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

TL;DR

ConceptMath is a bilingual benchmark that evaluates large language models' mathematical reasoning at a concept-wise level, revealing performance variations and guiding improvements.

Contribution

It introduces a hierarchical, concept-wise evaluation benchmark for bilingual mathematical reasoning and proposes a fine-tuning strategy to improve LLM performance.

Findings

Existing LLMs show significant variation across math concepts.

Many LLMs fail on basic math concepts despite high average accuracy.

Fine-tuning can enhance LLMs' weaknesses in mathematical reasoning.

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.