Pythagoras-LM/Pythagoras-Prover-4B

Pythagoras-Prover-4B: Efficient Lean 4 Theorem Proving

Pythagoras-Prover-4B is a 4 billion parameter autoregressive language model from Pythagoras-LM, optimized for formal theorem proving in Lean 4. It is distinguished by its compute efficiency and performance, achieved through a unique Lean-verified synthetic data pipeline and Augmented Lean Formalisation (ALF).

Key Capabilities & Innovations

• Formal Theorem Proving: Specifically trained for generating formal proofs in Lean 4.
• Compute Efficiency: Achieves strong performance with a relatively small parameter count (4B), outperforming models up to 167 times larger on certain benchmarks.
• Augmented Lean Formalisation (ALF): Utilizes a structured mutation scheme to expand a verified seed corpus into approximately 2 million formal variants, enabling robust training without extensive manual verification.
• Synthetic Data Pipeline: Employs a scalable pipeline that autoformalizes natural language problems into Lean, followed by a rubric-guided distillation stage to refine formalizations.
• Diffusion-based Prover: The family also includes Pythagoras-Prover-Diffusion, the first diffusion-based theorem prover that iteratively refines Lean proofs.

Performance Highlights

• MiniF2F-Test: Achieves 86.07% on MiniF2F-Test at Pass@32, surpassing DeepSeek-Prover-V2-671B despite being significantly smaller.
• No Self-Correction: Performance metrics are achieved without relying on inference-time self-correction or test-time reinforcement learning, indicating strong inherent reasoning capabilities.

Ideal Use Cases

• Developers and researchers working on formal verification and theorem proving in Lean 4.
• Applications requiring efficient and accurate automated proof generation.
• Environments where computational resources are a consideration, given its high performance-to-parameter ratio.