{"paper":{"title":"Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Math-Shepherd trains reward models on auto-generated step labels to verify and reinforce LLM math solutions without human annotations.","cross_cats":["cs.CL","cs.LG"],"primary_cat":"cs.AI","authors_text":"Damai Dai, Deli Chen, Lei Li, Peiyi Wang, R.X. Xu, Yifei Li, Y.Wu, Zhifang Sui, Zhihong Shao","submitted_at":"2023-12-14T13:41:54Z","abstract_excerpt":"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-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That automatically constructed process-wise supervision data accurately labels correct versus incorrect reasoning steps without systematic bias or noise from the generation process itself.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Math-Shepherd is an automatically trained process reward model that scores solution steps to verify and reinforce LLMs, lifting Mistral-7B from 77.9% to 89.1% on GSM8K and 28.6% to 43.5% on MATH.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Math-Shepherd trains reward models on auto-generated step labels to verify and reinforce LLM math solutions without human annotations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"31073cbe9ee9b6bb1cad67334a070dc6e908f2f330ea328d8692dcd2220d7195"},"source":{"id":"2312.08935","kind":"arxiv","version":3},"verdict":{"id":"d75c5099-d22d-4fbe-aebf-456ab69fe5f1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T22:29:38.954816Z","strongest_claim":"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.","one_line_summary":"Math-Shepherd is an automatically trained process reward model that scores solution steps to verify and reinforce LLMs, lifting Mistral-7B from 77.9% to 89.1% on GSM8K and 28.6% to 43.5% on MATH.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That automatically constructed process-wise supervision data accurately labels correct versus incorrect reasoning steps without systematic bias or noise from the generation process itself.","pith_extraction_headline":"Math-Shepherd trains reward models on auto-generated step labels to verify and reinforce LLM math solutions without human annotations."},"references":{"count":60,"sample":[{"doi":"10.18653/v1/2022.emnlp-main.225","year":2022,"title":"Red teaming language models with language models","work_id":"664322b7-6ac6-46c5-b1f2-193a778945d2","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"International Conference on Machine Learning , pages=","work_id":"1a650b5b-a768-4080-8629-3f3f3fe0d908","ref_index":10,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Proceedings of the 29th Symposium on Operating Systems Principles , pages=","work_id":"942205f6-1365-4509-8f46-700be8023817","ref_index":11,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Chi and Quoc V","work_id":"e5146dbc-54b0-40cd-a84c-3d72af59c83f","ref_index":13,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Xuezhi Wang and Jason Wei and Dale Schuurmans and Quoc V. Le and Ed H. Chi and Sharan Narang and Aakanksha Chowdhery and Denny Zhou , title =. The Eleventh International Conference on Learning Represe","work_id":"871bab98-59d0-4eff-8c2d-56c7055fbe92","ref_index":14,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":60,"snapshot_sha256":"efd9458cd4f2b4aedc77964b90d0c75b1942d7b59014aec8b5e9018a7f2bae28","internal_anchors":19},"formal_canon":{"evidence_count":2,"snapshot_sha256":"99ac36ec696a4495b7b2913802107dc7d447e534379a98c764abdc37ee66f038"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}