MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs

TL;DR

MathGenie introduces a novel data augmentation method using question back-translation to improve the mathematical reasoning capabilities of large language models, achieving state-of-the-art results among open-source models.

Contribution

The paper presents MathGenie, a new approach for generating diverse math problems from limited data, enhancing open-source LLMs' reasoning performance with a back-translation technique.

Findings

MathGenie models outperform previous open-source models on five datasets.

MathGenieLM-InternLM2 achieves 87.7% on GSM8K and 55.7% on MATH.

The augmentation technique significantly improves reasoning accuracy.

Abstract

Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. In this paper, we introduce MathGenie, a novel method for generating diverse and reliable math problems from a small-scale problem-solution dataset (denoted as seed data). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as MathGenieLM. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.