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Периодическая система машинного обучения

В MIT создали первую “периодическую таблицу” методов машинного обучения, при которых в исходных данных не задаются конкретные признаки (representation learning). Оказывается, многие (а может оказаться, что и все) методы, даже совсем друг на друга не похожие, сводятся по существу к одной и той же формуле. Причем не слишком сложной по своей форме. Работу представили в конце апреля на конференции ICLR 2025.

“Обучение представлениям” или “обучение признакам”, или “обучение представлений”, — кажется, в русскоязычной ML-среде нет единого устоявшегося термина, так что будем использовать понятный “representation learning”. До появления representation learning для создания модели нужно было вручную выделить признаки данных, по которым модель будет обучаться и делать прогнозы. Для задач попроще и попонятнее это рабочая схема, но для сложных задач обработки текста и изображений она практически не применима. Выделить вручную признаки, по которым можно определить, что на картинке изображён, например, кот, а не цветок — задача нетривиальная. Человек с этим справляется слабо, поэтому возникла идея отдать поиск определяющих признаков на откуп машине — пусть модель сама определяет, какие параметры будут ключевыми. Этот переход к representation learning стал одной из фундаментальных основ, которые потом привели к прорывному развитию ML.

За прошедшие десятилетия накопилось огромное множество техник на основе representation learning, которые используют разные архитектуры и вид. А в последние годы новые способы появляются чуть ли не каждый день. Какие-то приспособлены под конкретные задачи, другие более универсальные. В каких-то прослеживается схожесть, другие выглядят принципиально новыми. Понять, чем они действительно схожи и различны, — задача во-первых просто интересная, а во-вторых и очень важная, так как это поможет эффективнее применять различные техники.

Существует много работ, где находятся взаимосвязи 2–3 техник, но авторы из MIT решили пойти дальше и объединили в один математический фреймворк 23 метода, причём совершенно разных: с учителем, без учителя и self-supervised.

Оказалось, что во всех них по существу происходит минимизация одной и той же функции потерь. Точнее, для всех этих методов функцию потерь можно привести к одному и тому же виду.

Сначала покажем саму обобщающую формулу, которую авторы назвали I-Con:

А теперь разберём её смысл. Суть этой функции потерь в DKL — расстоянии Кульбака–Лейблера, которое определяет, насколько вероятностное распределение q “удалено” от распределения p. Название “расстояние” в данном случае немного не соответствует привычному пониманию. Функционал DKL несимметричен — расстояние от p до q не будет равно расстоянию от q до p. Можно понимать это как расхождение или как относительное расстояние, то есть отличие тестируемого распределения q относительно некоторого эталонного, истинного p. Изначально расстояние Кульбака–Лейблера появилось в теории информации и нужно было, чтобы определить, сколько лишней информации мы потратим, если применим для кодирования q вместо p. Отсюда и несимметричность.

Но вернёмся к машинному обучению. Пусть есть некоторое множество данных, например, набор картинок. Эталонное распределение p — это как раз “учитель” — оно показывает, с какой вероятностью одна картинка должна привести к другой. Это может быть что угодно — простое гауссово распределение, задание классов картинок (“коты”, “цветы”), задание набора разных ракурсов одной и той же картинки и так далее. Относительно этого эталона мы будем оценивать распределение q, которое и будет определять взаимосвязь тех самых признаков (representations).


То распределение, которое даст наименьшее DKL по сравнению с p, будет считаться наиболее правильным.

Несмотря на формальную простоту, уравнение обобщает многие существующие методы. Оказывается, все они являются частными случаями функции потерь DKL с точностью до выбора p и q. Распределения p и q становятся своего рода координатами, а разные методы становятся точками на пересечении этих координат. В итоге получается периодическая система методов representation learning.

Например, модель InfoNCE использует в качестве обучающего датасета набор искажённых, отражённых и всякими другими способами изменённых версий одной и той же картинки (“uniform over positive pairs” по горизонтальной оси), а признаки определяются простым Гауссом (Gaussian по вертикальной оси). Авторы MIT проанализировали 23 работы и последовательно доказали, что все они сводятся к одной и той же формуле, только с разными p и q. Всего 15 теорем, в некоторых случаях доказательство тривиальное и прямо следует из исходного определения функции потерь, некоторые — гораздо более изощрённые.

Для примера возьмем тот же InfoNCE. Обучающий набор — размеченное множество вариантов одной и той же картинки.

