Simon Coste ꙮ

@iammteah @PI010101 delete this nonsense please mr @iammteah

@__SimonCoste__ @PI010101 Why, do you believe in radiosophy? Actually it's not that surprising. The Gaussian distribution explains why orthogonality preserves independence, the rest is basic numerics.

Every subgaussian is a sum of Gaussians -- Antoine Song resolves Talagrand's conjectures arxiv.org/pdf/2602.22342

@kgourg @PI010101 Yeah that’s what I meant. A truly impressive result

@__SimonCoste__ @PI010101 Any Lipschitz map of a Gaussian, not any lip. fun. That’s lemma 2.4. Is there anything else?

@PI010101 and as far as I understand the paper, he also proves that any Lipschitz function is the sum of TWO gaussians.

@__SimonCoste__ Real valued centered sufficiently subgaussian is the sum of 3 standard gaussians, and 3 is optimal. But his result also implies that any subgaussian vector is a finite sum of Gaussians (not necessarily independent and standard of course).

This proof is due to Herman Schwarz, not Gelfand. It’s the reason why the inequality is called Cauchy-Schwarz

Like, a human with the same capabilities as a frontier model would almost certainly be producing incredible mathematics. The models are not. I am hesitant to attribute this to some human "secret sauce" but it's not clear what the alternative is.

interesting context here

où vont travailler les polytechniciens quand ils sortent de l’X ? lajauneetlarouge.com/x2020-pour-la-…

@__paleologo Judea Pearl has always been overselling his causal stuff. « The Book of Why » is almost unreadable for this reason. Huge respect for his research though

Every ML pioneer seems to believe that the breakthrough AI needs is *exactly* what they worked on at the beginning of their career. And what is the probability of *that*?

What counts as a PhD thesis is going to change quite a bit in this year.

Solution attempts from our model: cdn.openai.com/pdf/a430f16e-0…

Very excited about the "First Proof" challenge. I believe novel frontier research is perhaps the most important way to evaluate capabilities of the next generation of AI models. We have run our internal model with limited human supervision on the ten proposed problems. The problems require expertise in their respective domains and are not easy to verify; based on feedback from experts, we believe at least six solutions (2, 4, 5, 6, 9, 10) have a high chance of being correct, and some further ones look promising. We will only publish the solution attempts after midnight (PT), per the authors' guidance - the sha256 hash of the PDF is d74f090af16fc8a19debf4c1fec11c0975be7d612bd5ae43c24ca939cd272b1a . This was a side-sprint executed in a week mostly by querying one of the models we're currently training; as such, the methodology we employed leaves a lot to be desired. We didn't provide proof ideas or mathematical suggestions to the model during this evaluation; for some solutions, we asked the model to expand upon some proofs, per expert feedback. We also manually facilitated a back-and-forth between this model and ChatGPT for verification, formatting and style. For some problems, we present the best of a few attempts according to human judgement. We are looking forward to more controlled evaluations in the next round! 1stproof.org #1stProof

@WilcosX no. These problems are really not that hard for ppl working in the field

@__SimonCoste__ Bro one week is kinda brutal

Martin Hairer and colleagues released a set of hard maths problems, designed to be test cases for LLMs. We have *one week* to solve them, using LLMs. They encrypted the solutions at 1stproof.org and will reveal them just after. arxiv.org/pdf/2602.05192 (1/3)

@SonOfClawDraws For any regular graph (expander or not) I can find a subset S of *independent* vertices with more than c*eps*|V| vertices. So the assumption "its Laplacian L_S has largest eigenvalue bounded below by a positive constant c_1=c_1(d)>0" seems false ? am I missing smthg ?

Counterexample (constant-degree expanders). Let G=(V,E) be a d-regular expander on n vertices, with Laplacian L. For any subset S\subset V with |S|\ge c n, the induced subgraph G_S has maximum degree at most d, so its Laplacian L_S has largest eigenvalue bounded below by a positive constant c_1=c_1(d)>0. Hence there exists a vector x supported on S such that x^\top L_S x \ge c_1 \|x\|^2. On the other hand, since G is d-regular, x^\top L x \le 2d \|x\|^2. Therefore the condition L_S \preceq \varepsilon L implies \varepsilon \ge c_1/(2d). For any \varepsilon smaller than this constant, no subset S of linear size can be \varepsilon-light. Thus no universal constant c>0 exists such that every graph admits an \varepsilon-light subset of size at least c|V| for all \varepsilon\in(0,1).

@ludwigABAP @EmmanuelMacron please proceed

@EmmanuelMacron I could raise 30M before the summer off of 10 tweets and a single repo

In France, we believe in science. That is why, on May 5, I issued a clear and open call to the world: for science, choose France. I am very proud to see that this call has resonated so strongly. Around forty leading researchers have chosen France. Through “France 2030”, we have invested more than €30 million to advance health, climate action, artificial intelligence, and fundamental sciences. Science has found its home.

@peligrietzer @littmath it's really not comparable to IMO/Putnam. It's much more about navigating in the literature; the problem I'm working (n°6) on is *probably* already solved somewhere. If you know where to search, it should be feasible to adapt the proofs. But strong domain knowledge is needed...

@littmath Curious about the differences (in what it would measure) from IMO and from Putnam

This is a really nice test suite.

Can I recommend that labs or individuals working on 1st Proof arxiv.org/abs/2602.05192 encrypt their solutions also, and we agree not to release the keys until a future date? This goes for humans proving the results too.

Problem n°5 sounds like pure alchemy 🥹 (3/3)

For the people in my community, there are 3 relevant problems: - on the spectral theory of graphs, n°6 - on finding a Markov chain with a prescribed stat. dist. (involves MacDonald and ASEP), n°5 - finding the CP decomposition of a rank-r tensor, n°9