{"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/deepseek-prover-v2-advancing-formal","title":"DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition","arxiv_id":"2504.21801","date":"2025-04-30","proceeding":null,"authors":["Z. Z. Ren","Zhihong Shao","Junxiao Song","Huajian Xin","Haocheng Wang","Wanjia Zhao","Liyue Zhang","Zhe Fu","Qihao Zhu","Dejian Yang","Z. F. Wu","Zhibin Gou","Shirong Ma","Hongxuan Tang","Yuxuan Liu","Wenjun Gao","Daya Guo","Chong Ruan"],"abstract":"We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.","url_abs":"https://arxiv.org/abs/2504.21801v1","url_pdf":"https://arxiv.org/pdf/2504.21801v1.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":"deepseek-prover-v2-advancing-formal","repo_url":"https://github.com/deepseek-ai/deepseek-prover-v2","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"},{"task_slug":"large-language-model","task_name":"Large Language Model"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2504.21801","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}