arXiv:2607.11307cs.AI2026-07被引 2

通过智能分解证明步骤,用少量计算提升数学推理形式化准确率。

Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization

论文配图:Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization
图 1 · 摘自论文原文
  • 将证明拆解为独立单元,仅优化关键分解环节,节省推理开销。
  • 在ProofFlowBench上比最佳已有方法提升19.0%,兼顾语法正确与语义忠实。
  • 适合需要高效验证数学证明的AI系统开发者或研究者使用。

全证明自动形式化将自然语言中的长篇数学证明转化为可形式验证的推理过程,为提升可验证数学推理能力提供路径。与命题级形式化不同,证明自动形式化是长时程挑战,需协调多个证明步骤间的命题、上下文与依赖关系,但近期才受到关注。现有方法要么依赖昂贵模型训练,要么在推理时进行过度且无引导的修复。为此,我们提出ToMap,一个基于多智能体框架的分解-形式化-证明流水线,通过形式化验证与语义评价指标实现高效的测试时优化。我们分析发现,分解器(Decomposer)是瓶颈:其生成的原子性、自包含证明单元质量直接决定下游模块能否成功形式化与证明。因此,ToMap将形式化器与证明器视为下游执行者,将测试时算力集中于分解器优化。该优化采用受GEPA启发的循环机制,对候选分解方案演化提示,并结合形式化验证进展与语义评价指标定义帕累托前沿,指导下一次分解更新。在ProofFlowBench上的实验表明,ToMap在语法正确性与语义忠实性双指标上优于最先进方法19.0%,且测试时成本更低。缩放分析显示,多数增益在数次分解演化迭代内即显现,为测试时预算分配提供依据。

原文摘要 · Abstract (English)

Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning. Unlike statement-level formalization, proof autoformalization is a long-horizon challenge requiring coordination of claims, contexts, and dependencies across many proof steps, yet has only recently come under focused study. Current approaches either rely on costly model training or apply excessive, unguided repair at inference time. To this end, we introduce ToMap, a multi-agent framework that structures proof autoformalization as a Decomposer-Formalizer-Prover pipeline with efficient test-time optimization guided by formal verification and semantic rubrics for proof quality. Rather than distributing test-time compute across all agents, we perform bottleneck analysis and identify the Decomposer as the critical bottleneck: the quality of its atomic, self-contained proof units directly determines whether downstream agents can successfully formalize and prove each step. ToMap therefore treats the Formalizer and Prover as downstream executors and efficiently focuses test-time compute on Decomposer refinement. This refinement follows a loop inspired by GEPA, evolving prompts over candidate decompositions and using formal verification progress together with semantic proof rubrics to define a Pareto frontier that guides the next decomposition update. Experiments on ProofFlowBench show that ToMap improves over the best previous method by 19.0% when evaluated by both syntactic correctness and semantic faithfulness, while requiring lower test-time cost. Scaling analysis shows that most gains emerge within a few iterations of decomposition evolution, guiding test-time budget selection.

数学推理多智能体形式化测试时优化

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