---
title: "DeepSeek-R1: Incentivizing Reasoning — DeepSeek-AI 2025"
description: "Chain-of-thought prompting and supervised fine-tuning have made LLMs better at reasoning, but both rely on reasoning traces written by humans."
authors: ["DeepSeek-AI", "Daya Guo", "Dejian Yang", "Haowei Zhang", "Junxiao Song", "Peiyi Wang", "Qihao Zhu", "Runxin Xu", "Ruoyu Zhang", "Shirong Ma", "Xiao Bi", "Xiaokang Zhang", "Xingkai Yu", "Yu Wu", "Z. F. Wu", "Zhibin Gou", "Zhihong Shao", "Zhuoshu Li", "Ziyi Gao", "Aixin Liu", "Bing Xue", "Bingxuan Wang", "Bochao Wu", "Bei Feng", "Chengda Lu", "Chenggang Zhao", "Chengqi Deng", "Chenyu Zhang", "Chong Ruan", "Damai Dai", "Deli Chen", "Dongjie Ji", "Erhang Li", "Fangyun Lin", "Fucong Dai", "Fuli Luo", "Guangbo Hao", "Guanting Chen", "Guowei Li", "H. Zhang", "Han Bao", "Hanwei Xu", "Haocheng Wang", "Honghui Ding", "Huajian Xin", "Huazuo Gao", "Hui Qu", "Hui Li", "Jianzhong Guo", "Jiashi Li", "Jiawei Wang", "Jingchang Chen", "Jingyang Yuan", "Junjie Qiu", "Junlong Li", "J. L. Cai", "Jiaqi Ni", "Jian Liang", "Jin Chen", "Kai Dong", "Kai Hu", "Kaige Gao", "Kang Guan", "Kexin Huang", "Kuai Yu", "Lean Wang", "Lecong Zhang", "Liang Zhao", "Litong Wang", "Liyue Zhang", "Lei Xu", "Leyi Xia", "Mingchuan Zhang", "Minghua Zhang", "Minghui Tang", "Meng Li", "Miaojun Wang", "Mingming Li", "Ning Tian", "Panpan Huang", "Peng Zhang", "Qiancheng Wang", "Qinyu Chen", "Qiushi Du", "Ruiqi Ge", "Ruisong Zhang", "Ruizhe Pan", "Runji Wang", "R. J. Chen", "R. L. Jin", "Ruyi Chen", "Shanghao Lu", "Shangyan Zhou", "Shanhuang Chen", "Shengfeng Ye", "Shiyu Wang", "Shuiping Yu", "Shunfeng Zhou", "Shuting Pan", "S. S. Li", "Shuang Zhou", "Shaoqing Wu", "Shengfeng Ye", "Tao Yun", "Tian Pei", "Tianyu Sun", "T. Wang", "Wangding Zeng", "Wanjia Zhao", "Wen Liu", "Wenfeng Liang", "Wenjun Gao", "Wenqin Yu", "Wentao Zhang", "W. L. Xiao", "Wei An", "Xiaodong Liu", "Xiaohan Wang", "Xiaokang Chen", "Xiaotao Nie", "Xin Cheng", "Xin Liu", "Xin Xie", "Xingchao Liu", "Xinyu Yang", "Xinyuan Li", "Xuecheng Su", "Xuheng Lin", "X. Q. Li", "Xiangyue Jin", "Xiaojin Shen", "Xiaosha Chen", "Xiaowen Sun", "Xiaoxiang Wang", "Xinnan Song", "Xinyi Zhou", "Xianzu Wang", "Xinxia Shan", "Y. K. Li", "Y. Q. Wang", "Y. X. Wei", "Yang Zhang", "Yanhong Xu", "Yao Li", "Yao Zhao", "Yaofeng Sun", "Yaohui Wang", "Yi Yu", "Yichao Zhang", "Yifan Shi", "Yiliang Xiong", "Ying He", "Yishi Piao", "Yisong Wang", "Yixuan Tan", "Yiyang Ma", "Yiyuan Liu", "Yongqiang Guo", "Yuan Ou", "Yuduan Wang", "Yue Gong", "Yuheng Zou", "Yujia He", "Yunfan Xiong", "Yuxiang Luo", "Yuxiang You", "Yuxuan Liu", "Yuyang Zhou", "Y. X. Zhu", "Yanhong Xu", "Yanping Huang", "Yaohui Li", "Yi Zheng", "Yuchen Zhu", "Yunxian Ma", "Ying Tang", "Yukun Zha", "Yuting Yan", "Z. Z. Ren", "Zehui Ren", "Zhangli Sha", "Zhe Fu", "Zhean Xu", "Zhenda Xie", "Zhengyan Zhang", "Zhewen Hao", "Zhicheng Ma", "Zhigang Yan", "Zhiyu Wu", "Zihui Gu", "Zijia Zhu", "Zijun Liu", "Zilin Li", "Ziwei Xie", "Ziyang Song", "Zizheng Pan", "Zhen Huang", "Zhipeng Xu", "Zhongyu Zhang", "Zhen Zhang"]
year: 2025
venue: "arXiv:2501.12948 · Nature volume 645, pages 633-638 (2025)"
source: "https://arxiv.org/abs/2501.12948"
doi: "10.1038/s41586-025-09422-z"
arxiv: "2501.12948"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/deepseek-2025-ai-deepseek-r1-incentivizing-reasoning-capability/"
---
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# DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

