OpenAI's models proved the local smoothing conjecture in every dimension, refuted the Exponential Time Hypothesis, and formalized the Yang-Mills existence proof in Lean
AspireAI community · OpenAI
OpenAI announced three AI-derived results on October 26 with the manuscripts and Lean formalizations published in its openai/math repository. The mathematics result is a proof of the local smoothing conjecture in every dimension, which also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions, based on a novel auxiliary PDE; the AI output was obtained on October 18 and formalized in Lean the following day. The computer science result is a disproof of the Exponential Time Hypothesis, a longstanding conjecture closely tied to P vs. NP, found on October 16 and formalized in Lean on October 17. The physics result is a mathematically rigorous existence proof for interacting quantum field theories containing gauge fields and fermions in four dimensions, including QCD, which includes pure Yang-Mills existence as a subproblem. OpenAI is releasing the math and CS artifacts publicly and deferring the physics materials to an external group led by David Gross, and says it will not seek academic credit for the underlying discoveries. The honest limitation is that the proof work is new, not peer-reviewed, and the ETH refutation is still being shepherded by a group of complexity theorists who have invited an open examination of the claim.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.