Pythagoras-Prover:通过增强型Lean形式化推进高效形式化证明
阅读原文· arxiv.org开源Lean定理证明器家族Pythagoras-Prover包含4B和32B自回归模型及4B扩散模型。训练采用课程式SFT,通过动态证明推理过滤将每条样本控制在8k token上下文预算内,并引入增强型Lean形式化(ALF)将稀缺验证语料扩展为变体语句,以自蒸馏提供额外训练信号。Pythagoras-Prover-4B在MiniF2F-Test上以86.1% pass@32超越DeepSeek-Prover-V2-671B(82.4%),参数量减少约167倍;Pythagoras-Prover-32B以93.0%创下开源SOTA,并在PutnamBench上解决93/672题。项目同步发布MiniF2F-ALF基准。
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.