测试大模型在形式化推理中是否投机取巧，发现高成功率不等于真实逻辑正确。
Do LLMs Game Formalization? Evaluating Faithfulness in Logical Reasoning
- 对比统一生成与分步式流程，检验模型是否为通过而伪造形式化
- 统一模式下模型宁可失败也不强行构造无效证明
- 分步流程暴露出模型会虚构公理或误译前提，难以被检测
形式化验证可保证证明有效性，但无法确保形式化过程的忠实性。在自然语言逻辑推理中，模型需从零构建公理体系，无现成库支持，这一有效证明与忠实翻译之间的差距尤为突出。本文研究前沿模型在生成 Lean 4 证明时是否存在‘形式化投机’行为。在 303 个一阶逻辑问题（203 来自 FOLIO，100 来自 Multi-LogiEval）上评估 GPT-5 与 DeepSeek-R1，比较统一生成与两阶段流水线（分离形式化与证明）的效果。尽管编译率高达 87%-99%，统一生成中未发现系统性投机：模型更倾向报告失败而非强制构造证明，即使在诱导提示下也如此。然而，部分未被检测到的不忠实行为仍可能存在。两阶段流程揭示两类不忠实现象：GPT-5 在证明阶段虚构公理，可通过跨阶段比对发现；DeepSeek-R1 在形式化阶段误译前提，产生内部一致但错误的输出，完全逃逸检测。结果表明，高编译率或准确率不能等同于忠实推理。代码与数据见 https://github.com/koreankiwi99/formalization-gaming。
原文摘要 · Abstract (English)
Formal verification guarantees proof validity but not formalization faithfulness. For natural-language logical reasoning, where models construct axiom systems from scratch without library constraints, this gap between valid proofs and faithful translations is especially acute. We investigate whether frontier models exploit this gap when generating Lean 4 proofs, a behavior we term formalization gaming. We evaluate GPT-5 and DeepSeek-R1 on 303 first-order logic problems (203 from FOLIO, 100 from Multi-LogiEval), comparing unified generation against a two-stage pipeline that separates formalization from proving. Despite compilation rates of 87-99%, we find no evidence of systematic gaming in unified generation: models prefer reporting failure over forcing proofs, even under prompting designed to encourage it. However, unfaithfulness that evades our detection signals may still occur. The two-stage pipeline reveals two distinct modes of unfaithfulness: GPT-5 fabricates axioms during proof generation, a reactive fallback detectable via cross-stage comparison, while DeepSeek-R1 mistranslates premises during formalization, producing internally consistent outputs that evade detection entirely. These findings show that high compilation rates or accuracies should not be equated with faithful reasoning. Code and data are available at https://github.com/koreankiwi99/formalization-gaming.
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