Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction

TL;DR

This paper introduces a new evaluation framework for mathematical reasoning in large language models, focusing on error identification and correction from the examiner's perspective, and provides a dataset and insights for improving LLM performance.

Contribution

It defines four new evaluation tasks for error correction, creates a dataset with annotated error types, and assesses eleven LLMs, highlighting the impact of prompting strategies.

Findings

GPT-4 outperforms all models

LLaMA-2-7B performs comparably to GPT-3.5 and Gemini Pro

Calculation errors are the most challenging

Abstract

The rapid advancement of Large Language Models (LLMs) in the realm of mathematical reasoning necessitates comprehensive evaluations to gauge progress and inspire future directions. Existing assessments predominantly focus on problem-solving from the examinee perspective, overlooking a dual perspective of examiner regarding error identification and correction. From the examiner perspective, we define four evaluation tasks for error identification and correction along with a new dataset with annotated error types and steps. We also design diverse prompts to thoroughly evaluate eleven representative LLMs. Our principal findings indicate that GPT-4 outperforms all models, while open-source model LLaMA-2-7B demonstrates comparable abilities to closed-source models GPT-3.5 and Gemini Pro. Notably, calculation error proves the most challenging error type. Moreover, prompting LLMs with the error types can improve the average correction accuracy by 47.9\%. These results reveal potential directions for developing the mathematical reasoning abilities of LLMs. Our code and dataset is available on https://github.com/LittleCirc1e/EIC.