Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?

Kuei-Chun Kao, Ruochen Wang, Cho-Jui Hsieh


Abstract
Large Language Models have demonstrates remarkable performance in solving math problems, a hallmark of human intelligence.Despite high success rates on current benchmarks, however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.
Anthology ID:
2024.findings-emnlp.980
Volume:
Findings of the Association for Computational Linguistics: EMNLP 2024
Month:
November
Year:
2024
Address:
Miami, Florida, USA
Editors:
Yaser Al-Onaizan, Mohit Bansal, Yun-Nung Chen
Venue:
Findings
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
16821–16843
Language:
URL:
https://aclanthology.org/2024.findings-emnlp.980
DOI:
Bibkey:
Cite (ACL):
Kuei-Chun Kao, Ruochen Wang, and Cho-Jui Hsieh. 2024. Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 16821–16843, Miami, Florida, USA. Association for Computational Linguistics.
Cite (Informal):
Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns? (Kao et al., Findings 2024)
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