mindgitrwx @mindgitrwx

2023: LLMs struggle with 4th grade word problems 2024: LLMs can do high school math 2025: LLMs get a gold medal at the IMO Now, GPT-5.6 solves famous frontier math/stat questions. The IMO is today and 5.6 one-shotting a perfect score isn't even news. Where will we be next year?

Edgar Dobriban @EdgarDobriban

5 days ago

AI has helped resolve an important question in statistics. In the area of multiple hypothesis testing, the goal of controlling the false discovery rate (FDR) has been introduced in a seminal paper by Benjamini and Hochberg (1995). They also introduced a method (the

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What begins as a single point transforms into a complex network of 1,024 interconnected vertices by the tenth dimension. These diagrams depict the graphs of hypercubes in dimensions 0 to 10, each with 2^n vertices where edges connect those differing in one bit. Low dimensions use basic geometric forms like points, lines, squares and cube projections, while higher dimensions employ radial concentric layouts to visualize the recursive structure of doubling copies joined by edges. Hypercubes provide the basis for interconnection networks in parallel computing, enabling efficient communication in systems with many processors.

Stanford professor just released the lecture that explains the math behind every reinforcement learning system. 83 minutes. Free. From Stanford. Before agents learn to trade, optimize, or make decisions, they all start with the same problem: How do you choose the best action when the future is uncertain? This lecture breaks down the foundation: • turning environments into Markov Decision Processes • policy evaluation and why value functions matter • Q-value recurrence equations behind modern RL • value iteration and convergence limits Every RL algorithm built today is just a variation of these ideas. The math has been public for decades. The hard part was never knowing the Bellman equation. The hard part is knowing when your model actually understands the environment and when it is just fitting noise. Bookmark this before it gets buried in your feed.

Roan @RohOnChain

2 weeks ago

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Gödel's Incompleteness Theorems ✍️ To understand Gödel's incompleteness theorems, we first need to look at the state of mathematics before Gödel and what mathematicians aimed to achieve. Mathematics was always seen as the most certain and reliable form of human knowledge. Unlike science, which relies on experiments that can change with new evidence, mathematical proofs were viewed as permanent and definite. By the early twentieth century, mathematicians wanted to make this certainty completely systematic. The mathematician David Hilbert led a movement to build all of mathematics on a strong foundation. This would start from a small set of clear truths called axioms and derive every mathematical truth through logical reasoning. The hope was that this foundation would be consistent, meaning it would never lead to contradictions, and complete, meaning it could prove every mathematical truth without exception. Every true statement would be provable, and every provable statement would be true. The left diagram illustrates this dream as a single circle where true statements and provable statements are perfectly identical, with no gap between them. In 1931, Kurt Gödel, a twenty-five-year-old Austrian mathematician in Vienna, proved that this dream was unattainable. To grasp his proof, you must understand what a formal system is. A formal system is a precise mathematical framework with three parts. It includes a formal language with specific symbols and strict rules for combining them into statements. It has axioms, which are basic statements assumed to be true without needing proof. It also has rules of inference, which are mechanical rules for deriving new statements from existing ones. A proof in such a system is a sequence of steps where each step is either an axiom or follows from previous steps based on the allowed rules. Remarkably, checking whether something is a valid proof is a mechanical task that requires no insight or understanding, just a check to see that each step follows the rules. Gödel's theorems apply specifically to formal systems that can express basic arithmetic, meaning they can talk about numbers, addition, and multiplication. The most brilliant part of Gödel's work was the technique he invented called Gödel numbering. He realized that every symbol, statement, and proof in a formal system is just a sequence of symbols, and these sequences can be encoded as numbers. By assigning numbers to symbols and using arithmetic to encode entire statements and proofs as single large numbers, Gödel gave arithmetic the hidden ability to make statements about itself. A statement that looks like ordinary arithmetic about numbers secretly becomes a statement about other statements or proofs within the system. With this trick, the formal system can discuss its own workings and its own provability, which was essential for Gödel to create his masterpiece. Using this self-referential technique, Gödel carefully constructed a specific mathematical statement now known as the Gödel statement, labeled G in the right diagram. When decoded from its numerical form, this statement makes an extraordinary claim about itself. It essentially says this: this very statement cannot be proven within this formal system. Now, think through the logic of this carefully. If the Gödel statement is provable, then the system has proven something that claims to be unprovable, meaning the system has proven a false statement, leading to inconsistency and rendering the system useless. But if the system is consistent and therefore useful, then the Gödel statement cannot be provable. If it is not provable, then what it asserts is actually true, since it accurately claims its own unprovability. This results in a statement that is genuinely true but that the system cannot prove. This is the first incompleteness theorem: any consistent formal system capable of expressing arithmetic must have true statements that it cannot prove.

