形式化证明领域终于有了计算高效的实用方案——4B 模型就能超越 671B 巨无霸，做定理证明或形式化验证的团队可以直接用，省下大量算力成本。
Pythagoras-Prover 是一个计算高效的 Lean 定理证明器系列，包含 4B 和 32B 参数的自回归模型，以及首个基于扩散的证明器（4B）。通过课程式监督微调和动态证明过滤，训练效率大幅提升。其 4B 模型在 MiniF2F-Test 上以 86.1% 的 pass@32 超越 DeepSeek-Prover-V2-671B（82.4%），参数减少约 167 倍；32B 模型达到 93.0%，创下开源新纪录。团队还提出了增强型 Lean 形式化方法（ALF），通过扰动已知问题生成变体，减少对表面形式的依赖，并发布了 MiniF2F-ALF 基准。
Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation
Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B.