MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis

TL;DR

This paper introduces MathAgent, a hierarchical, adversarial framework for synthesizing complex mathematical reasoning data by evolving constraint graphs, leading to improved model performance and generalization.

Contribution

It presents a novel Legislator-Executor paradigm that decouples logical structure creation from language realization for better data synthesis.

Findings

Models trained on 1K synthesized samples outperform existing datasets across benchmarks.

The method enhances out-of-distribution generalization in mathematical reasoning tasks.

Experiments involve 10 models from Qwen, Llama, Mistral, and Gemma series.

Abstract

Synthesizing high-quality mathematical reasoning data without human priors remains a significant challenge. Current approaches typically rely on seed data mutation or simple prompt engineering, often suffering from mode collapse and limited logical complexity. This paper proposes a hierarchical synthesis framework that formulates data synthesis as an unsupervised optimization problem over a constraint graph followed by semantic instantiation, rather than treating it as a direct text generation task. We introduce a Legislator-Executor paradigm: The Legislator adversarially evolves structured generation blueprints encoding the constraints of the problem, while the Executor instantiates these specifications into diverse natural language scenarios. This decoupling of skeleton design from linguistic realization enables a prioritized focus on constructing complex and diverse logical structures, thereby guiding high-quality data synthesis. Experiments conducted on a total of 10 models across the Qwen, Llama, Mistral, and Gemma series demonstrate that our method achieves notable results: models fine-tuned on 1K synthesized samples outperform widely-used datasets of comparable scale (LIMO, s1K) across eight mathematical benchmarks, exhibiting superior out-of-distribution generalization.