая природа, развивая мозг. А следовательно, решая эти задачи, познаём и сам мозг, его устройство и механизмы.

Такой нетривиальной RL-проблемой видится разработка агента, который научается играть в компьютерные игры. Агент должен сам разобраться с тем, как воспринимать внешнюю среду (например, видеопоток), постичь внутреннюю логику игр, выработать политику поведения для каждой и поддерживать память, чтобы не забыть прошлый опыт. Для этих экспериментов шикарно подходит Atari Learning Environment (ALE) [8][9] + Gymnasium [10].

Frostbite Box Art
Обложка игры Frostbite (1983). Права на изображение принадлежат Activision. Использовано в ознакомительных (информационных) целях. Источник: Wikipedia

В ALE много разных игр: от простых аркадных (типа Breakout) до стратежно многоходовых (типа Montezuma’s Revenge). Я выбрал Atari Frostbite. Эскимос должен прыгать по льдинам, уворачиваться от врагов, собирать ледяной домик (иглу) и потом в нём прятаться, чтобы пережить заморозки. Игра очень динамичная: враги меняют своё поведение и скорость, форма и движение льдин мутируют, день сменяется ночью и наоборот, и т.д. Награда распределена неравномерно: есть небольшие очки за конкретное действие (съел рыбу, собрал кирпичик иглу), но гораздо больше обламывается агенту, когда он проходит уровень. Налицо нестационарная игра с разреженной наградой и иерархическим целеполаганием — всё как в жизни!

Итак, план такой:

№

Цель

Почему

1

Агент проходит 1 уровень Atari Frostbite

освоение базовых механик игры и иерархического целеполагания

2

Агент проходит 5 уровней Atari Frostbite

первая сильная нестационарность (полярный день → полярная ночь)

3

Агент проходит 10 уровней Atari Frostbite

так далеко я сам не проходил

4

Агент зарабатывает 136k+ очков в Atari Frostbite (примерно 25+ уровней)

амбиция

5

Агент освоил другие Atari игры

навык обобщения и сохранения опыта

6

Агент умеет играть в Doom/Starcraft

другой класс игр

Важная оговорка

Вопрос. А почему бы не взять какую-нибудь LLM типа GPT-6 Astra или Claude Sonnet для получения такого играющего агента?

Ответ. Разные цели. Если надо решить задачу здесь и сейчас для бизнеса, то так и надо сделать — взять готовый инструмент и прикрутить его. Только тогда не получится проникнуть в суть происходящих процессов. Мы просто сыграем в интеграцию а-ля CRUD: возьми данные из игры, передай в модель (чёрный ящик), верни ответ обратно и не расплескай по пути.

Хотя сейчас даже и CRUD не нужен — Claude Code или Openclaw сами во всём разберутся, и останется только объявить себя владельцем результата. В этом же путешествии хочется увидеть и познать скрытые механизмы мозга, а раз так, то придётся идти более тернистым путём и обдирать себе бока =)

Почему 136k+ очков?

Frostbite — вытоптанная площадка в RL теме и включена в известные бенчмарки:

  • Atari-57 - “насколько ты силён, если учиться тебе не жалко?” В пуле 57 игр и щедрый бюджет: стандартный протокол даёт 200 млн кадров на игру (~920 часов игры), а чтобы обойти человека на всех играх, уходят на миллиарды кадров. Мерят потолок мастерства: до чего агент дотянется, если дать ресурсов от души.

  • Atari-100k - “насколько ты быстро соображаешь, если данных почти нет?” В пуле 26 игр и всего 100 000 шагов или два часа реальной игры, один вечер за приставкой. Мерят сэмпл-эффективность: сколько мастерства выжимается из крох опыта.

Свежие цифры такие:

Бенчмарк

Модель

Бюджет, кадров

Бюджет, шагов*

Очки на Frostbite

Atari-100k

26 игр, «спринт» 100k шагов (≈2 ч игры)

DreamerV3

400 тыс.

100 тыс.

909

EfficientZero V2

400 тыс.

100 тыс.

1 136,3

BBF

400 тыс.

100 тыс.

2 384,8

Человек (средний, ≈2 ч игры)

400 тыс.

100 тыс.

