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    <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 large-scale 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 training-free framework that leverages formal language to detect ill-defined problems, where a variable-constraint 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.</abstract>
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%0 Conference Proceedings
%T VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning
%A Tian, Shi-Yu
%A Zhou, Zhi
%A Yu, Kun-Yang
%A Yang, Ming
%A Jia, Lin-Han
%A Guo, Lan-Zhe
%A Li, Yu-Feng
%Y Christodoulopoulos, Christos
%Y Chakraborty, Tanmoy
%Y Rose, Carolyn
%Y Peng, Violet
%S Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing
%D 2025
%8 November
%I Association for Computational Linguistics
%C Suzhou, China
%@ 979-8-89176-332-6
%F tian-etal-2025-vcsearch
%X 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 large-scale 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 training-free framework that leverages formal language to detect ill-defined problems, where a variable-constraint 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.
%U https://aclanthology.org/2025.emnlp-main.642/
%P 12721-12742

Markdown (Informal)

[VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning](https://aclanthology.org/2025.emnlp-main.642/) (Tian et al., EMNLP 2025)

• VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning (Tian et al., EMNLP 2025)

ACL

• Shi-Yu Tian, Zhi Zhou, Kun-Yang Yu, Ming Yang, Lin-Han Jia, Lan-Zhe Guo, and Yu-Feng Li. 2025. VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 12721–12742, Suzhou, China. Association for Computational Linguistics.