ControlMath: Controllable Data Generation Promotes Math Generalist Models

TL;DR

ControlMath introduces an iterative data generation framework with diverse math problems, significantly enhancing the generalization of math reasoning models beyond specific domains using a large, high-quality dataset.

Contribution

The paper presents a novel iterative method for generating diverse math problems, improving model generalization with fewer high-quality data points.

Findings

Generated 190k diverse math problems with ControlMathQA

Combining ControlMathQA with existing datasets improves reasoning performance

Enhanced model generalization beyond specific domains

Abstract

Utilizing large language models (LLMs) for data augmentation has yielded encouraging results in mathematical reasoning. However, these approaches face constraints in problem diversity, potentially restricting them to in-domain/distribution data generation. To this end, we propose ControlMath, an iterative method involving an equation-generator module and two LLM-based agents. The module creates diverse equations, which the Problem-Crafter agent then transforms into math word problems. The Reverse-Agent filters and selects high-quality data, adhering to the "less is more" principle, achieving better results with fewer data points. This approach enables the generation of diverse math problems, not limited to specific domains or distributions. As a result, we collect ControlMathQA, which involves 190k math word problems. Extensive results prove that combining our dataset with in-domain datasets like GSM8K can help improve the model's mathematical ability to generalize, leading to improved performances both within and beyond specific domains.