4 334,7

Atari-57

57 игр, «марафон» разный бюджет

Agent57

1 млрд

250 млн

980,2

Agent57

90 млрд

22,5 млрд

507 775,7

MEME (200× faster)

200 млн

50 млн

136 691,8

MEME (200× faster)

1 млрд

250 млн

526 239,5

* шагов = кадров / 4 (frameskip=4)

У меня нет своего датацентра с сотней другой жирных GPU, поэтому бюджет в миллиарды кадров для меня закрыт. А вот про 200 млн ещё как-то можно думать.

Короче, побить SOTA модель MEME - заманчивая абмиция!

Ещё важная оговорка

Вопрос. А почему тогда не взять за базу ту же MEME и не развить её?

Ответ. Это тоже срезание углов, только более тонкое, чем если поручить работу современным LLM. Важно самому пройти путь от начала и до конца, иначе проблемы будут замаскированы уже готовыми ответами. Надо столкнуться с проблемами, прочувствовать их, попытаться самому решить - только так идёт познание. Как говорил Х.Д. Борхес: “Нет такого интеллектуального упражнения, которое в итоге не принесло бы пользы” (“Пьер Менар, автор «Дон Кихота»”).

При этом отказываться от заимствования идей или запчастей тоже глупо - дажи при оголтелом заимствовании в конце концов всё равно выйдет как-то своя история =)

Азбука PPO

Будем использовать Proximal Policy Optimization (PPO) [1] — популярный RL-алгоритм. Большой плюс в том, что он хорошо масштабируется, и цикл обучения получается быстрее, чем, например, у DQN [2].

PPO и DQN как сборка пазла

DQN — бережливый: каждую деталь (шаг в игре) кладёт в коробку и возвращается перебирать её снова и снова, поэтому выжимает из деталей больше. PPO — расточительный: схватил горсть деталей, разложил, а старые выбросил, чтобы взять свежие. Когда что важно:

  • Дорогой шаг (реальный робот, медленный симулятор, платный API) → лучше выбрать DQN, SAC (off-policy).

  • Дешёвый и параллелизуемый шаг (Atari, быстрые симуляторы) → выигрывает PPO (on-policy) с массовой параллельностью. Нам подходит.

Схема работы PPO
Схема работы с PPO алгоритмом

Для работы PPO нам нужна сама модель (агент) и батарея игровых окружений (инстансов игры). Чем больше батарея, тем быстрее получится собрать траектории. Например, 32 одновременных окружения — хорошее стартовое число. Ключевые методы в интерфейсе окружения очень простые:

  • reset() — сбросить игру (типа нажали кнопку “Reset” на игровой приставке). Делается в самом начале, или когда случился game over, чтобы начать заново.

  • step(action) — выполнить очередной шаг. 99% времени будет вызываться этот метод.

Каждый из этих методов возвращает observation — то, что игрок должен увидеть на экране. Для ALE — это RGB-картинка размером 210x160. Т.к. у нас N окружений, то и на вход надо подать массив из N действий, а взамен мы получим N картинок.

Вместе с observation метод step ещё возвращает награду (reward) и флаг done — закончилась ли игра или нет. Для Frostbite reward будет ненулевым, когда выполняется какое-то полезное промежуточное действие (например, агент добыл кирпичик для иглу), или когда агент прошёл уровень и началась его зачистка (таймер времени убавляется, иглу разбирается, очки начисляются). В остальное время reward равен нулю, т.е. агент что-то делает, но ничего не получает.

На стадии раскатки мы берём и прогоняем нашу модель шаг за шагом через все эти окружения одновременно. На вход модели подаём наблюдение (что сейчас на экране). Для этого у модели должен быть какой-то входной интерфейс по приёму картинок — Encoder. На выходе модель должна выдать action (какую кнопку надо нажимать, например, UP или FIRE) и value (сколько в данной игре получится заработать очков). Для этого в модели должны быть выходные интерфейсы Action Head и Value Head. По сути мы делаем так, чтобы агент, каким бы глупым или умным он ни был, играл в игру и при этом на каждом шаге возвращал оценку очков, которые он может заработать. В итоге накапливаются кортежи: (наблюдение, действие, награда, value, done). Набор кортежей называется траекторией. Если игра в каком-либо окружении закончилась, мы эту игру сбрасываем и всё заново — получается непрерывный майнинг траекторий.

