Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

2026-06-10 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

Pythagoras-Prover is an open-source family of Lean theorem provers designed for compute efficiency, addressing the high training and inference costs of modern provers. It includes autoregressive models at 4B and 32B parameters, plus a 4B diffusion-based prover that refines proofs iteratively. To enhance training, the project developed a Lean-verified corpus stratified for curriculum SFT, allowing models to learn progressively. A dynamic proof-reasoning filtering scheme maintains informative traces within an 8k-token context. Additionally, Augmented Lean Formalisation (ALF) expands scarce verified corpora into statement variants via self-distillation, reducing reliance on surface forms. Empirically, Pythagoras-Prover-4B outperforms DeepSeek-Prover-V2-671B at 86.1% vs 82.4% pass@32 on MiniF2F-Test with ~167x fewer parameters. The 32B model achieves 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems, setting a new open-source benchmark.

Key takeaway

For AI Scientists and Research Scientists developing formal verification tools, Pythagoras-Prover demonstrates that significant performance gains are achievable with substantially fewer parameters. You should explore curriculum SFT, dynamic proof-reasoning filtering, and Augmented Lean Formalisation (ALF) to improve training efficiency and data utilization. Consider these techniques to build more accessible and performant theorem provers without requiring massive compute resources.

Key insights

Compute-efficient Lean theorem provers can surpass larger models through strategic data augmentation and curriculum learning.

Principles

• Stratified curriculum SFT improves proof skill acquisition.
• Dynamic filtering preserves informative proof traces efficiently.
• Perturbing known problems via self-distillation expands training data.

Method

Train models using a curriculum SFT on a stratified corpus, applying dynamic proof-reasoning filtering. Augment data with Augmented Lean Formalisation (ALF) via self-distillation.

In practice

• Implement curriculum SFT for complex reasoning tasks.
• Use dynamic filtering to manage context windows.
• Apply self-distillation for data augmentation.

Topics

• Lean Theorem Provers
• Formal Verification
• Compute Efficiency
• Curriculum SFT
• Augmented Lean Formalisation
• MiniF2F-Test

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.