{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/math-shepherd-a-label-free-step-by-step","title":"Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations","arxiv_id":"2312.08935","date":"2023-12-14","proceeding":null,"authors":["Peiyi Wang","Lei LI","Zhihong Shao","R. X. Xu","Damai Dai","Yifei Li","Deli Chen","Y. Wu","Zhifang Sui"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2312.08935v3","url_pdf":"https://arxiv.org/pdf/2312.08935v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"math-shepherd-a-label-free-step-by-step","repo_url":"https://github.com/chang-github-00/llm-predictive-decoding","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"math-shepherd-a-label-free-step-by-step","repo_url":"https://github.com/hkust-nlp/b-star","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"math-shepherd-a-label-free-step-by-step","repo_url":"https://huggingface.co/datasets/peiyi9979/Math-Shepherd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"arithmetic-reasoning","task_name":"Arithmetic Reasoning"},{"task_slug":"gsm8k","task_name":"GSM8K"},{"task_slug":"math","task_name":"Math"},{"task_slug":"math-word-problem-solving","task_name":"Math Word Problem Solving"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"},{"task_slug":"reranking","task_name":"Reranking"}],"methods":[{"method_slug":"entropy-regularization","method_name":"Entropy Regularization"},{"method_slug":"ppo","method_name":"PPO"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/arithmetic-reasoning-on-gsm8k","task":"Arithmetic Reasoning","dataset":"GSM8K","model":"Shepherd+Mistral-7B (SFT on MetaMATH + PRM RL+ PRM rerank, k=256)","rank_in_archive_order":24,"of":164,"metrics":{"Accuracy":"89.1","Parameters (Billion)":"7"},"uses_additional_data":true},{"leaderboard":"/sota/arithmetic-reasoning-on-gsm8k","task":"Arithmetic Reasoning","dataset":"GSM8K","model":"Shepherd + Mistral-7B (SFT on MetaMATH + PRM RL)","rank_in_archive_order":52,"of":164,"metrics":{"Accuracy":"84.1","Parameters (Billion)":"7"},"uses_additional_data":true},{"leaderboard":"/sota/math-word-problem-solving-on-math","task":"Math Word Problem Solving","dataset":"MATH","model":"Shepherd + DeepSeek-67B (SFT on MetaMATH + PRM rerank, k=256)","rank_in_archive_order":55,"of":135,"metrics":{"Accuracy":"48.1","Parameters (Billions)":"67"},"uses_additional_data":true},{"leaderboard":"/sota/math-word-problem-solving-on-math","task":"Math Word Problem Solving","dataset":"MATH","model":"Shepherd+Mistral-7B (SFT on MetaMATH + PRM RL+ PRM rerank, k=256)","rank_in_archive_order":71,"of":135,"metrics":{"Accuracy":"43.5","Parameters (Billions)":"7"},"uses_additional_data":true},{"leaderboard":"/sota/math-word-problem-solving-on-math","task":"Math Word Problem Solving","dataset":"MATH","model":"Shepherd + Mistral-7B (SFT on MetaMATH + PRM RL)","rank_in_archive_order":84,"of":135,"metrics":{"Accuracy":"33.0","Parameters (Billions)":"7"},"uses_additional_data":true}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2312.08935","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}