**Authors:** [DeepSeek-AI](https://md.research.elamur.ai/free/en/authors/deepseek-ai/), [Daya Guo](https://md.research.elamur.ai/free/en/authors/daya-guo/), [Dejian Yang](https://md.research.elamur.ai/free/en/authors/dejian-yang/), [Haowei Zhang](https://md.research.elamur.ai/free/en/authors/haowei-zhang/), [Junxiao Song](https://md.research.elamur.ai/free/en/authors/junxiao-song/), [Peiyi Wang](https://md.research.elamur.ai/free/en/authors/peiyi-wang/), [Qihao Zhu](https://md.research.elamur.ai/free/en/authors/qihao-zhu/), [Runxin Xu](https://md.research.elamur.ai/free/en/authors/runxin-xu/), Ruoyu Zhang, [Shirong Ma](https://md.research.elamur.ai/free/en/authors/shirong-ma/), [Xiao Bi](https://md.research.elamur.ai/free/en/authors/xiao-bi/), Xiaokang Zhang et al. (200 authors) · **Year:** 2025 · **Venue:** arXiv:2501.12948 · Nature volume 645, pages 633-638 (2025) · **Licence:** [arXiv — non-exclusive licence to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://doi.org/10.1038/s41586-025-09422-z) · [PDF](https://arxiv.org/pdf/2501.12948) · [DOI 10.1038/s41586-025-09422-z](https://doi.org/10.1038/s41586-025-09422-z) · [arXiv 2501.12948](https://arxiv.org/abs/2501.12948) · [OpenAlex](https://openalex.org/W4414281281)

**Citations:** 1099 citations (openalex-snapshot · 2026-10-14) · [3492](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
Chain-of-thought prompting and supervised fine-tuning have made LLMs better at reasoning, but both rely on reasoning traces written by humans. That is expensive to scale, and it also limits the model to the strategies people demonstrate. DeepSeek-AI shows that reasoning can instead come from reinforcement learning alone. They started from DeepSeek-V3-Base, skipped supervised fine-tuning entirely and trained with GRPO. The reward was rule-based: it checked final answers in math, code and logic tasks and required a simple think/answer output format. No neural reward model was used. The resulting model, DeepSeek-R1-Zero, taught itself to write longer reasoning, check its own work, reflect and try alternative approaches. It also had flaws: its output was hard to read, it mixed English and Chinese, and it was weak on general tasks. DeepSeek-R1 fixes these with a multi-stage pipeline that combines rejection sampling, RL and SFT on additional non-reasoning data. The team also distilled R1's reasoning into smaller open models. The work matters because it shows that verifiable rewards can replace human demonstrations as the main way to teach reasoning.

## Key points
- On AIME 2024 during RL training, R1-Zero's pass@1 rose from 15.6% to 77.9%. With self-consistency voting over 16 samples it reached 86.7%, above the average human contestant.
- GRPO computes each answer's advantage by comparing its reward with the other answers sampled for the same question, so it needs no separate critic model as in PPO. Training used 16 samples per question, 10,400 steps (about 1.6 epochs), and a maximum response length that grew from 32,768 to 65,536 tokens at step 8.2k.
- The reward is accuracy plus format, weighted equally. The authors avoided neural reward models because they found them vulnerable to reward hacking at large scale.
- Response length grew steadily during training, and the model showed an "aha moment" in which it stopped and re-checked its own solution.
- The DeepSeek-R1 models and the distilled smaller models are publicly available at huggingface.co/deepseek-ai. The distilled models outperform the original instruction-tuned versions of the same models.

*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: [Mathematics & statistics](https://md.research.elamur.ai/free/en/shelves/mathematics/)

## Cited by

Cited by

3492 papers of our library cite it (of the 140673 whose bibliographies we read); 58 of them have a page here, 3434 not yet.