Вместе с траекториями на раскатке ещё рассчитываются advantages — то, насколько исполненное действие оказалось лучше ожиданий агента. Например, агент думал, что, исполнив действие A, получит 10 очков награды, а получил 50. Значит, advantages будет это учитывать в виде положительного коэффициента. В обратную сторону тоже — если исполненное действие принесло меньше, чем планировалось, то коэффициент будет отрицательным.

Раскатка закончилась, переходим к оптимизации. Здесь берём и за несколько эпох пробегаемся по накопленным траекториям и advantages. Выходной интерфейс агента Action Head выдаёт вектор. Каждый элемент вектора соответствует какой-то кнопке (FIRE, UP, DOWN и т.д.). Поэтому размерность вектора равна количеству кнопок, которое игра поддерживает, например 18 или 6. Значение элемента вектора — это ненормализованная вероятность (логит). Поэтому цель оптимизации так крутить эти логиты, чтобы наиболее вероятным становилось то действие, которое соответствует более высокому advantage. Или наоборот, если advantage отрицательный (т.е. плохое было действие), то надо крутить в обратную сторону. Эти advantages — как маяк: показывают, куда надо крутить политику, чтобы агент действовал лучше и лучше. Но сильно резко крутить логиты тоже нельзя, т.к. в RL резкие изменения политики могут её необратимо поломать — менять политику нужно мелкими шагами. Поэтому в PPO встроен “предохранитель”, или clipping [1]. Мы насильно обрезаем направление изменения, например коэффициентом 0.2.

Чтобы правильно считать advantages, нужно правильно считать value. На оптимизации мы одновременно с Action Head оптимизируем и Value Head. Для этого берутся value из кортежа траектории и сопоставляются с тем, сколько реально агент заработал по траектории. Это расхождение между “агент думал, что заработает” и “агент по факту заработал” используется для уточнения Value Head.

Интерфейсы Encoder, Action Head и Value Head — суть части одной модели (в которой ещё много скрытых частей), поэтому они крутятся все сразу и вместе. Т.е., подкручивая логиты и предсказание value, мы сразу оптимизируем скопом и всю модель: заставляем её зрение (Encoder) выделять значимые элементы на сцене, Value Head — учиться правильно предсказывать награду, Action Head — какие действия в той или иной ситуации нужно предпринимать.

Резюме

Сначала агент глупый и совершает случайные телодвижения: например, сразу плюхается в воду и тонет, или просто слоняется по берегу, пока не замёрзнет. Но со временем будут обнаруживаться ходы, ведущие к награде. Обнаружению помогает стохастичность — действие, которое нужно совершить, выбирается случайным образом (сэмплируется) из распределения, задаваемого теми самыми логитами. Чем выше энтропия распределения, тем рандомнее будут выбранные действия, чем ниже энтропия, тем более детерминированно будет действовать агент. В начале энтропия велика, и распределение близко к равномерному. Найденные удачные ходы являются подкреплением — такие ходы будут на оптимизации врезаться в память агенту, и он будет их чаще совершать. Со временем агент в своей памяти начинает накапливать всё больше и больше удачных ходов, его поведение будет приводить ко всё более длинным роллаутам и более обильным наградам. Удачное поведение будет кристаллизоваться, неудачное — вычищаться.

Лейтмотив модели агента (мозг)

Лейтмотив
Лейтмотив модели агента и обработки информации

На вход поступает упорядоченный во времени набор наблюдений (observations). Нужен именно набор, чтобы модель могла понимать то, как на сцене всё передвигается. Чем длиннее набор, тем лучше — модель сможет понимать как высокочастотные изменения, так и более медленные. Но есть физические ограничения на память (VRAM) и вычислительные ресурсы, которые нужны для обработки — чем длиннее, тем больше ресурсов. Поэтому длина набора — вещь компромиссная.

Каждое наблюдение — это картинка. Сырая картинка ALE — RGB 210x160 (uint8). Энкодер преобразует эти картинки в вектора более низкой размерности — латентные вектора, или латенты. Например, кадр 210x160 (uint8) конвертируется в латент размерности 384 (float). Сжатие примерно в 66 раз (3x210x160x1 / 384x4).

Что находится в латенте наблюдения?

