用依赖图保持证明逻辑,让AI翻译数学证明更忠实。
ProofFlow: A Dependency Graph Approach to Faithful Proof Autoformalization
- 构建步骤间依赖图,确保形式化保留原论证结构。
- 在184个本科级题目上达0.545的综合得分,远超基线。
- 适合数学自动化、AI推理研究者使用。
证明自动形式化是将自然语言定理与证明转化为可机器验证代码的关键步骤,对整合大模型到严谨数学工作流至关重要。现有方法重在生成可执行代码,但常丢失原始论证的语义和逻辑结构。为此,我们提出ProofFlow,将结构保真度作为首要目标。该方法首先构建有向无环图(DAG)以映射证明步骤间的逻辑依赖关系;随后采用创新的引理驱动策略,将每一步系统地形式化为中间引理,从而保留原始论证的逻辑结构。为支持评估,我们构建了一个包含184个本科水平问题的新基准,均经手动标注步骤解法与逻辑依赖图,并提出ProofScore复合指标,用于衡量语法正确性、语义忠实度与结构保真度。实验表明,我们的管道在自动形式化任务上达到新最优,ProofScore为0.545,显著优于全证明形式化(0.123)与逐步形式化(0.072)等基线。相关代码、数据集与评估指标已开源,欢迎进一步研究。
原文摘要 · Abstract (English)
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.123), which processes the entire proof at once, and step-proof formalization (0.072), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://github.com/Huawei-AI4Math/ProofFlow.
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