{"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/internlm2-5-stepprover-advancing-automated","title":"InternLM2.5-StepProver: Advancing Automated Theorem Proving via Expert Iteration on Large-Scale LEAN Problems","arxiv_id":"2410.15700","date":"2024-10-21","proceeding":null,"authors":["Zijian Wu","Suozhi Huang","Zhejian Zhou","Huaiyuan Ying","Jiayu Wang","Dahua Lin","Kai Chen"],"abstract":"Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. The major learning paradigm is expert iteration, which necessitates a pre-defined dataset comprising numerous mathematical problems. In this process, LLMs attempt to prove problems within the dataset and iteratively refine their capabilities through self-training on the proofs they discover. We propose to use large scale LEAN problem datasets Lean-workbook for expert iteration with more than 20,000 CPU days. During expert iteration, we found log-linear trends between solved problem amount with proof length and CPU usage. We train a critic model to select relatively easy problems for policy models to make trials and guide the model to search for deeper proofs. InternLM2.5-StepProver achieves open-source state-of-the-art on MiniF2F, Lean-Workbook-Plus, ProofNet, and Putnam benchmarks. Specifically, it achieves a pass of 65.9% on the MiniF2F-test and proves (or disproves) 17.0% of problems in Lean-Workbook-Plus which shows a significant improvement compared to only 9.5% of problems proved when Lean-Workbook-Plus was released. We open-source our models and searched proofs at https://github.com/InternLM/InternLM-Math and https://huggingface.co/datasets/internlm/Lean-Workbook.","url_abs":"https://arxiv.org/abs/2410.15700v1","url_pdf":"https://arxiv.org/pdf/2410.15700v1.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":"internlm2-5-stepprover-advancing-automated","repo_url":"https://github.com/internlm/internlm-math","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":null,"task_name":"CPU"},{"task_slug":"math","task_name":"Math"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2410.15700","atlas_url":"https://app.syntology.ai/?focus=2410.15700","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.15700"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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