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MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling

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Computer Science > Machine Learning

arXiv:2606.13473 (cs)
[Submitted on 11 Jun 2026]

Title:MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling

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Abstract:We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
Cite as: arXiv:2606.13473 [cs.LG]
  (or arXiv:2606.13473v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2606.13473
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Jiacheng Chen [view email]
[v1] Thu, 11 Jun 2026 15:27:06 UTC (2,912 KB)
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