RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library
This addresses the need for scalable, verifiable reasoning datasets in mathematics for AI research, representing a novel method for a known bottleneck rather than a foundational breakthrough.
The paper tackles the challenge of generating high-quality mathematical reasoning data for LLMs by proposing RV-Syn, a method that uses a structured function library to create verifiable computational graphs as solutions, which are then back-translated into problems, resulting in superior performance over existing synthesis methods and enabling efficient data scaling.
The advancement of reasoning capabilities in Large Language Models (LLMs) requires substantial amounts of high-quality reasoning data, particularly in mathematics. Existing data synthesis methods, such as data augmentation from annotated training sets or direct question generation based on relevant knowledge points and documents, have expanded datasets but face challenges in mastering the inner logic of the problem during generation and ensuring the verifiability of the solutions. To address these issues, we propose RV-Syn, a novel Rational and Verifiable mathematical Synthesis approach. RV-Syn constructs a structured mathematical operation function library based on initial seed problems and generates computational graphs as solutions by combining Python-formatted functions from this library. These graphs are then back-translated into complex problems. Based on the constructed computation graph, we achieve solution-guided logic-aware problem generation. Furthermore, the executability of the computational graph ensures the verifiability of the solving process. Experimental results show that RV-Syn surpasses existing synthesis methods, including those involving human-generated problems, achieving greater efficient data scaling. This approach provides a scalable framework for generating high-quality reasoning datasets.