Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist

TL;DR

This paper introduces MathCheck, a comprehensive checklist and evaluation tool for assessing the genuine mathematical reasoning and robustness of large language models across diverse tasks, revealing significant performance gaps.

Contribution

The paper presents MathCheck, a novel, versatile checklist and automatic generation tool for evaluating mathematical reasoning and robustness in language models, improving upon traditional benchmarks.

Findings

Frontier models like GPT-4o perform well on MathCheck.

Many models show significant decline in reasoning robustness.

MathCheck better reflects true mathematical abilities than traditional benchmarks.

Abstract

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, presenting a substantial risk of model overfitting and fails to accurately measure the genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly applied across a diverse array of tasks. To this end, we introduce MathCheck, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MathCheck includes multiple mathematical reasoning tasks and robustness tests to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MathCheck, we develop MathCheck-GSM and MathCheck-GEO to assess math textual reasoning and multi-modal reasoning abilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MathCheck-GSM and MathCheck-GEO to evaluate 26 LLMs and 17 MLLMs. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MathCheck better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. Using MathCheck, we can efficiently conduct informative behavior analysis to deeply investigate models. Finally, we show that our checklist paradigm can easily extend to other reasoning tasks.