Поэтому, если для каждой картинки i есть k вариантов, то распределение p для каждой картинки j будет равно 1/k, если это вариация картинки i, и 0, если нет.

Обучаемое распределение q основано на сходствах между эмбеддингами картинок i и j — f(xi) и f(xj):

𝜏 — здесь просто параметр, который авторы называют температурой. А функция потерь определяется соответственно как

Это в точности равно перекрестной энтропии (количеству информации, нужному, чтобы описать событие с помощью распределения q вместо p). Так как в данном случае распределение p фиксированное, то минимизация перекрестной энтропии в точности эквивалентна минимизации DKL ( ее можно определить как разность между перекрестной энтропией и энтропией эталонного p). В итоге InfoNCE является частным случаем I-Con.

Теперь пару менее строгих примеров (в статье есть строгие доказательства и для них). Stochastic Neighbor Embedding (SNE) — классический пример подхода “соседи остаются соседями”. Изначальное распределение p можно представить в виде гауссова распределения, то есть каждая точка обучающего датасета “размазана” гауссом, чтобы определить соседство с другими точками. Итоговое распределение, которое обычно задается на пространстве меньшей размерности, тоже задается гауссовым размазыванием эмбеддинга каждой точки.

Разбиение на кластеры тоже сводится к I-con. Для подходов K-Means и DSD распределение p это снова Гаусс, а q отражает являются ли эмбеддинги соседями по кластерам.



В получившейся “периодической таблице” заполнены не все ячейки, прямо как и в таблице Менделеева. Для некоторых из них (закрашены серым) авторы предлагают свои интерпретации, например, модель, которая будет использовать в качестве обучающего набора размеченные пары, а в качестве q — распределение гаусса с малой дисперсией, будет моделью “частоты ошибок”.

Ту ячейку, которая показалась авторам наиболее перспективной, они заполнили самостоятельно и создали модель InfoNCE Clustering. Там, в отличие от простого InfoNCE, гауссово распределение заменяется на взвешенное k-ближайших соседей. На ImageNet-1K результат на 8% превзошел предыдущий state-of-the-art среди моделей без учителя.


Авторы призывают читателей дополнять результаты другими моделями, которые они пока не успели рассмотреть. Само по себе объединение разных методов в принципиально единственный — уже теоретически важно. Но гораздо важнее, что это не просто объединение, а и некоторая структуризация, которая сразу же показывает белые пятна и указывает куда копать. Химию это привело к большим прорывам и процветанию, может и в этом случае окажется так же.

Больше наших обзоров AI‑статей — на канале Pro AI.

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    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 12.10.25 19:53 Tonerdomark

    A crook swiped my Dogecoin. It ruined my whole world. Then Mr. Sylvester showed up. He fixed it all. He pulled back €211,000 for me. Not one cent missing from my profits. His steady cool and sharp tech know-how won back my trust. I got my money smooth and sound. After endless worry, relief hit me hard. I trusted him completely. Lost cash to a scam? Hit him up now at { yt7cracker@gmail . com }. His aid turned my life around. WhatsApp at +1 512 577 7957.

  • 12.10.25 21:36 blessing

    Writing this review is a joy. Marie has provided excellent service ever since I started working with her in early 2018. I was worried I wouldn't be able to get my coins back after they were stolen by hackers. I had no idea where to begin, therefore it was a nightmare for me. However, things became easier for me after my friend sent me to [email protected] and +1 7127594675 on WhatsApp. I'm happy that she was able to retrieve my bitcoin so that I could resume trading.

  • 13.10.25 01:11 elizabethrush89

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

  • 13.10.25 01:11 elizabethrush89

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

  • 14.10.25 01:15 tyleradams

    Hi. Please be wise, do not make the same mistake I had made in the past, I was a victim of bitcoin scam, I saw a glamorous review showering praises and marketing an investment firm, I reached out to them on what their contracts are, and I invested $28,000, which I was promised to get my first 15% profit in weeks, when it’s time to get my profits, I got to know the company was bogus, they kept asking me to invest more and I ran out of patience then requested to have my money back, they refused to answer nor refund my funds, not until a friend of mine introduced me to the NVIDIA TECH HACKERS, so I reached out and after tabling my complaints, they were swift to action and within 36 hours I got back my funds with the due profit. I couldn’t contain the joy in me. I urge you guys to reach out to NVIDIA TECH HACKERS on their email: [email protected]

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.10.25 18:07 crypto

    Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.

  • 15.10.25 21:52 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.10.25 21:52 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

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