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Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models
来源日期（仅到月份） 2026-07
来源记录日期 2026-07
雷达观测 2026-11-01 22:02
摘要
Large reasoning models ( e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets and reliance on purely numerical evaluation often mask their true reasoning shortcomings. To address this, we propose leveraging the inherent rigor and methodological complexity of mathematical proofs as a diagnostic tool to expose these hidden failures. Specifically, we introduce the RFMDataset (Reveal Failure Modes), a collection of 200 diverse mathematical proof problems to thoroughly evaluate the performance of advanced models. Our in-depth analysis of their failures uncovers 10 fine-grained error types, which shows fundamental limitations in current large reasoning models: 1) Large reasoning models still have limited capability in generating entirely correct mathematical proofs, with some models solving less than 20% of problems and even making mistakes on fundamental ones; 2) models exhibit a diverse spectrum of reasoning failures, prominently demonstrating the lack of guarantees for the correctness and rigor intermediate reasoning steps; and 3) models show hallucination and incompleteness during the reasoning process. Our findings also reveal that directly prompting models to self-reflect on specific failure modes is insufficient to resolve the current logical dilemmas, necessitating domain knowledge and formal verification.
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记录 #1 · 2026-07 · 最新观测版本
Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models
Large reasoning models ( e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets and reliance on purely numerical evaluation often mask their true reasoning shortcomings. To address this, we propose leveraging the inherent rigor and methodological complexity of mathematical proofs as a diagnostic tool to expose these hidden failures. Specifically, we introduce the RFMDataset (Reveal Failure Modes), a collection of 200 diverse mathematical proof problems to thoroughly evaluate the performance of advanced models. Our in-depth analysis of their failures uncovers 10 fine-grained error types, which shows fundamental limitations in current large reasoning models: 1) Large reasoning models still have limited capability in generating entirely correct mathematical proofs, with some models solving less than 20% of problems and even making mistakes on fundamental ones; 2) models exhibit a diverse spectrum of reasoning failures, prominently demonstrating the lack of guarantees for the correctness and rigor intermediate reasoning steps; and 3) models show hallucination and incompleteness during the reasoning process. Our findings also reveal that directly prompting models to self-reflect on specific failure modes is insufficient to resolve the current logical dilemmas, necessitating domain knowledge and formal verification.
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