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1/6
Codex found a proof of a 2017 conjecture in algebraic combinatorics—one I often revisited in grad school.
Of the original paper’s 14 numbered conjectures, it was one of only 3 with no substantial follow-up in the literature.
Write-up + Lean: github.com/steven-le-thien/v… 🧵
Thien Le retweeted
Proof of the 40-year old Bandelt-Dress conjecture on the maximum quartet distance between phylogenetic trees (and an interesting connection to independence testing). arxiv.org/abs/2608.03542
Thien Le retweeted
Exciting result: k-Coloring is in (2-eps_k)^n time, where eps_k>0 for every fixed k!
Algorithms faster than the 2^n time needed to compute the chromatic number were previously known only for k<=6.
arxiv.org/abs/2607.25973
5/6
I gave the problem to GPT-5.6 Sol in Codex (Extra High). Over ~5.5 hours, it wrote and ran code to test ideas, conjectured an explicit candidate hole, and built a general argument using (non-elementary) tools such as Jack polynomials and a Dyson constant-term identity.
6/6
My advisor @mweber_PU and I checked the argument line by line, filled in gaps, simplified the proof, and formalized the full theorem in Lean.
Seeing it hold up under that scrutiny was genuinely exciting. AI-assisted mathematics now feels much more concrete to me.
I'm presenting a poster at @NeurIPSConf DiffCoALG workshop today throughout the day in Upper Level Room 25ABC. I will present our initial theoretical findings on how choosing the right learning architectures can help with model distillation, under a linear rep hypothesis!
Thien Le retweeted
It's been wild to see our work on Muon and the anthology start to get scaled up by the big labs.
After @Kimi_Moonshot released Moonlight, people have asked whether Muon is compatible with muP. I wanted to write up an explainer, as there is something deeper going on here!
(1/8)
Thien Le retweeted
Are you canonicalizing your data? Depending on the group, you might be unavoidably introducing discontinuity...but there's a fix!
Come to our ICML poster, #511, on Wednesday 1:30 - 3:00 PM to hear more! Joint work with Nadav Dym and Jonathan Siegel
arxiv.org/pdf/2402.16077
How do you robustly subsample vertices of large graphs that are changing in size? By marrying the theory of spectral clustering and graph limit! Check out our poster #36 in Halle B on Friday, 10:45-12:45, presented by the amazing Luana Ruiz!
🔗:openreview.net/pdf?id=l3qtSN…
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Interestingly, by using connections to spectral clustering geometry, we show that if the graphon is well-fitted to a mixture model (e.g., stochastic-block), then the necessary number of vertices to sample can be as small as the (finite!) number of components in the mixture.(3/4)
Can group equivariance counteract the computational (SQ/CSQ) hardness of learning neural nets? Swing by our poster #202, presented by the wonderful Bobak Kiani and @HLawrenceCS, on Thursday, 10:45 - 12:45 to find out! #ICLR2024
🔗: openreview.net/pdf?id=ARPrtu…
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In contrast, for real-valued functions, we demonstrate a large family of shallow GNNs that are almost orthogonal in Gaussian space, thus requiring exponentially many correlational SQ queries (subsuming noisy gradient descent computations) to distinguish. (4/5)