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Н Новости

Новые модели ИИ Google DeepMind теперь могут решать сложные математические задачи

Изображение сгенерировано ИИ.

Две новые модели искусственного интеллекта AlphaProof и AlphaGeometry, разработанные Google DeepMind, успешно решили четыре из шести задач престижной Международной математической олимпиады (IMO). Используя продвинутую систему логических рассуждений, они завоевали эквивалент серебряной медали, продемонстрировав беспрецедентный для ИИ успех в решении задач такого типа.

IMO проводится раз в год с 1959 года и является крупнейшим и старейшим международным математическим соревнованием. Чтобы принять в нем участие, молодые математики со всего мира (доуниверситетского уровня) тренируются, иногда в течение тысяч часов. Соревнование включает в себя решение шести чрезвычайно сложных задач по алгебре, комбинаторике (область математики, занимающаяся подсчетом и упорядочиванием объектов), геометрии и теории чисел.

С недавних пор IMO также стал эталоном для оценки способностей систем искусственного интеллекта к расширенному мышлению. Однако до сих пор они далеки от навыков логического мышления, необходимых для решения сложных и общих математических задач. Последние требуют сложного иерархического планирования, а также определения подцелей, проверки ответов и опробования новых методов.

С другой стороны, когда речь идет о математике, ИИ сталкивается с огромной нехваткой обучающих данных. "Зачастую проще обучить модель математике, если у вас есть возможность проверить ее ответы (на формальном языке), но формальных данных по математике в сети сравнительно меньше, чем данных по естественному языку (неформальному языку)", — рассказала MIT Review Кэти Коллинз, исследователь из Кембриджского университета, специализирующаяся на математике и ИИ.

Чтобы восполнить эти пробелы, компания Google DeepMind разработала AlphaProof и AlphaGeometry 2. Участвуя в конкурсе IMO в этом году, обе модели показали впечатляющие результаты. "Ни одна из разработанных на сегодняшний день систем такого типа не способна решать задачи с таким высоким процентом успеха и таким высоким уровнем сложности", — говорит Пушмит Кохли, вице-президент по исследованиям Google DeepMind.

Сложная система проверки

AlphaProof - это система, основанная на обучении с подкреплением, которая сама обучается доказывать математические утверждения на формальном языке программирования Lean. Для того чтобы ИИ мог легче обрабатывать данные, их необходимо было перевести на формальный математический язык. В отличие от обработки на естественном языке, обработка на формальном языке позволяет эффективно проверять точность математических рассуждений. Подходы на основе естественного языка, с другой стороны, могут генерировать правдоподобные, но, как правило, неверные ответы.

Математические данные на естественном языке были автоматически переведены в формальный язык с помощью усовершенствованной версии Gemini, самого мощного генеративного ИИ Google. В результате была создана большая библиотека формальных математических задач различной сложности. Затем Gemini был объединен с алгоритмом обучения с подкреплением AlphaZero, который ранее освоил игры в шахматы, сёги и го.

Эти две модели были объединены для создания AlphaProof, который генерирует ответы-кандидаты, а затем выполняет процесс обратной связи, чтобы доказать или опровергнуть их точность. По мере проверки ответов система становится все более эффективной, что позволяет впоследствии решать более сложные задачи. Этот цикл обучения повторялся в течение нескольких недель перед соревнованиями.

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Компьютерная графика процесса цикла обучения с подкреплением AlphaProof: около миллиона неформальных математических задач переводятся на формальный математический язык сетью формализаторов. Затем разрешающая сеть ищет доказательства или опровержения этих задач, постепенно обучаясь с помощью алгоритма AlphaZero решать более сложные задачи. © Google DeepMind

AlphaGeometry 2 - это улучшенная версия AlphaGeometry, модели, предназначенной для решения математических задач, связанных с движением объектов и уравнений с углами, соотношениями и расстояниями. Новая модель основана на движке, который в два раза быстрее своего предшественника, и обучена на гораздо большем количестве синтетических данных, что позволяет решать гораздо более сложные геометрические задачи.

Не дотянули до золотой медали, набрав 28 баллов из 42

Во время соревнования ответы моделей оценивали и отмечали два выдающихся математика: Тимоти Гауэрс, золотой медалист IMO и обладатель медали Филдса, и Джозеф Майерс, двукратный золотой медалист IMO и председатель комитета по выбору задач IMO 2024. Как и студентам, системам искусственного интеллекта было отведено две сессии по 4,5 часа на решение шести конкурсных задач.

Одну из задач системы решили всего за несколько минут, а на решение других ушло до 3 дней. AlphaProof решил две задачи по алгебре и одну задачу по теории чисел, определив ответ и доказав его правильность. Последняя задача была самой сложной на конкурсе, и ее решили всего пять участников. AlphaGeometry 2 решила одну из задач по геометрии, а две другие задачи по комбинаторике остались без ответа.

График, показывающий результаты работы искусственного интеллекта Google DeepMind в сравнении с человеческими конкурентами на IMO 2024. ИИ набрал 28 баллов из 42, что соответствует уровню серебряного призера соревнований. © Google DeepMind

Каждая из шести задач оценивается в семь баллов, поэтому максимально возможный результат - 42. Золотую медаль можно получить, набрав 29 баллов. Вместе две системы набрали 28 баллов, не дотянув до золотой медали. Это первый случай, когда система искусственного интеллекта достигла такого уровня производительности в конкурсе IMO. "Как математик, я считаю, что это очень впечатляет и представляет собой значительный прогресс по сравнению с тем, что было возможно раньше", — сказал Гауэрс на пресс-конференции.

Этот новый результат может проложить путь к сотрудничеству человека и ИИ в математических исследованиях. Это также может позволить расшифровать способ, которым наш мозг решает эти задачи, — аспект, который до сих пор остается во многом непонятным.

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    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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