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Reinforcement Learning for Reasoning in Large Language Models with One Training Example

Paper · 2025 · Yiping Wang, Qing Yang, Zhiyuan Zeng et al.

Summary

The paper asks how small a training set can be for reinforcement learning with verifiable reward (RLVR). RLVR is the outcome-rewarded RL now used to strengthen math reasoning in LLMs. The authors draw a random sample of 1,209 problems from the DeepScaleR dataset (DSR-sub). They rank each problem by how much its training accuracy fluctuated across epochs of a preliminary full-data run. They then train with GRPO, and also PPO, on just one or two of these problems. With a single problem, Qwen2.5-Math-1.5B rises on MATH500 from 36.0% to 73.6%, essentially matching training on all of DSR-sub. Two problems do slightly better. The gains carry over to Qwen2.5-Math-7B, Llama-3.2-3B-Instruct and DeepSeek-R1-Distill-Qwen-1.5B, transfer across math topics, and even help on ARC. Test scores keep rising long after the model has fully memorised its lone training problem. Ablations show the policy-gradient term drives the effect rather than weight decay, so it is not grokking. An entropy bonus aids exploration. The results suggest base models already contain latent reasoning ability and that data selection for RLVR deserves closer study.

Key points

  • On Qwen2.5-Math-1.5B, one example (π13) lifts the six-benchmark average from 17.6% to 35.7%, versus 35.9% for the 1.2k DSR-sub. This is about 7.0 points beyond what format correction alone gives. Two examples {π1, π13} reach 74.8% on MATH500 and 36.6% on average, close to the full 7.5k MATH train set (36.7%).
  • The six benchmarks are MATH500, AIME24, AMC23, Minerva Math, OlympiadBench and AIME25. On ARC-Easy, 1-shot training on π13 scores 55.8%, compared with 51.6% for full MATH-set RLVR.
  • The authors call the continued test gains after training accuracy saturates "post-saturation generalization." Overfitting appears only after roughly 1.4k steps. Even then, the model's outputs on the training item turn into multilingual gibberish, while its test outputs stay readable and accurate.
  • Training with policy-gradient loss alone already comes close to the full GRPO loss. Adding a suitably weighted entropy loss gives a further +4.0 points on MATH500 and +2.5 on AIME24. Entropy loss with no reward at all still yields a smaller boost (MATH500: 63.4%, versus 65.0% for the format-reward baseline).
  • Many individual problems, including ones with low variance scores, work for 1-shot RLVR. Slightly incorrect labels do little harm. Code, models and data are released at github.com/ypwang61/One-Shot-RLVR.

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

🏢MicrosoftRedmond · United States378 works · 161,630 citations🎓University of WashingtonSeattle · United States402 works · 212,762 citations🎓University of Southern CaliforniaLos Angeles · United States175 works · 37,047 citations🎓Georgia Institute of TechnologyAtlanta · United States152 works · 27,763 citations🎓Shanghai Jiao Tong UniversityShanghai · China212 works · 19,544 citations🎓Chinese University of Hong KongHong Kong · China159 works · 16,154 citations🎓University of California San DiegoSan Diego · United States89 works · 54,032 citations🎓Hefei University of TechnologyHefei · China17 works · 1,702 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 works

🧭 Topics 2Research subjects and languages the work is about.Language models & pretraining · 3,894 worksReasoning · 1,685 works

Cite

Cite as Yiping Wang, Qing Yang, Zhiyuan Zeng, Liliang Ren, Liyuan Liu, Baolin Peng, Hao Cheng, Xuehai He, Kuan Wang, Jianfeng Gao, Weizhu Chen, Shuohang Wang, Simon Shaolei Du and Yelong Shen. 2025. Reinforcement Learning for Reasoning in Large Language Models with One Training Example. arXiv:2504.20571.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2504.20571 · arXiv 2504.20571

@misc{wang2025reinforcement,
  title = {{Reinforcement Learning for Reasoning in Large Language Models with One Training Example}},
  author = {Yiping Wang, Qing Yang, Zhiyuan Zeng, Liliang Ren, Liyuan Liu, Baolin Peng, Hao Cheng, Xuehai He, Kuan Wang, Jianfeng Gao, Weizhu Chen, Shuohang Wang, Simon Shaolei Du and Yelong Shen},
  year = {2025},
  doi = {10.48550/arxiv.2504.20571},
  eprint = {2504.20571},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2504.20571}
}

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