A different way to visualize the building blocks of matter. This 3D spiral arranges the elements in order of increasing atomic number, forming a continuous path from the lightest elements at the center to transition metals, lanthanides, actinides, and the heaviest known elements toward the outer layers. The color-coded regions highlight periodic patterns and relationships, making the structure of the periodic table easier to explore from a new perspective.

I feel like I haven't recommended something interesting for theoretical computer scientists in a little while, hence I will propose, this time around, this incredibly interesting and short primer (25 pages) titled 'Galois Theory of Algorithms' by Yanofsky. This paper is not a way to learn Galois theory for a beginner (I would suggest to you Milne's text on his website), and I would suggest a strong background in theory of computation, metamathematics, abstract algebra, discrete mathematics, some category theory ++ ...yes the list is a bit long! If the pre requisites didn't scare you (and it shouldn't), this is a fantastic read that had me looking a bit more into Rohit Parikh's work. gl, hf! 🔗👇

What really happens during LLM training? Can we ever disentangle those billions of interacting parameters? In our latest preprint, we present a promising direction. Under certain data symmetries, the parameter space turns out to have a low-dimensional subspace with self-contained dynamics during training. If training begins in this subspace, it never leaves. The subspace has a low dimensionality, which means that we can reduce the training dynamics to a small number of pseudo-parameters. This makes theoretical and experimental analysis much more tractable. Moreover, the subspace is highly interpretable: each coordinate corresponds to a clear mechanism. For example, an induction head is composed of 3 directions in this subspace. Big thanks to my co-authors @tpimentelms @NicolasZucchet Paper link in the first reply 👇🏻

Quantum mechanics uses specialized symbols to describe the behavior of matter and energy at microscopic scales. An alphabetical guide highlights core concepts like angular momentum, bound states, the fine structure constant 1/137, photon energy hν, the Schrödinger equation EΨ=ĤΨ, reduced mass mM/(M+m), Laplacian ∇², and uncertainty ΔxΔp. These ideas are used to build the transistors in every computer chip and the lasers in fiber optic networks that connect the world.

Bernhard Riemann introduced the metric tensor to quantify distances and angles in curved spaces. The equation is ds² = ∑ gᵢⱼ dxⁱ dxʲ where ds² is the infinitesimal squared distance, gᵢⱼ the metric tensor components and dxⁱ the coordinate differentials. It extends the dot product idea to Riemannian manifolds and equals the Kronecker delta in flat space but changes with position in curved space. This is essential for general relativity. It is used to determine spacetime curvature effects on satellite orbits and light propagation in astronomy.

📌 미쳐야 성공한다는 말, 사실 생존자만 인터뷰해서 그런 거임 (메타인지로 뜯어봄) - 생존자 편향(survivorship bias) : 성공한 미친놈만 보이고 망한 미친놈은 안 보임 - 스탠퍼드 노동시간 연구 : 주 50시간 넘으면 생산성 꺾임 - 몰입 밀도 : 시간이 아니라 에너지 배분이 진짜 변수 1) 미쳐야 성공한다는 서사, 사실 반은 착시임 왜냐하면 우리가 접하는 건 극단적으로 몰입해서 성공한 소수의 스토리뿐이고 똑같이 미치도록 몰입했다가 조용히 망한 사람들은 아무도 인터뷰 안 하기 때문 2) 근데 그렇다고 설렁설렁 해도 된다는 것도 틀림 스탠퍼드 연구 보면 주 50시간 넘어가는 순간부터 생산성이 꺾이고, 55시간 넘으면 추가 시간은 거의 무의미해진다고 함 심지어 보스턴대 연구에서는 80시간 일한 척한 직원과 진짜 80시간 일한 직원을 관리자가 구분도 못 했다고 함 결국 오래 앉아있는 거 자체는 성공 변수가 아니라는 뜻 3) 그래서 진짜 변수는 미쳤냐 설렁설렁이냐가 아니라 몰입의 밀도임 시간을 얼마나 쓰냐보다 그 시간에 에너지를 어디에 쏟냐가 결과를 가름 반면에 특정 기술 영역은 절대적인 시간 투입 자체가 실력이 되는 경우도 있어서 (예: 손기술, 반복 숙련 영역) 이 공식이 모든 곳에 통하는 건 아님 어쩌면 미쳤다 vs 설렁설렁이라는 이분법 자체가 잘못된 질문일 수도 있음 근데 이것도 틀릴 수 있음, 영역마다 다를 거라 확신은 못 함 💬 미친 듯이 일한 사람보다 밀도 있게 일한 사람이 이긴다, 시간 자랑은 이제 그만 🧠 왜 확인해야 하냐면, 이거 감이 아니라 실제 연구로 나온 수치라서 링크 열어보면 장시간 노동이 왜 생산성이랑 상관없는지 구체적으로 나옴 안 믿겨도 괜찮다, 출처 열어보면 된다 #생산성 #생존자편향 #메타인지 🔗 참고한 정보: •“80시간 일한 척한 직원과 실제 직원, 관리자가 구분 못함” — marriott.byu.edu/magazine/featu…

