ControlMath: Controllable Data Generation Promotes Math Generalist Models
This addresses the need for more diverse math problem generation to enhance AI models' mathematical reasoning, though it is incremental as it builds on existing LLM-based data augmentation methods.
The authors tackled the problem of limited diversity in LLM-generated math problems by proposing ControlMath, an iterative method using an equation-generator and two LLM-based agents to create diverse math word problems, resulting in the ControlMathQA dataset of 190k problems that improved model generalization when combined with in-domain datasets like GSM8K.
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.