UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models

• URL: http://arxiv.org/abs/2501.13766v1
• Date: Thu, 23 Jan 2025 15:46:43 GMT
• Title: UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models
• Authors: Xin Xu, Jiaxin Zhang, Tianhao Chen, Zitong Chao, Jishan Hu, Can Yang,
• Abstract summary: UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Our evaluation of 23 leading LLMs reveals that the highest EAcc robustness achieved is 56.3% by OpenAI-o1-mini, with large $Delta$ values observed across different models.
• Score: 11.964085209696051
• License:
• Abstract: Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap ($\Delta$), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large $\Delta$ values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and $\Delta = 0$. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

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