MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
- Published
- Source
- arXiv
- Paper number
- 405
- Field
- Machine Learning
- arXiv ID
- 2606.13473
Key points
- The paper trains three specialized capabilities for proof generation, verification, and repair separately and then merges them into a single M3 model.
- Its defense-in-depth verifier minimizes false positives using bad-case filtering, normalization, multiple judgments, and pessimistic minimum aggregation.
- MaxProof test-time scaling uses 32 initial candidates and up to 10 rounds of PATCH and REWRITE refinement.
- It achieves 27 to 35 points, a gain of 8, on IMO 2025, and 26 to 36 points, a gain of 10, on USAMO 2026, exceeding the gold-medal threshold in both contests.
- It documents four reward-hacking patterns discovered in the M2 cycle and the corresponding defenses.
- It is cost-efficient: using GLM-5.1, it sets a new SOTA on 26-circle packing for less than 11 dollars in API cost.
Paper links
External research summaries. These are not HDATF publications or measured product results.