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S²R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning

Paper · 2025 · Ruotian Ma, Peisong Wang, Cheng Liu et al.

Summary

S$^2$R targets a practical gap. Methods that give LLMs o1-style "deep thinking" usually need huge datasets, heavy compute, or distillation from much stronger models, and it is unclear how to help weaker base models reason better. The authors treat reasoning as a sequence of alternating "solve" and "verify" actions. The model checks each attempt and either stops or tries again.

Training has two stages:

  • Stage 1 (behavior initialization): supervised fine-tuning on a small curated set of trial-and-error trajectories. Failed attempts are sampled from the model itself, and trajectory length is matched to problem difficulty.
  • Stage 2 (reinforcement learning): both outcome-level and process-level RL, using only rule-based rewards.

For verification, the authors prefer a "Confirmative" style, which checks the given answer without re-solving the problem.

With only 3.1k SFT samples, Qwen2.5-Math-7B rises from 51.0% to 81.6% on MATH500, and RL pushes it further. This beats training on the same amount of long-CoT data distilled from QwQ-32B-Preview. The work shows that small models can learn useful test-time scaling cheaply.

Key points

  • Data efficiency: 3.1k behavior-initialization samples lift Qwen2.5-Math-7B on MATH500 from 51.0% to 81.6%, versus 80.2% with equally sized QwQ-32B-Preview distillation. Outcome-level RL reaches 84.4%.
  • Scope of evaluation: 3 base models (up to 8B parameters, including Qwen2.5-Math-7B and Qwen2-7B-Instruct) on 7 math benchmarks. Results also generalize to out-of-domain tasks such as MMLU-PRO.
  • Baselines outperformed: Eurus-2-7B-PRIME, rStar-Math-7B and Qwen2.5-7B-SimpleRL-Zero, with S$^2$R using far less training data.
  • RL insights:
    • Process-level supervision mainly helps weaker base models by making intermediate verification more accurate.
    • Outcome-level supervision gives more consistent gains for stronger models by allowing freer exploration.
    • Offline RL performs roughly on par with online RL, making it a cheaper option.
  • Resource: code and data are released at github.com/NineAbyss/S2R.

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

 Fields, topics and concepts

📚 Shelves 4The 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 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,320 works

Cite

Cite as Ruotian Ma, Peisong Wang, Cheng Liu, Xingyan Liu, Jiaqi Chen, Bang Zhang, Xin Zhou, Nan Du and Jia Li. 2025. S²R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2025.acl-long.1104

@inproceedings{ma2025teaching,
  title = {{S²R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning}},
  author = {Ruotian Ma, Peisong Wang, Cheng Liu, Xingyan Liu, Jiaqi Chen, Bang Zhang, Xin Zhou, Nan Du and Jia Li},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.1104},
  url = {https://doi.org/10.18653/v1/2025.acl-long.1104}
}

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