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DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition

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Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition

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Type
Open Source
Company
DeepSeek
Visit Website GitHub (40 stars)

About DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition

DeepSeek-Prover-V2 is an open-source large language model designed for formal theorem proving in Lean 4. It leverages reinforcement learning and subgoal decomposition, initialized with data from a recursive theorem proving pipeline powered by DeepSeek-V3. The model synthesizes cold-start reasoning data by prompting DeepSeek-V3 to decompose complex problems into subgoals, then combines successful subgoal proofs with chain-of-thought reasoning to train a 7B prover model. After fine-tuning, reinforcement learning with binary correct/incorrect feedback further enhances the model's ability to bridge informal reasoning and formal proof construction. The resulting DeepSeek-Prover-V2-671B achieves state-of-the-art performance with an 88.9% pass ratio on the MiniF2F-test and solves 49 out of 658 problems from PutnamBench. The project also introduces ProverBench, a benchmark dataset of 325 problems (including 15 from AIME) to evaluate formalization and proof capabilities.

Key Features

Recursive theorem proving pipeline using DeepSeek-V3 for subgoal decomposition and formalization
Cold-start data synthesis by pairing step-by-step formal proofs with chain-of-thought reasoning
Reinforcement learning with binary correct/incorrect feedback to improve reasoning-to-formalization bridging
State-of-the-art performance: 88.9% pass ratio on MiniF2F-test and 49/658 PutnamBench problems solved
Open-source model weights and dataset (MiniF2F solutions available)
ProverBench benchmark dataset (325 formalized problems, including AIME 2022-2024)

Pros & Cons

Pros
  • Achieves state-of-the-art results on MiniF2F and PutnamBench
  • Open-source and freely available for research and development
  • Integrates informal mathematical reasoning with formal proof construction
  • Uses reinforcement learning to improve model performance beyond supervised fine-tuning
  • Provides a new benchmark (ProverBench) for further research
Cons
  • Requires significant computational resources (671B parameter model)
  • Currently focused on Lean 4, limiting applicability to other proof assistants
  • Performance on real-world, non-competition mathematics not fully evaluated
  • Cold-start data generation depends on the proprietary DeepSeek-V3 model

Best For

Formal theorem proving in Lean 4Automated mathematical reasoning and proof generationBenchmarking and research in neural theorem provingEvaluating formalization of contest-level mathematics (e.g., AIME, Putnam)

FAQ

What is DeepSeek-Prover-V2?
DeepSeek-Prover-V2 is an open-source large language model designed for formal theorem proving in Lean 4. It uses reinforcement learning and subgoal decomposition to achieve state-of-the-art performance on mathematical competition problems.
How does DeepSeek-Prover-V2 work?
It initializes by using DeepSeek-V3 to decompose complex theorems into subgoals and formalizes them in Lean 4. A 7B model proves each subgoal, and successful proofs are combined with chain-of-thought reasoning to create cold-start data. The model is then fine-tuned on this data and further improved via reinforcement learning with binary feedback.
What performance does DeepSeek-Prover-V2 achieve?
It achieves an 88.9% pass ratio on the MiniF2F-test and solves 49 out of 658 problems from PutnamBench, setting state-of-the-art results in neural theorem proving.
Is DeepSeek-Prover-V2 open-source?
Yes, the model weights, code, and solved MiniF2F proofs are publicly available on GitHub under an open-source license (LICENSE-MODEL file).
What is ProverBench?
ProverBench is a benchmark dataset introduced with DeepSeek-Prover-V2, containing 325 formalized problems from number theory and algebra, including 15 from recent AIME competitions (2022-2024).