GRIP: A Graph-Based Reasoning Instruction Producer
This addresses the need for high-quality, diverse synthetic data to enhance reasoning capabilities in LLMs, particularly in mathematical reasoning, with incremental advancements over existing methods.
The paper tackles the problem of limited scalability and diversity in synthetic data generation for large language models by introducing GRIP, a graph-based method that synthesizes reasoning instructions, resulting in the creation of GRIP-MATH with 2.1 million question-answer pairs and showing substantial improvements on mathematical reasoning benchmarks.
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 \textit{\textbf{GRIP}}, a \textbf{G}raph-based \textbf{R}easoning \textbf{I}nstruction \textbf{P}roducer that efficiently synthesizes high-quality and diverse reasoning instructions. \textit{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 \textit{GRIP} to the critical and challenging domain of mathematical reasoning. Starting from a seed set of 7.5K math reasoning samples, we construct \textbf{GRIP-MATH}, a dataset containing 2.1 million synthesized question-answer pairs. Compared to similar synthetic data methods, \textit{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.