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- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://md.research.elamur.ai/free/en/papers/microsoft-2025-phi-4-mini-technical-report/)
- [s1: Simple test-time scaling](https://md.research.elamur.ai/free/en/papers/muennighoff-2025-s1-simple-test-time-scaling/)
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- [Datasets for Verb Alternations across Languages: BLM Templates and Data Augmentation Strategies](https://md.research.elamur.ai/free/en/papers/samo-2026-datasets-verb-alternations-across-languages/)
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- [LIMO: Less is More for Reasoning](https://md.research.elamur.ai/free/en/papers/ye-2025-limo-less-more-reasoning/)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://md.research.elamur.ai/free/en/papers/yeo-2025-demystifying-long-chain-thought-reasoning/)
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## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{deepseekai2025deepseek,
  title = {{DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning}},
  author = {DeepSeek-AI and Guo, Daya and Yang, Dejian and Zhang, Haowei and Song, Junxiao and Wang, Peiyi and Zhu, Qihao and Xu, Runxin and Zhang, Ruoyu and Ma, Shirong and Bi, Xiao and Zhang, Xiaokang and Yu, Xingkai and Wu, Yu and Wu, Z. F. and Gou, Zhibin and Shao, Zhihong and Li, Zhuoshu and Gao, Ziyi and Liu, Aixin and Xue, Bing and Wang, Bingxuan and Wu, Bochao and Feng, Bei and Lu, Chengda and Zhao, Chenggang and Deng, Chengqi and Zhang, Chenyu and Ruan, Chong and Dai, Damai and Chen, Deli and Ji, Dongjie and Li, Erhang and Lin, Fangyun and Dai, Fucong and Luo, Fuli and Hao, Guangbo and Chen, Guanting and Li, Guowei and Zhang, H. and Bao, Han and Xu, Hanwei and Wang, Haocheng and Ding, Honghui and Xin, Huajian and Gao, Huazuo and Qu, Hui and Li, Hui and Guo, Jianzhong and Li, Jiashi and Wang, Jiawei and Chen, Jingchang and Yuan, Jingyang and Qiu, Junjie and Li, Junlong and Cai, J. L. and Ni, Jiaqi and Liang, Jian and Chen, Jin and Dong, Kai and Hu, Kai and Gao, Kaige and Guan, Kang and Huang, Kexin and Yu, Kuai and Wang, Lean and Zhang, Lecong and Zhao, Liang and Wang, Litong and Zhang, Liyue and Xu, Lei and Xia, Leyi and Zhang, Mingchuan and Zhang, Minghua and Tang, Minghui and Li, Meng and Wang, Miaojun and Li, Mingming and Tian, Ning and Huang, Panpan and Zhang, Peng and Wang, Qiancheng and Chen, Qinyu and Du, Qiushi and Ge, Ruiqi and Zhang, Ruisong and Pan, Ruizhe and Wang, Runji and Chen, R. J. and Jin, R. L. and Chen, Ruyi and Lu, Shanghao and Zhou, Shangyan and Chen, Shanhuang and Ye, Shengfeng and Wang, Shiyu and Yu, Shuiping and Zhou, Shunfeng and Pan, Shuting and Li, S. S. and Zhou, Shuang and Wu, Shaoqing and Ye, Shengfeng and Yun, Tao and Pei, Tian and Sun, Tianyu and Wang, T. and Zeng, Wangding and Zhao, Wanjia and Liu, Wen and Liang, Wenfeng and Gao, Wenjun and Yu, Wenqin and Zhang, Wentao and Xiao, W. L. and An, Wei and Liu, Xiaodong and Wang, Xiaohan and Chen, Xiaokang and Nie, Xiaotao and Cheng, Xin and Liu, Xin and Xie, Xin and Liu, Xingchao and Yang, Xinyu and Li, Xinyuan and Su, Xuecheng and Lin, Xuheng and Li, X. Q. and Jin, Xiangyue and Shen, Xiaojin and Chen, Xiaosha and Sun, Xiaowen and Wang, Xiaoxiang and Song, Xinnan and Zhou, Xinyi and Wang, Xianzu and Shan, Xinxia and Li, Y. K. and Wang, Y. Q. and Wei, Y. X. and Zhang, Yang and Xu, Yanhong and Li, Yao and Zhao, Yao and Sun, Yaofeng and Wang, Yaohui and Yu, Yi and Zhang, Yichao and Shi, Yifan and Xiong, Yiliang and He, Ying and Piao, Yishi and Wang, Yisong and Tan, Yixuan and Ma, Yiyang and Liu, Yiyuan and Guo, Yongqiang and Ou, Yuan and Wang, Yuduan and Gong, Yue and Zou, Yuheng and He, Yujia and Xiong, Yunfan and Luo, Yuxiang and You, Yuxiang and Liu, Yuxuan and Zhou, Yuyang and Zhu, Y. X. and Xu, Yanhong and Huang, Yanping and Li, Yaohui and Zheng, Yi and Zhu, Yuchen and Ma, Yunxian and Tang, Ying and Zha, Yukun and Yan, Yuting and Ren, Z. Z. and Ren, Zehui and Sha, Zhangli and Fu, Zhe and Xu, Zhean and Xie, Zhenda and Zhang, Zhengyan and Hao, Zhewen and Ma, Zhicheng and Yan, Zhigang and Wu, Zhiyu and Gu, Zihui and Zhu, Zijia and Liu, Zijun and Li, Zilin and Xie, Ziwei and Song, Ziyang and Pan, Zizheng and Huang, Zhen and Xu, Zhipeng and Zhang, Zhongyu and Zhang, Zhen},
  year = {2025},
  doi = {10.1038/s41586-025-09422-z},
  eprint = {2501.12948},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1038/s41586-025-09422-z}
}
```

- [← previous DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://md.research.elamur.ai/free/en/papers/ren-2025-deepseek-prover-v2-advancing-formal/)
- [next → DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://md.research.elamur.ai/free/en/papers/deepseek-2025-ai-deepseek-v3-2-pushing/)
- [↑ back to papers of 2025](https://md.research.elamur.ai/free/en/papers/2025/)

## References

97 references, 42 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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