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.

本研究解决了大语言模型在数学推理中对高质量推理数据的需求，针对现有数据合成方法在生成过程中的逻辑掌握和解决方案可验证性问题，提出了RV-Syn，一种新的合理且可验证的数学合成方法。实验结果表明，RV-Syn在数据规模扩展效率上超过了现有方法，为生成高质量推理数据集提供了可扩展的框架。

RV-Syn：基于结构化函数库的合理且可验证的数学推理数据合成