Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Peiyi Wang, Lei LI, Zhihong Shao, R. X. Xu, Damai Dai, Yifei Li, Deli Chen, Y. Wu, Zhifang Sui
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Abstract
In this paper, we present an innovative process-oriented math process reward model called Math-Shepherd, which assigns a reward score to each step of math problem solutions. The training of Math-Shepherd is achieved using automatically constructed process-wise supervision data, breaking the bottleneck of heavy reliance on manual annotation in existing work. We explore the effectiveness of Math-Shepherd in two scenarios: 1) Verification: Math-Shepherd is utilized for reranking multiple outputs generated by Large Language Models (LLMs); 2) Reinforcement Learning: Math-Shepherd is employed to reinforce LLMs with step-by-step Proximal Policy Optimization (PPO). With Math-Shepherd, a series of open-source LLMs demonstrates exceptional performance. For instance, the step-by-step PPO with Math-Shepherd significantly improves the accuracy of Mistral-7B (77.9\%84.1\% on GSM8K and 28.6\%33.0\% on MATH). The accuracy can be further enhanced to 89.1\% and 43.5\% on GSM8K and MATH with the verification of Math-Shepherd, respectively. We believe that automatic process supervision holds significant potential for the future evolution of LLMs.
Tasks
Benchmark Results
| Dataset | Model | Metric | Claimed | Verified | Status |
|---|---|---|---|---|---|
| GSM8K | Shepherd+Mistral-7B (SFT on MetaMATH + PRM RL+ PRM rerank, k=256) | Accuracy | 89.1 | — | Unverified |
| GSM8K | Shepherd + Mistral-7B (SFT on MetaMATH + PRM RL) | Accuracy | 84.1 | — | Unverified |