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

Paper · 2026 · Jiapeng Wang, Jinhao Jiang, Zhiqiang Zhang et al.

Summary

RV-Syn tackles the shortage of reliable, complex mathematical training data for LLMs. Prior synthesis methods either rework existing annotated sets such as GSM8K and MATH, which limits diversity, or have a model write questions directly from documents or knowledge points. The authors argue that direct generation lacks advance planning, so it often yields contradictory, unsolvable or trivial problems whose answers are hard to check.

RV-Syn reverses the usual order and designs the solution before the question:

  • LLMs rewrite the solutions of seed problems as executable Python function sequences, and a run of the code against known answers filters out errors.
  • The surviving functions are validated, labeled by topic, merged when structurally or semantically similar, and linked by co-occurrence and topic into a graph-shaped library.
  • Sampled functions are composed into new computational graphs, executed to obtain ground truth, and back-translated into natural-language problems.

Across five benchmarks, the resulting data beats earlier synthetic and human-written sets. It is more data-efficient and has a very low error rate, which makes it a scalable route to verifiable reasoning data.

Key points

  • On LLaMA-3-8B, RV-Syn gains 6.3% over the previous best synthetic dataset and outperforms competitors with half the data (50k vs. 100k samples). Baselines include Numina-Math, ScaleQuest, MathScale, Jiuzhang3.0 and Mammoth2.
  • In a manual error audit, RV-Syn shows a 0.9% problem error rate and a 1.4% solution error rate. Baseline solution error rates range from 4.9% to 10.6%.
  • Three node-sampling strategies (co-occurrence, topic-based, edgeless) each lead on different benchmarks: co-occurrence on GSM8K, edgeless on MATH-500, and topic-based on GSM-Hard and OlympiadBench. The final dataset therefore mixes all three.
  • The number of sampled nodes controls difficulty:
    • Single-node data scores best on MATH-500 (49.0).
    • GSM-Hard accuracy rises with more nodes, from 42.6 with one node to 44.4 with three.
  • For Long-CoT distillation, answers were generated by DeepSeek-R1-Distill-Qwen-7B and used to train Qwen2.5-7B-Instruct on 20k samples. In this setting RV-Syn data outperforms ScaleQuest.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Renmin University of ChinaBeijing · China114 works · 16,118 citations🏢Ant GroupHangzhou · China42 works · 1,131 citations

 Fields, topics and concepts

📚 Shelves 7The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksMathematics · 177 worksComputational Theory and Mathematics · 252 worksApplied Mathematics · 46 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,426 works

Cite

Cite as Jiapeng Wang, Jinhao Jiang, Zhiqiang Zhang, Jun Zhou and Xin Zhao. 2026. RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library. Findings of the Association for Computational Linguistics: EACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-eacl.93

@inproceedings{wang2026rv,
  title = {{RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library}},
  author = {Jiapeng Wang, Jinhao Jiang, Zhiqiang Zhang, Jun Zhou and Xin Zhao},
  booktitle = {Findings of the Association for Computational Linguistics: EACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-eacl.93},
  url = {https://doi.org/10.18653/v1/2026.findings-eacl.93}
}

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