ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models

• URL: http://arxiv.org/abs/2402.14660v2
• Date: Fri, 23 Feb 2024 07:13:00 GMT
• Title: ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models
• Authors: Yanan Wu, Jie Liu, Xingyuan Bu, Jiaheng Liu, Zhanhui Zhou, Yuanxing Zhang, Chenchen Zhang, Zhiqi Bai, Haibin Chen, Tiezheng Ge, Wanli Ouyang, Wenbo Su, Bo Zheng
• Abstract summary: This paper introduces ConceptMath, a fine-grained benchmark that evaluates concept-wise mathematical reasoning of Large Language Models (LLMs) Unlike traditional benchmarks that evaluate general mathematical reasoning with an average accuracy, ConceptMath systematically organizes math problems under a hierarchy of math concepts.
• Score: 67.32868432113587
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: This paper introduces ConceptMath, a bilingual (English and Chinese), fine-grained benchmark that evaluates concept-wise mathematical reasoning of Large Language Models (LLMs). Unlike traditional benchmarks that evaluate general mathematical reasoning with an average accuracy, ConceptMath systematically organizes math problems under a hierarchy of math concepts, so that mathematical reasoning can be evaluated at different granularity with concept-wise accuracies. Based on our ConcepthMath, we evaluate a broad range of LLMs, and we observe existing LLMs, though achieving high average accuracies on traditional benchmarks, exhibit significant performance variations across different math concepts and may even fail catastrophically on the most basic ones. Besides, we also introduce an efficient fine-tuning strategy to enhance the weaknesses of existing LLMs. Finally, we hope ConceptMath could guide the developers to understand the fine-grained mathematical abilities of their models and facilitate the growth of foundation models.

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