VC Search: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning

• URL: http://arxiv.org/abs/2406.05055v2
• Date: Tue, 18 Feb 2025 05:14:48 GMT
• Title: VC Search: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning
• Authors: Shi-Yu Tian, Zhi Zhou, Kun-Yang Yu, Ming Yang, Lin-Han Jia, Lan-Zhe Guo, Yu-Feng Li,
• Abstract summary: We develop a benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different large language models.
• Score: 46.25056744404318
• License:
• Abstract: Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

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