DeepSeek-Prover-V2: Advancing Formal Reasoning

We introduce DeepSeek-Prover-V2, a large language model designed for formal mathematical theorem proving, particularly in Lean 4. The model is trained using a recursive theorem-proving pipeline that utilizes DeepSeek-V3 to break down complex problems into smaller subgoals and formalize them. Reinforcement learning, starting from synthetic data generated by combining DeepSeek-V3's chain-of-thought reasoning with formalized subgoal proofs, further improves the model's ability to connect informal and formal mathematical reasoning. DeepSeek-Prover-V2-671B demonstrates state-of-the-art performance on various benchmarks, including MiniF2F-test, PutnamBench, and the newly introduced ProverBench, which includes problems from AIME competitions. The research highlights the effectiveness of subgoal decomposition and reinforcement learning in advancing automated theorem proving and shows the shrinking gap between informal and formal reasoning in large language models.

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