Работает алгебра высоких размерностей. Возьмём даже размерность 384. Можно сгенерировать два таких случайных вектора — и о, чудо! — они будут практически ортогональны друг другу. То есть для размерности 384 можно нагенерить миллионы, если не миллиарды почти ортогональных векторов [11]. Каждый вектор — это независимое направление или ось, которое может описывать ту или иную фичу. Например, положение игрока, сколько кирпичей иглу собрано, счёт и т.д. Можно взять несколько десятков таких фичей и сложить в латент, и всё там прекрасно будет храниться и оттуда восстанавливаться. Конечно, тысячу векторов в один вектор уже запихнуть не получится, т.к. пусть слабая, но всё-таки корреляция осей кумулятивно внесёт много шума; но несколько десятков — легко. Поэтому вектор размерности 384 может легко описывать то, что происходит на сцене.

Хотя латенты и упорядочены физически в памяти, для трансформера они всё равно выглядят как просто мешок. Всё из-за того, что трансформер оперирует контентом — ему всё равно, по какому адресу латент расположен. Чтобы трансформер мог корректно различать, где какой латент во времени, их нужно пропатчить — к латентам добавляется вектор с временным кодированием (temporal encoding) [6]. Теперь трансформер готов потреблять данные. Он берёт набор латентов с временным кодированием и прогоняет через свои слои. На каждом слое отрабатывают последовательно MultiHeadAttention и MLP [6]. MHA работает сразу со всеми латентами, вычисляет отношения между ними — латенты как бы разговаривают друг с другом (cross-talk) и обмениваются информацией [6]. За счёт этого трансформер научается понимать физику игры, с какими скоростями кто движется, и т.д. В MLP-слое накапливается экспертиза — что делать в конкретной ситуации [7]. Проходя между слоями, понимание сцены мутирует от более простых вещей к более абстрактным.

На выходе трансформера получаем также набор латентов, но обогащённых опытом. В них уже сидит вся информация, необходимая для принятия решения. Рабочая схема — это просто потребовать, чтобы эта информация осела в последнем латенте, который соответствует последнему наблюдению. Value Head и Action Head берут этот латент и извлекают из него информацию:

  • Value Head извлекает оценку награды — сколько можно получить до конца игры;

  • Action Head рассчитывает вектор логитов, из которого потом сэмплится наиболее вероятное действие и отдаётся в окружение.

Почему ставка на трансформер

  1. заточенность на работу с последовательностями. Здесь у нас как раз последовательность наблюдений (точнее, их латентов);

  2. отсутствие состояния (stateless). Скорость тренировки в разы, если не на порядки, выше, чем если бы использовался какой-нибудь рекуррентный мотив;

  3. отдельные слоты для экспертизы (MLP) и для вычисления отношений (MHA). По идее, ёмкость для впитывания опыта огромна;

  4. на задачах обработки языка показывают себя феноменально, что указывает на их “умение” извлекать полезные абстракции и делать глубокие обобщения. Прямо как наш мозг.

Хочется всего и сразу: Transformer-XL

Вдохновляемся статьёй “Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents” [5]. Авторы взяли архитектуру Transformer-XL и прикрутили её через PPO для научения агента играть в игры, где нужна длинная и точная память. Например, в одной из игр агент должен пробираться по бесконечному лабиринту, который генерируется на лету. Сама архитектура Transformer-XL решала задачу, как дёшево расширить контекстное окно трансформера без квадратичной сложности [4].

Особенно приятно, что в библиотеке CleanRL нашлась референсная реализация этой концепции [3] — не надо изобретать велосипед и можно быстро стартануть. Получается картина ниже.

Transformer-XL
Transformer-XL и кеширование латентов

В ванильном мотиве на каждый шаг нужно сделать одно и то же: взять цепочку наблюдений, прогнать через энкодер, потом отдать трансформеру. При обработке нового наблюдения надо обновить буфер цепочки по FIFO-принципу и повторить. Налицо повторная обработка одних и тех же входных данных. Если длина входной цепочки 10 наблюдений, то на каждом шаге мы будем обрабатывать 90% старой информации. Неэкономно и медленно.