OfficeCLI 미쳤다. AI가 자연어로 Word/Excel/PPT 다 조작함. 16k 스타 오픈소스 ㅋㅋ 문서 노동자들 필수템

Serena @369Serena

5 days ago

卧槽，Office 开放 Cli 了！！ 每天都在被 Word、Excel、PPT 等 Office 三件套纠缠？ 那请你一定要看看 GitHub 上这个已经有 16.2K Star 的开源工具：OfficeCLI 有了它之后，办公室里的文档处理和文案工作，真的可以开始释放双手了！！ 它可以让 AI Agent 用自然语言去操作 Office 文件： ① 生成

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게임 가짜 성취 이야기 논문에서 이미 함 게임의 가치는 성취감이 아니라 실패하게 만드는 데 있다는 것 kci.go.kr/kciportal/ci/s…

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A free guide that answers key reinforcement learning questions: shorturl.at/zcciv v/@arjunkocher & @sheriyuo

Reescribieron PostgreSQL completo en Rust... y ya pasa el 100% de los tests oficiales de Postgres! Ojo, no es un fork, es una reimplementación desde cero en Rust que actualmente: • Pasa las 46.066 queries del regression suite de PostgreSQL 18.3 • Es disk-compatible (puedes bootearlo directamente con tu data directory actual) • Tiene demo funcional en el browser El objetivo Es hacer que una de las bases de datos más complejas del mundo sea mucho más fácil de modificar, extender y optimizar desde dentro usando Rust + programación asistida por IA. Y lo más loco: ya existe una versión WIP (aún no publicada) que promete ser 50% más rápida en workloads transaccionales y ~300x más rápida en workloads analíticos. REPOOO👇

The Well Just Dropped: 15 Terabytes of Pure Physics Gold Is Now Open Source The scientific AI world just got a massive upgrade.Polymathic AI, in collaboration with the Flatiron Institute and researchers from Princeton, Cambridge, NYU, Berkeley, Los Alamos, and more, has released The Well: a staggering 15TB collection of high-fidelity physics simulations. This isn’t toy data. These are real, expensive-to-run simulations across 16 different physical domains, including turbulent fluid dynamics, supernova explosions, magneto-hydrodynamic cosmic flows, acoustic scattering, and active biological matter. Until now, reproducing this level of data required weeks on national supercomputers and grant money most teams will never see. The Well changes everything. It’s purpose-built for training PDE surrogate models the AI systems that can replace slow, costly physics solvers with a single fast neural network forward pass. Everything is fully open source, easy to load with PyTorch, and ready to drop straight into your training pipeline. Researchers and builders can now train on world-class physics data without the insane compute barriers that used to stand in the way. This is more than just another dataset drop. It’s a serious accelerator for scientific machine learning.The future of physics-informed AI just got a whole lot more accessible.Get it here: polymathic-ai.org/the_well/

