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a1: Steep Test-time Scaling Law via Environment Augmented Generation

Paper · 2026 · Lingrui Mei, Shenghua Liu, Yiwei Wang et al.

Summary

LLMs often fail at long multi-step reasoning. They usually generate a whole solution in one pass with no intermediate checks, so an early mistake carries through to the final answer. The authors propose Environment Augmented Generation (EAG), which casts reasoning as a Markov Decision Process. While generating, the model calls an external environment (mainly a Python sandbox) and receives structured feedback on each step. The feedback contains a value or error code, a semantic type, and a textual description. A branch value function based on information gain decides when to start, prune or abandon alternative solution paths, so the model can backtrack and replan. Validated successful trajectories then become fine-tuning data, collected in the compact EAG-2K set, which is derived from s1. The resulting a1-32B model leads its size class on reasoning benchmarks and reaches o1-level results on competition mathematics. The gains grow with task difficulty: interaction costs tokens at first, but this overhead pays off on harder, longer reasoning chains.

Key points

  • a1-32B beats similarly sized models by margins reaching 24.4 percentage points and matches o1 on competition mathematics. A smaller a1-14B variant also exists.
  • Compared with the s1-32B baseline, the full a1-32B scores:
    • AIME24: 74.4 vs 50.0
    • MATH500: 94.8 vs 93.0
    • GPQA: 63.4 vs 59.6
  • Ablations on AIME24:
    • Removing dynamic branch exploration cuts accuracy by 21.1 pp, to 53.3.
    • Limiting feedback to numbers only cuts it by 17.7 pp, to 56.7.
  • The two components work together: branching provides the ability to recover from mistakes, and rich feedback shows which branch to follow. The benefit of the full system is small on MATH500 (1.4 pp over the best ablation) but large on AIME24.
  • Limitations: the work focuses on math and computational tasks with Python feedback, uses extra inference-time compute, relies on a small training set, and depends on how reliable the execution environment is.

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

🎓University of Chinese Academy of SciencesBeijing · China147 works · 8,480 citations🎓University of California, MercedMerced · United States11 works · 425 citations🤝Union Bank of SwitzerlandZurich · Switzerland2 works · 6 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 Lingrui Mei, Shenghua Liu, Yiwei Wang, Baolong Bi, Yuyao Ge, Jun Wan, Yurong Wu and Xueqi Cheng. 2026. a1: Steep Test-time Scaling Law via Environment Augmented Generation. 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.1240

@inproceedings{mei2026a1,
  title = {{a1: Steep Test-time Scaling Law via Environment Augmented Generation}},
  author = {Lingrui Mei, Shenghua Liu, Yiwei Wang, Baolong Bi, Yuyao Ge, Jun Wan, Yurong Wu and Xueqi Cheng},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.1240},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.1240}
}

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