В концепции Transformer-XL латенты кешируются, а не вычисляются на каждом шагу. Это очень здорово и позволяет замахнуться на длину входной цепочки в сотню латентов и больше. Правда, в реальном прогоне окно пришлось урезать до 16 наблюдений — сотня обрабатывается очень долго. Каждые 4 кадра эмулятора сливаются в один для скорости, поэтому 16 наблюдений соответствуют 2.1 секундам игрового времени. Не густо, но Frostbite — игра полностью наблюдаемая. Здесь нет, как в Starcraft, невидимых областей, нет тумана войны, все враги — всё на экране. Поэтому даже пары секунд истории должно быть достаточно, чтобы осознать происходящее и правильно среагировать.

Сборка готова: https://github.com/kocherovms/neurolab/blob/main/17_rl/17d_ppo_trxl_atari_mp_01.ipynb. Отрезвление быстрое. Оно как бы работает, но быстро обнаруживается потолок. Агент научается прыгать по льдинам и разбирать их, чтобы продлить свою жизнь. Но в собранный иглу не заходит. Заработок агента - 526 очков (лучший запуск 17d_ppo_trxl_atari_mp_01/3) — это очень мало.

Скорее всего проблема с обучаемостью кроется в закешированных латентах. И тут две проблемы:

  1. чтобы их закешировать и переиспользовать, их надо заморозить, т.е. отцепить от графа вычисления градиентов. В итоге они работают только на read-only, а на оптимизации ведущую роль играет только последний латент — градиенты как бы текут только через него. Если бы латенты были разморожены, то они бы все участвовали в расчёте градиентов, что способствовало бы более быстрому познанию агентом внутренней логики игры, а так агент становится очень близоруким;

  2. десинхронизация замороженных латентов с весами модели. На шаге оптимизации после первой же эпохи веса модели обновляются, и закешированные латенты уже не совместимы с ними. В той или иной степени. После 2-й или 3-й эпохи расхождение становится ещё больше. В итоге эти закешированные латенты превращаются в шум и никак не помогают.

Проблематика обновления латентов в концепции Transformer-XL
Проблематика обновления латентов в концепции Transformer-XL

В исходной работе по Transformer-XL авторы использовали комбинацию: замороженные латенты + достаточно длинная живая цепочка, что нивелировало вышеописанные проблемы. Здесь же живая цепочка выродилась до одного элемента, и проблемы показали себя в полный рост.

А почему тогда работало у ребят из “Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents”? [5] Скорее всего дело в стационарности. Динамика и объём происходящего в Memory Gym не меняется так быстро, как в Frostbite. Размерность наблюдения (картинка) тоже несравненно меньше. Поэтому вероятнее всего, что проблемы кеширования и десинхронизации проявляются, но в меньшей степени.

Каждому своё

Решения, работающие в одних условиях, не всегда будут работать в других. Когда система небольшая (в модели всего несколько миллионов параметров), то даже небольшое внешнее возмущение заставляет её штормить. Короче, всё надо перепроверять.

Возвращение к истокам

Одного живого латента недостаточно, значит логичная идея — расширить это число до, скажем, 4. Таким образом станем чуть ближе к корректной реализации, которая была в оригинальной работе по Transformer-XL. Живых латентов держать много дорого: требование к памяти (VRAM) и времени растёт нелинейно, а тренировка нескольких десятков агентов в параллель — это много часов даже на нескольких GPU. Получаются какие-то вилы: добавить 4 живых латента к уже имеющимся замороженным - это сделать ещё медленней, а не добавлять нельзя, так как страдает обучение. Но раз так, то тогда проще вообще избавиться от замороженных латентов и посмотреть, что получится на исключительно живых. Бонусом мы получаем более чистую архитектуру без дополнительных сложностей.

Больше живых латентов
Добавление живых латентов для "лечения" проблем тренировки

Сказано — сделано: https://github.com/kocherovms/neurolab/blob/main/17_rl/17e_ppo_tr_atari_mp_03.ipynb. Делаем пару десятков прогонов. Ну уже получше, один из агентов нахоботил аж 779 очков (лучший запуск — 17e_ppo_tr_atari_mp_03/8). Это недалеко от 980 очков для Agent57 на 1 млрд. бюджета - есть первое положительное подкрепление! Хотя видно, что агенты выходят на плато и дальше особо ничему не учатся.

Количество заработанных очков
Количество заработанных очков

В записи видео агент чувствует себя увереннее. Научился обходить гусей, освоил горизонтальное перемещение, а не только вертикальное. Но также заметно, что он почему-то глупым образом соскальзывает со льдин, иногда ни с того, ни с сего прыгает в воду, а в конце дал гусю себя утащить.

