LLMs score poorly on CounterMATH, a new counterexample-based university math benchmark, and a 1,025-sample counterexample fine-tune yields small and partly inconsistent gains.
ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models
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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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One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs
LLMs score poorly on CounterMATH, a new counterexample-based university math benchmark, and a 1,025-sample counterexample fine-tune yields small and partly inconsistent gains.