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Lean-STaR: Learning to Interleave Thinking and Proving

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arxiv 2407.10040 v5 pith:MF5KXMPK submitted 2024-07-14 cs.AI

Lean-STaR: Learning to Interleave Thinking and Proving

classification cs.AI
keywords modellean-starproofprovingthoughtslanguagetheoremtraining
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models ($\boldsymbol{43.4\% \rightarrow 46.3\%,}$ Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Goedel-Architect introduces blueprint generation and iterative refinement for Lean 4 theorem proving, reaching 99.2% on MiniF2F-test and 75.6% on PutnamBench with DeepSeek-V4-Flash.

  2. Event-B Agent: Towards LLM Agent for Formal Model Synthesis and Repair

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  3. CAM-Bench: A Benchmark for Computational and Applied Mathematics in Lean

    cs.AI 2026-05 accept novelty 7.0

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  4. From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier

    cs.CL 2026-07 accept novelty 6.0

    LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.

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