Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
This addresses the challenge of enhancing LLM performance in mathematical problem-solving for AI researchers and developers, offering an automated alternative to manual annotation, though it is incremental in building on existing reward modeling techniques.
The paper tackles the problem of improving LLMs' mathematical reasoning by introducing Math-Shepherd, a process-oriented reward model that assigns scores to each step of solutions without human annotations, resulting in significant accuracy improvements, such as boosting Mistral-7B from 77.9% to 89.1% on GSM8K and from 28.6% to 43.5% on MATH.
In this paper, we present an innovative process-oriented math process reward model called \textbf{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) \textit{Verification}: Math-Shepherd is utilized for reranking multiple outputs generated by Large Language Models (LLMs); 2) \textit{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\%$\to$84.1\% on GSM8K and 28.6\%$\to$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.