GRIP: A Graph-Based Reasoning Instruction Producer

Large-scale, high-quality data is essential for advancing the reasoning capabilities of large language models (LLMs). As publicly available Internet data becomes increasingly scarce, synthetic data has emerged as a crucial research direction. However, existing data synthesis methods often suffer from limited scalability, insufficient sample diversity, and a tendency to overfit to seed data, which constrains their practical utility. In this paper, we present $\mathit{\text{GRIP}}$, a $\mathbf{\text{G}}$raph-based $\mathbf{\text{R}}$easoning $\mathbf{\text{I}}$nstruction $\mathbf{\text{P}}$roducer that efficiently synthesizes high-quality and diverse reasoning instructions. $\mathit{\text{GRIP}}$ constructs a knowledge graph by extracting high-level concepts from seed data, and uniquely leverages both explicit and implicit relationships within the graph to drive large-scale and diverse instruction data synthesis, while employing open-source multi-model supervision to ensure data quality. We apply $\mathit{\text{GRIP}}$ to the critical and challenging domain of mathematical reasoning. Starting from a seed set of 7.5K math reasoning samples, we construct $\mathbf{\text{GRIP-MATH}}$, a dataset containing 2.1 million synthesized question-answer pairs. Compared to similar synthetic data methods, $\mathit{\text{GRIP}}$ achieves greater scalability and diversity while also significantly reducing costs. On mathematical reasoning benchmarks, models trained with GRIP-MATH demonstrate substantial improvements over their base models and significantly outperform previous data synthesis methods.