用可验证的计算图生成数学推理数据,提升模型训练质量。
RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library
- 基于函数库构建计算图,实现逻辑清晰的问题生成。
- 生成数据在数学推理任务上表现优于人类标注数据。
- 适合需要高质量数学推理数据的研究者使用。
大型语言模型(LLM)的推理能力提升依赖于大量高质量的数学推理数据。现有数据合成方法如基于标注数据集的增强或基于知识点的直接生成,虽扩大了数据规模,但在生成过程中难以掌握问题的内在逻辑,且难以确保解题过程的可验证性。为此,我们提出RV-Syn:一种基于结构化函数库的理性且可验证的数学推理数据合成方法。该方法从初始种子问题构建结构化的数学运算函数库,通过组合库中格式为Python的函数生成计算图作为解法,并将计算图回译为复杂问题。基于生成的计算图,实现解法引导的逻辑感知问题生成。同时,计算图的可执行性保证了解题过程的可验证性。实验表明,RV-Syn在生成效率与数据质量上均优于现有合成方法,包括人工生成数据,在数据规模扩展方面展现出更强的可扩展性。该方法为高质量推理数据的生成提供了可扩展框架。
原文摘要 · Abstract (English)
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.
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