Но главная беда — это непонимание, что нужно собирать иглу и заходить в него. Агент охотно разбирает иглу (это делается изменением направления движения льдин), что позволяет ему дольше оставаться в цикле сбора кирпичиков и зарабатывания очков. Агент нащупал локальный минимум и в нём застрял.

Больше очков != понял игру

Локальный минимум — не баг агента, а сигнал о том, что награда за «зайти в иглу» слишком редка, чтобы её нашёл случайный поиск.

Чтобы пройти первый уровень, агент каким-то образом должен перестать разбирать иглу. Трёх жизней достаточно, чтобы, даже просто тупо прыгая по льдинам вверх-вниз, достроить иглу — иглу переживает потерю жизни. А потом он должен каким-то образом вылезти на берег и потопать в сторону иглу, и зайти в дверь (надо нажать на кнопку UP, будучи в створе двери). Какова вероятность, что агент это сделает случайным образом? Очень близко к 0. Просто нет никаких нативных подкреплений, зачем ему так делать.

Выводы

Формула [трансформер + PPO] выглядит рабочей для Frostbite. Заработано 779 очков на 30 млн шагов, тогда как Atari57 на 1 млрд. зарабтал 980.

Агент успешно научается базовым механикам игры, но не способен постичь иерархическое целеполагание. Возможно, что это можно побороть грубой силой — просто выполнить пару сотен, а может и тысяч запусков. Глядишь, какой-нибудь счастливчик и появится, который случайным образом соберёт иглу, зайдёт в него и закрепит это знание. В конце концов Atari57 так и делает и у него получается.

Но лучше поискать более управляемое решение.

Будем искать. В следующем эпизоде.

Github: https://github.com/kocherovms/neurolab

Технические заметки: https://kocherovms.github.io/

Литература

  1. Schulman J., Wolski F., Dhariwal P., Radford A., Klimov O. Proximal Policy Optimization Algorithms. — arXiv:1707.06347, 2017. arxiv.org/abs/1707.06347

  2. Mnih V. et al. Human-level control through deep reinforcement learning (DQN). — Nature 518:529–533, 2015. nature.com/articles/nature14236

  3. Huang S., Dossa R. F. J., Ye C., Braga J., Chakraborty D., Mehta K., Araújo J. G. M. CleanRL: High-quality Single-file Implementations of Deep Reinforcement Learning Algorithms. — JMLR 23(274):1–18, 2022. jmlr.org/papers/v23/21-1342.html

  4. Dai Z., Yang Z., Yang Y., Carbonell J., Le Q., Salakhutdinov R. Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context. — ACL 2019. arxiv.org/abs/1901.02860

  5. Pleines M., Pallasch M., Zimmer F., Preuss M. Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents. — JMLR 26, 2025. arxiv.org/abs/2309.17207

  6. Vaswani A. et al. Attention Is All You Need. — NeurIPS 2017. arxiv.org/abs/1706.03762

  7. Geva M., Schuster R., Berant J., Levy O. Transformer Feed-Forward Layers Are Key-Value Memories. — EMNLP 2021. arxiv.org/abs/2012.14913

  8. Bellemare M. G., Naddaf Y., Veness J., Bowling M. The Arcade Learning Environment: An Evaluation Platform for General Agents. — JAIR 47:253–279, 2013. jair.org/index.php/jair/article/view/10819

  9. Machado M. C., Bellemare M. G., Talvitie E., Veness J., Hausknecht M., Bowling M. Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents. — JAIR 61:523–562, 2018. arxiv.org/abs/1709.06009

  10. Towers M. et al. Gymnasium: A Standard Interface for Reinforcement Learning Environments. — arXiv:2407.17032, 2024. arxiv.org/abs/2407.17032

  11. Kanerva P. Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors. — Cognitive Computation 1(2):139–159, 2009. link.springer.com/article/10.1007/s12559-009-9009-8

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  • 04.08.26 11:05 Kisnoles

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    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

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  • 20.08.26 11:32 michaeldavenport218

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

  • 23.08.26 20:02 leslieyee

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

  • 25.08.26 13:44 lydiassmith567

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  • 25.08.26 13:44 lydiassmith567

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  • 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]

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  • 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

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  • 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

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  • 13.10.26 14:14 lisalisa22

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