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RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library

Jiapeng Wang, Jinhao Jiang, Zhiqiang Zhang, Jun Zhou, Wayne Xin Zhao

TL;DR

RV-Syn addresses the need for high-quality mathematical reasoning data by building a graph-based library of mathematical operations and synthesizing problems from executable computational graphs. It ensures verifiability through executable graphs and back-translation, yielding ground-truth answers. Empirical results show RV-Syn outperforms existing synthesis methods and even some human-crafted datasets while using less data, highlighting improved data efficiency and reasoning coverage, including multi-hop and modular structures. The framework offers a scalable path for advancing reasoning data generation and has potential applicability beyond mathematics to other reasoning domains.

Abstract

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.

RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library

TL;DR

RV-Syn addresses the need for high-quality mathematical reasoning data by building a graph-based library of mathematical operations and synthesizing problems from executable computational graphs. It ensures verifiability through executable graphs and back-translation, yielding ground-truth answers. Empirical results show RV-Syn outperforms existing synthesis methods and even some human-crafted datasets while using less data, highlighting improved data efficiency and reasoning coverage, including multi-hop and modular structures. The framework offers a scalable path for advancing reasoning data generation and has potential applicability beyond mathematics to other reasoning domains.

Abstract

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.
Paper Structure (32 sections, 5 figures, 9 tables)

This paper contains 32 sections, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Mathematical Reasoning.
  4. Data Synthesis for Math Instruction.
  5. Approach
  6. Problem Decomposition
  7. Graph-based Function Library Construction
  8. Structure and Semantic-aware Function Merging
  9. Co-occurrence and Topic-based Node Connecting
  10. Problem Synthesis
  11. Computational Graph Regeneration
  12. Problem Back-translation
  13. Comparison to Previous Work
  14. Experiments
  15. Experimental Setup
  16. ...and 17 more sections

Figures (5)

  • Figure 1: (Left) Illustration of the limitations of existing synthesis methods; (Right) Examples of data synthesized by RV-Syn, which naturally support sophisticated reasoning structures and provide ground-truth answers.
  • Figure 2: The pipeline of our proposed method. The upper part demonstrates the construction of the operation function library. The lower part illustrates the synthesis process.
  • Figure 3: The performance of the model as the training data size increases. The "Average" refers to the mean performance across five datasets: MATH-500, GSM8K, GSM-Hard, College Math, and OlympiadBench.
  • Figure 4: Performance comparison of distilling Long-CoT on 20k data.
  • Figure :