Absolutely fascinating work by @SakanaAILabs reproducing @kenneth0stanley Picbreeder in a non-interactive, VLM-agentic way. I've had years to reflect on Kenneth Stanley's ideas as originally communicated in the book Why Greatness Cannot Be Planned. The most load-bearing term is "serendipity", and what that actually means. > We’re inspired by the idea that serendipity requires chance As we laid out in our creativity article, I think chance is actually the wrong way to think about serendipity. It's mostly about respecting constraints, and the chance, if there is any, happens in the degrees of freedom not covered by the constraints. I think open-endedness can be thought of in a privileged, symbolic/non-statistical way. The more recent work with Kenneth and @akarshkumar0101 elucidated to me that it's about three main things: First of all, the lack of any externalised agency ("following your own gradient of interest") or only non-complex internal agency or intelligence (as explained in his original book, framed there as "non-optimization"), secondly -- "deep understanding" (respecting constraints upstream in the phylogeny), or, in their terms "path dependence". And thirdly: "evolvability". It's also taken as a given that if the constraints are sparse/factorised/world-aligned, the more the better. Actually, the best possible sign of success of any representation learning architecture is sparsity, factorization, world-alignment and/or canalisation. I was able to breed the anthropomorphic images below by manually navigating an extremely deceptive search space over many, many iterations and starting with something that didn't look anything like a face. The reason Picbreeder works through interactive human supervision is that we understand the world at an abstract level, and we can easily spot abstract motifs in the generated images. As @fchollet said, the ability to decompose perceptual information into its abstract constituent blocks is a core feature of human cognition. So Picbreeder was bootstrapping the iterative creation of a highly factorised modular architecture, by leveraging humans' ability to do just this. It's interesting that the Sakana guys referred to serendipity as a "je ne sais quoi". It is paradoxical because it IS the state of understanding abstractly, perhaps without the conscious awareness of it. It's certainly true that when I was breeding the image below, I locked into a particular feature, and it became a convergent, "goal-orientated process". But the important thing is it was completely individual agency. I was following my own path, and it was extremely shallow agency. I wasn't trying to achieve a complex objective. I was merely trying to encourage the materialisation of the abstract feature I initially recognised. When we look at the phylogeny created in this non-interactive way, we see that deep abstractions are not locked in and shared in deep lineages above. I think the two main problems of automating this process with LLMs are: convergence in sampling, and the inability to understand perceptual information in an abstract and systematic way. Both of these problems are directly explained by the fractured entangled representation hypothesis. So if this was an experiment trying to find if we could produce a factorised phylogeny from a non-factorised phylogeny (LLMs), it seems to have proven otherwise at this scale. However, we shouldn't give up so easily, if there is, indeed, even the slightest gradient of factorization, this process could presumably be scaled and repeated. I'm also intrigued by some of the work from Goodfire, which seems to suggest that factorization does meaningfully increase with scale, even on SGD networks (@banburismus_ ). Anyway, in my opinion, this is one of the most important research directions in the whole field of AI: leveraging open-ended methods and building networks with factorised representations. Looking forward to lots more exciting work from Sakana!

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Sakana AI @SakanaAILabs

a week ago

VLMは人間のような創造性を持てるか？ ケネス・スタンレー教授らの『目標という幻想（Why Greatness Cannot Be Planned）』は、明確な目標を設定することが、かえって真に偉大な発見を遠ざけてしまうという逆説を論じた書籍です。その議論の中核にあったのが「PicBreeder」の実験でした。 PicBreeder

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5.6 Sol 나왔는데 아직도 5.5 때처럼 프롬프트 하는 사람들이 많음 이 모델은 훨씬 더 집요하고 철저하게 일함. 그냥 막 던지면 오래 걸리고 토큰만 낭비시킴. 핵심 팁 작업 범위(sandbox) 확실히 정해주기 어떻게 검증할지 알려주기 "완료된 모습이 어떤지" 정확히 정의하기 모호하면 모델이 끝없이 헤매고 토큰 사용량 폭발함.

eric provencher @pvncher

a week ago

With 5.6 Sol, a lot of people are still prompting the model exactly as they did 5.5 It's important to note that 5.6 Sol is a lot more tenacious and thorough than previously models. Check out the guide I wrote here to get better outcomes learn.chatgpt.com/docs/prompting

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Why would anyone need LaTeX in the terminal? I asked the same thing. Then i built a math rendering engine. I'm never going back.

Nature Medicine’da yeni yayınlanan makale👇 Yaşlanma lineer değil❗️ Ortalama 7 çalışmada “yaşlanma dalgaları” tespit edildi: ✔️33 yaş civarı → İlk büyük sıçrama ✔️60 yaş → İkinci büyük dalga ✔️69 ve 78 yaş → Ek dalgalar Vücudumuz belirli yaşlarda “reset” oluyor. Bu kritik pencerelerde sağlıklı alışkanlıklara daha çok yatırım yaparsak gelecekteki sağlığımızı ciddi etkileyebiliriz. Bilimsel anti-aging’in yeni çağı başlıyor. #Yaşlanma #Longevity

Show GN: 대한민국 제도 100개를 한장씩 체계도로 만들었습니다. AI리터러시를 조금 다른 방향으로 고민해봤습니다. 일반인이 AI를 배우는 것이 아니라 AI를 통해서 다른 전문 영역의 리터러시를 높이는 것입니다. 저는 행정직 공무원이라 공공행정 영역에서 전문성, … news.hada.io/topic?id=31313…