Rahul Madhavan

[LG] Efficient RL Training for LLMs with Experience Replay C Arnal, V Cabannes, T Cohen, J Kempe… [FAIR at Meta] (2026) arxiv.org/abs/2604.08706

In July 2024, DeepMind unveiled AlphaProof — an AlphaZero-inspired agent that constructs mathematical arguments in Lean, a programming language for proofs. It broke new ground in mathematical performance, achieving a silver medal in the 2024 International Math Olympiad. One year later, in July 2025, OpenAI announced that they had achieved a gold medal in the 2025 International Math Olympiad using a raw LLM — no reinforcement learning in Lean space, no translation between natural language and formal proof languages. In the span of a few weeks, this same model would go on to add a gold medal at the International Olympiad in Informatics and a 2nd place finish at the AtCoder World Tour Finals to its achievements. Since July 2025, I kept coming back to this puzzle: Why would a general-purpose language model, one just as comfortable answering questions about lasagna recipes in ChatGPT as it is answering mathematical questions, end up looking stronger at Olympiad math than a much more math-specific theorem-proving system? In my new blog post, I use legendary mathematician Jacques Hadamard's analysis of the phenomenology of mathematical discovery to attempt to answer this question. And to probe where LLMs are headed next. Link in the replies below.

30% random noise does not reduce performance? 🤔 If this is reproducible across more models and datasets, one has to wonder why.

The Illusion of Learning from Observational Data: An Empirical Bayes Perspective Bohan Wu, Sebastian Salazar, Donald P. Green, David M. Blei arxiv.org/abs/2604.08853

Outstanding researchers excel at the art of finding problems right at the edge of our understanding — that can actually be solved.

대통령님의 말씀은 누군가의 고통을 외면하지 말자는 상식이었습니다. 그 상식에 반발한 이스라엘의 태도는 오히려 더 많은 질문을 남깁니다. 함께 아파하는 것, 침묵하지 않는 것, 우리가 지켜온 길입니다. 대한민국은 인권과 민주주의를 말하는 나라로 더 당당하게 나아가야 합니다.

never lose sight of universal human rights as the foundation of human civilization

<끊임없는 반인권적 반국제법적 행동으로 고통받고 힘들어하는 전 세계인들의 지적을 한번쯤은 되돌아볼 만도 한데 실망입니다. 내가 아프면 타인도 그만큼 아픕니다. 나의 필요 때문에 누군가 고통받으면 미안한 것이 인지상정입니다. 아닌 밤중에 홍두깨라고 아무 잘못없는 우리 국민들께서 뜬금없이 겪고 있는 이 엄청난 고통과 국가적 어려움을 지켜보는 마음이 매우 불편합니다. 보편적 인권과 대한민국의 국익을 위해 할 수 있는 일을 더 열심히 찾아봐야겠습니다.> 이스라엘, ‘전시 살해=유대인 학살’ 李대통령 발언에 “용납 못해” v.daum.net/v/202604110641…

Paper link: arxiv.org/abs/2510.25741

Twitter’s algorithm is optimized for addiction, not for us. We deserve better. We’re releasing Bouncer today so you can take back control of your feed. Describe what you don't want, and Bouncer removes it. It’s free, doesn’t collect your data, and will be open source soon.

This year, the world is marking the 200th anniversary of the birth of mathematician Bernhard Riemann. Renown historian David Rowe has undertaken a deep study of Riemann's life and work, completing what should be his definitive biography. It will be published in June, stay tuned!

Can the machine watch itself. Can it have a sense of self? Can it watch the universe, the effects of the actions of that self on the universe... Then is the universe observing itself? If it is, then it must be, that it is conscious.

Maybe in future a machine could also create an equivalent world, say in a distant planet. But taking action by itself does not create consciousness. The only question, maybe, is whether the Universe is observing itself through that machine.

Are we doomed to never knowing whether any entity other than us is conscious? What a profound question!

The hypergraph of math arxiv.org/abs/2604.06107