← 研踪 PaperTrailarXiv:2605.06660 · v2
Verifier-Backed Hard Problem Generation for Mathematical Reasoning
首次提交 2026-05-08 01:58
版本更新 2026-11-07 05:52
雷达观测 2026-11-10 10:11
摘要
Large Language Models (LLMs) demonstrate strong capability in solving scientific and mathematical problems, yet they struggle to produce valid and challenging novel problems -- an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-backed hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin. Our code is available at https://github.com/Miaow-Lab/VHG.
作者备注：29 pages, 19 figures. Accepted at NeurIPS 2026
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v2 · 2026-11-07 05:52 · 最新观测版本
Verifier-Backed Hard Problem Generation for Mathematical Reasoning
Large Language Models (LLMs) demonstrate strong capability in solving scientific and mathematical problems, yet they struggle to produce valid and challenging novel problems -- an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-backed hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin. Our code is available at https://github.com/Miaow-Lab/VHG.
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