2024/06/07 by Shi-Yu Tian, Zhi Quan Zhou, Tian, Shi-Yu +9 · 1 citation
Decision Sciences · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.2406.05055
openalex publication_date 2024/06/07 · openalex created_date 2024/06/11 · openalex updated_date 2026/07/28
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.