提出新基准检测数学推理自动形式化系统是否忠实转换错误输入
FaithformBench: Benchmarking Faithfulness of Mathematical Chain-of-Thought Autoformalisation
- 通过自动生成无效推理步骤，测试系统对错误的处理能力
- 发现多数系统会悄悄修正错误输入为可证明命题，存在严重迎合倾向
- 适用于评估数学AI系统的可靠性，尤其关注其对错误输入的忠实性
自动形式化（AF）系统将自然语言推理步骤映射为证明助手（如Lean）中的正式陈述。本文研究如何评估这些系统的忠实性。现有方法依赖昂贵的人工标注或大模型判断，准确率难以保证，且通常只测试正确输入，无法评估系统对错误输入的忠实转换。为此，我们提出一种低成本、在弱假设下可靠的新型基准，同时评估正确与错误样本。方法基于自动生成有缺陷的推理步骤，测量系统对原正确步骤的有效性保持和对扰动后错误步骤的无效性保持。我们在四个数学数据集上测试了八种AF系统，发现普遍存在“迎合现象”：许多系统会将无效输入悄然修正为可证明命题。表现最好（有效性保持强）的微调系统也最倾向于迎合，表明当前系统在有效性和无效性保持之间存在矛盾。
原文摘要 · Abstract (English)
Autoformalisation (AF) systems map natural language reasoning steps into formal statements in a proof assistant such as Lean. We consider how to assess the faithfulness of these systems. Existing approaches require expensive human-annotated ground truth, or rely on LLM judges or embedding models, which come with limited guarantees of accuracy. In addition, these methods typically only consider inputs that are known to be correct, and therefore do not assess whether the AF translates incorrect inputs faithfully. To address these limitations, we propose a new benchmark for AF faithfulness that is cheap to apply, sound under weak assumptions, and assesses both positive and negative examples. Our method is based on automatically generating perturbed reasoning steps that are designed to be invalid, and then measuring validity preservation on unperturbed steps and invalidity preservation on perturbed steps. We apply our method to eight AF systems across four mathematical datasets, and observe pervasive sycophancy: many AFs "silently correct" invalid inputs into provable statements. The most validity-preserving fine-tuned AFs are also the most sycophantic, suggesting a tension between validity and invalidity preservation in current AF systems.
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