UTMath: Math Evaluation with Unit Test via Reasoning-to-Coding Thoughts

TL;DR

UTMath introduces a comprehensive benchmark with extensive unit tests across multiple mathematical domains to evaluate LLMs' reasoning and generality, along with a reasoning-to-coding approach to improve performance.

Contribution

The paper presents the UTMath benchmark and the RCoT method, offering a new framework for assessing and enhancing LLMs' mathematical reasoning capabilities.

Findings

Best model solves 32.57% of problems

UTMath contains 1,053 problems across nine domains

RCoT improves reasoning and solution quality

Abstract

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing benchmarks such as GSM8K and MATH present limitations, including narrow problem definitions with specific numbers and reliance on predetermined rules that hinder accurate assessments of reasoning and generality. This paper introduces the UTMath Benchmark, a robust evaluation framework designed to assess LLMs through extensive unit tests, with a focus on both the accuracy and generality of model responses. It comprises 1,053 cutting-edge problems spanning nine mathematical domains, with an average of 68 test cases per problem. UTMath is highly challenging, with the best-performing model, o1-mini, solving only 32.57\% of the problems, followed by o1-preview at 27.16\%, and GPT-4o at 26.93\%. Furthermore, we present the Reasoning-to-Coding of Thoughts (RCoT) approach, which encourages LLMs to engage in explicit reasoning prior to code generation, thereby facilitating the production of more sophisticated solutions and enhancing overall performance and efficiency. Additionally, we also release the UTMath-Train training dataset (more than 70k samples), to support the community in further exploring mathematical reasoning. Our benchmark can be accessed via the following link: https://github.com/UTMathGroup/UTMath