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AI Research
arXiv CS.AI·Jun 12·5 min read
Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation
TL;DR
Formal proof systems struggle with high computational costs due to limited verified proof data. Pythagoras-Prover is an open-source family of Lean theorem provers designed for efficiency, utilizing autoregressive and diffusion-based models.
✦ Why It Matters
Engineers can leverage Pythagoras-Prover for more efficient formal verification in their projects, reducing computational costs.
Key Takeaways
- Utilize Pythagoras-Prover for efficient formal verification tasks.
- Implement curriculum training with stratified problem sets.
- Explore ALF for generating diverse formal statement variants.
- Adopt dynamic filtering to optimize proof reasoning processes.
Full Summary
Formal proving, essential for verifying mathematical theorems and software correctness, often requires significant computational resources, primarily due to the scarcity of verified proof data and the complexity of reasoning traces. Pythagoras-Prover introduces a family of Lean theorem provers that includes autoregressive models with 4 billion and 32 billion parameters, as well as a novel diffusion-based prover.
To enhance training efficiency, a Lean-verified corpus is created, categorizing problems into easy, medium, and hard levels, allowing models to learn progressively. A dynamic proof-reasoning filtering scheme is employed to maintain informative proof traces within an 8k-token context limit.
Additionally, Augmented Lean Formalisation (ALF) generates diverse formal statement variants through self-distillation, reducing dependency on specific problem formulations. Empirical results show that Pythagoras-Prover-4B outperforms a larger model, DeepSeek-Prover-V2-671B, while the 32B model achieves a remarkable 93.0% accuracy on MiniF2F-Test, solving 93 of 672 PutnamBench problems.
These advancements suggest significant improvements in the efficiency and effectiveness of formal proving tools.