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MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis

Paper · 2026 · Zixiong Yu, Jun Rao, Guhan Chen et al.

Summary

Synthetic data for mathematical reasoning is often built either by mutating human-curated seed problems, which limits diversity to the seeds' scope, or by prompting models from scratch, which tends toward repetitive, shallow problems (mode collapse). MathAgent instead treats synthesis as a two-level process. First, the structure of a problem is designed and optimized. Only afterwards is it turned into text.

Each problem skeleton is a constraint graph whose nodes are mathematical concepts and whose edges are logical relations, plus style tokens that set attributes such as difficulty and question type. A "Legislator" made up of three LLM agents adversarially refines this graph to increase complexity while keeping it solvable. An "Executor" then writes natural-language questions and reasoning chains from the finished blueprint, and a judge model filters the output. The pipeline starts from basic concept primitives, so it needs no seed dataset.

Across 10 models, fine-tuning on just 1K MathAgent samples beat comparable-size curated sets on eight math benchmarks. This points to a scalable, annotation-light route to hard reasoning data.

Key points

  • Legislator agents: The Proposer expands or revises the graph, the Critic checks internal consistency, alignment with the style tokens and room for improvement, and the Moderator decides whether to approve the graph or keep iterating. An adaptive early-stop mechanism regulates how complex the resulting data distribution becomes.
  • Main benchmark result: Experiments cover 10 models from the Qwen, Llama, Mistral and Gemma families. With 1K synthesized samples, the fine-tuned models outperform those trained on LIMO and s1K across eight benchmarks, with stronger out-of-distribution generalization.
  • Diversity and data scaling:
    • A t-SNE projection of knowledge-point tags from 10K instances shows MathAgent's coverage largely enclosing that of Magpie and OpenR1-Math.
    • In scaling tests with Qwen2.5-Math-7B (3 epochs), performance peaks near 100K samples and stays above the baselines throughout.
  • Human evaluation: On a blinded 5-point rating of 100 samples per source, MathAgent scores 4.2, ahead of OpenR1 at 3.9 and Magpie at 3.5. Experts judged Magpie fluent but logically simple, and they caught flaws that the LLM judge missed.
  • Stated limitations: The method is focused on mathematics, the multi-round evolution adds computational cost, and verifying ground-truth answers becomes harder as problems grow more complex. The authors suggest formal verifiers or symbolic solvers as future work.

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

🎓Tsinghua UniversityBeijing · China333 works · 87,019 citations🎓Harbin Institute of TechnologyHarbin · China158 works · 28,841 citations🏢Huawei TechnologiesShenzhen · China75 works · 12,975 citations🎓Kyoto UniversityKyoto · Japan40 works · 8,235 citations

 Fields, topics and concepts

📚 Shelves 5The 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 worksComputer Vision and Pattern Recognition · 2,869 works

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

Cite

Cite as Zixiong Yu, Jun Rao, Guhan Chen, Songtao Tian, Bohan Li, Jiansheng Wei, Min Zhang and Xiaojun Meng. 2026. MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.findings-acl.1410

@inproceedings{yu2026mathagent,
  title = {{MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis}},
  author = {Zixiong Yu, Jun Rao, Guhan Chen, Songtao Tian, Bohan Li, Jiansheng Wei, Min Zhang and Xiaojun Meng},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1410},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1410}
}

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