MathScale: Scaling Instruction Tuning for Mathematical Reasoning

TL;DR

MathScale introduces a scalable method to generate extensive mathematical reasoning datasets using frontier LLMs, significantly enhancing the mathematical problem-solving abilities of open-source models like LLaMA-2 and Mistral.

Contribution

We propose MathScale, a novel approach to create large-scale math reasoning data and demonstrate its effectiveness in improving LLMs' mathematical capabilities.

Findings

Created MathScaleQA with 2 million math QA pairs.

Achieved state-of-the-art performance on MwpBench with MathScale-7B.

Significant accuracy improvements over peers of similar size.

Abstract

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., {\tt GPT-3.5}). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct {\sc MwpBench}, a benchmark of Math Word Problems, which is a collection of ten datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on {\sc MwpBench}, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.9\% in micro average accuracy and 43.7\% in macro average accuracy, respectively.