---
title: "DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement — DeepSeek-AI 2025"
description: "DeepSeek-AI shows that reasoning can instead come from reinforcement learning alone. 97 references, cited by 3,494 papers here."
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-ai-2025-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, Xingkai Yu, [Yu Wu](https://md.research.elamur.ai/free/en/authors/yu-wu/), Z. F. Wu, [Zhibin Gou](https://md.research.elamur.ai/free/en/authors/zhibin-gou/), [Zhihong Shao](https://md.research.elamur.ai/free/en/authors/zhihong-shao/), Zhuoshu Li, Ziyi Gao, Aixin Liu, [Bing Xue](https://md.research.elamur.ai/free/en/authors/bing-xue/), [Bingxuan Wang](https://md.research.elamur.ai/free/en/authors/bingxuan-wang/), [Bochao Wu](https://md.research.elamur.ai/free/en/authors/bochao-wu/), Bei Feng, [Chengda Lu](https://md.research.elamur.ai/free/en/authors/chengda-lu/), Chenggang Zhao, [Chengqi Deng](https://md.research.elamur.ai/free/en/authors/chengqi-deng/), Chenyu Zhang, [Chong Ruan](https://md.research.elamur.ai/free/en/authors/chong-ruan/), [Damai Dai](https://md.research.elamur.ai/free/en/authors/damai-dai/), [Deli Chen](https://md.research.elamur.ai/free/en/authors/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](https://md.research.elamur.ai/free/en/authors/haocheng-wang/), Honghui Ding, [Huajian Xin](https://md.research.elamur.ai/free/en/authors/huajian-xin/), [Huazuo Gao](https://md.research.elamur.ai/free/en/authors/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](https://md.research.elamur.ai/free/en/authors/lean-wang/), Lecong Zhang, [Liang Zhao](https://md.research.elamur.ai/free/en/authors/liang-zhao/), Litong Wang, [Liyue Zhang](https://md.research.elamur.ai/free/en/authors/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](https://md.research.elamur.ai/free/en/authors/wanjia-zhao/), [Wen Liu](https://md.research.elamur.ai/free/en/authors/wen-liu/), Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, W. L. Xiao, Wei An, [Xiaodong Liu](https://md.research.elamur.ai/free/en/authors/xiaodong-liu/), Xiaohan Wang, [Xiaokang Chen](https://md.research.elamur.ai/free/en/authors/xiaokang-chen/), Xiaotao Nie, Xin Cheng, [Xin Liu](https://md.research.elamur.ai/free/en/authors/xin-liu/), Xin Xie, [Xingchao Liu](https://md.research.elamur.ai/free/en/authors/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](https://md.research.elamur.ai/free/en/authors/yang-zhang/), Yanhong Xu, Yao Li, [Yao Zhao](https://md.research.elamur.ai/free/en/authors/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](https://md.research.elamur.ai/free/en/authors/z-z-ren/), Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, [Zhenda Xie](https://md.research.elamur.ai/free/en/authors/zhenda-xie/), [Zhengyan Zhang](https://md.research.elamur.ai/free/en/authors/zhengyan-zhang/), Zhewen Hao, Zhicheng Ma, Zhigang Yan, [Zhiyu Wu](https://md.research.elamur.ai/free/en/authors/zhiyu-wu/), Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, [Zizheng Pan](https://md.research.elamur.ai/free/en/authors/zizheng-pan/), [Zhen Huang](https://md.research.elamur.ai/free/en/authors/zhen-huang/), Zhipeng Xu, Zhongyu Zhang and Zhen Zhang · **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:** 1,099 citations (OpenAlex, 2026-10-14) · [3494](https://md.research.elamur.ai/free/en/papers/deepseek-ai-2025-deepseek-r1-incentivizing-reasoning-capability/cited-by/) in our library, of the 140,884 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/)

Topics: [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/)

## Institutions

- [Tsinghua University](https://md.research.elamur.ai/free/en/universities/tsinghua-university/) — University, Beijing, China · 92 works · 77,045 citations
- [Peking University](https://md.research.elamur.ai/free/en/universities/peking-university/) — University, Beijing, China · 74 works · 31,748 citations
- [University of Science and Technology of China](https://md.research.elamur.ai/free/en/universities/university-of-science-and-technology-of-china/) — University, Hefei, China · 18 works · 109,489 citations
- [DeepSeek](https://md.research.elamur.ai/free/en/companies/deepseek/) — Company, Hangzhou, China · 5 works · 7,409 citations

## Cite

Cite as: 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 and Zhen Zhang. 2025. DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning. arXiv:2501.12948 · Nature volume 645, pages 633-638 (2025).

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, 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 and Zhen Zhang},
  year = {2025},
  doi = {10.1038/s41586-025-09422-z},
  eprint = {2501.12948},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1038/s41586-025-09422-z}
}
```

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