Nature

DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning

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

Abstract

Abstract General reasoning represents a long-standing and formidable challenge in artificial intelligence (AI). Recent breakthroughs, exemplified by large language models (LLMs)1,2 and chain-of-thought (CoT) prompting3, have achieved considerable success on foundational reasoning tasks. However, this success is heavily contingent on extensive human-annotated demonstrations and the capabilities of models are still insufficient for more complex problems. Here we show that the reasoning abilities of LLMs can be incentivized through pure reinforcement learning (RL), obviating the need for human-labelled reasoning trajectories. The proposed RL framework facilitates the emergent development of advanced reasoning patterns, such as self-reflection, verification and dynamic strategy adaptation. Consequently, the trained model achieves superior performance on verifiable tasks such as mathematics, coding competitions and STEM fields, surpassing its counterparts trained through conventional supervised learning on human demonstrations. Moreover, the emergent reasoning patterns exhibited by these large-scale models can be systematically used to guide and enhance the reasoning capabilities of smaller models.

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Article Details

Journal Nature
Volume / Issue Vol. 645, Issue 8081
Published September 18, 2025
Pages 633-638
ISSN 0028-0836
Publisher Nature Portfolio

Journal Info

Nature

Nature Portfolio
ISSN: 0028-0836 Health Sciences

Authors (194)

D

Daya Guo

D

Dejian Yang

H

Haowei Zhang

J

Junxiao Song

P

Peiyi Wang

Q

Qihao Zhu

R

Runxin Xu

R

Ruoyu Zhang

S

Shirong Ma

X

Xiao Bi

X

Xiaokang Zhang

X

Xingkai Yu

Y

Yu Wu

Z

Z. F. Wu

Z

Zhibin Gou

Z

Zhihong Shao

Z

Zhuoshu Li

Z

Ziyi Gao

A

Aixin Liu

B

Bing Xue

B

Bingxuan Wang

B

Bochao Wu

B

Bei Feng

C

Chengda Lu

C

Chenggang Zhao

C

Chengqi Deng

C

Chong Ruan

D

Damai Dai

D

Deli Chen

D

Dongjie Ji

E

Erhang Li

F

Fangyun Lin

F

Fucong Dai

F

Fuli Luo

G

Guangbo Hao

G

Guanting Chen

G

Guowei Li

H

H. Zhang

H

Hanwei Xu

H

Honghui Ding

H

Huazuo Gao

H

Hui Qu

H

Hui Li

J

Jianzhong Guo

J

Jiashi Li

J

Jingchang Chen

J

Jingyang Yuan

J

Jinhao Tu

J

Junjie Qiu

J

Junlong Li

J

J. L. Cai

J

Jiaqi Ni

J

Jian Liang

J

Jin Chen

K

Kai Dong

K

Kai Hu

K

Kaichao You

K

Kaige Gao

K

Kang Guan

K

Kexin Huang

K

Kuai Yu

L

Lean Wang

L

Lecong Zhang

L

Liang Zhao

L

Litong Wang

L

Liyue Zhang

L

Lei Xu

L

Leyi Xia

M

Mingchuan Zhang

M

Minghua Zhang

M

Minghui Tang

M

Mingxu Zhou

M

Meng Li

M

Miaojun Wang

M

Mingming Li

N

Ning Tian

P

Panpan Huang

P

Peng Zhang

Q

Qiancheng Wang

Q

Qinyu Chen

Q

Qiushi Du

R

Ruiqi Ge

R

Ruisong Zhang

R

Ruizhe Pan

R

Runji Wang

R

R. J. Chen

R

R. L. Jin

R

Ruyi Chen

S

Shanghao Lu

S

Shangyan Zhou

S

Shanhuang Chen

S

Shengfeng Ye

S

Shiyu Wang

S

Shuiping Yu

S

Shunfeng Zhou

S

Shuting Pan

S

S. S. Li

S

Shuang Zhou

S

Shaoqing Wu

T

Tao Yun

T

Tian Pei

T

Tianyu Sun

T

T. Wang

W

Wangding Zeng

W

Wen Liu

W

Wenfeng Liang

W

Wenjun Gao

W

Wenqin Yu

W

Wentao Zhang

W

W. L. Xiao

W

Wei An

X

Xiaodong Liu

X

Xiaohan Wang

X

Xiaokang Chen

X

Xiaotao Nie

X

Xin Cheng

X

Xin Liu

X

Xin Xie

X

Xingchao Liu

X

Xinyu Yang

X

Xinyuan Li

X

Xuecheng Su

X

Xuheng Lin

X

X. Q. Li

X

Xiangyue Jin

X

Xiaojin Shen

X

Xiaosha Chen

X

Xiaowen Sun

X

Xiaoxiang Wang

X

Xinnan Song

X

Xinyi Zhou

X

Xianzu Wang

X

Xinxia Shan

Y

Y. K. Li

Y

Y. Q. Wang

Y

Y. X. Wei

Y

Yang Zhang

Y

Yanhong Xu

Y

Yao Li

Y

Yao Zhao

Y

Yaofeng Sun

Y

Yaohui Wang

Y

Yi Yu

Y

Yichao Zhang

Y

Yifan Shi

Y

Yiliang Xiong

Y

Ying He

Y

Yishi Piao

Y

Yisong Wang

Y

Yixuan Tan

Y

Yiyang Ma

Y

Yiyuan Liu

Y

Yongqiang Guo

Y

Yuan Ou

Y

Yuduan Wang

Y

Yue Gong

Y

Yuheng Zou

Y

Yujia He

Y

Yunfan Xiong

Y

Yuxiang Luo

Y

Yuxiang You

Y

Yuxuan Liu

Y

Yuyang Zhou

Y

Y. X. Zhu

Y

Yanping Huang

Y

Yaohui Li

Y

Yi Zheng

Y

Yuchen Zhu

Y

Yunxian Ma

Y

Ying Tang

Y

Yukun Zha

Y

Yuting Yan

Z

Z. Z. Ren

Z

Zehui Ren

Z

Zhangli Sha

Z

Zhe Fu

Z

Zhean Xu

Z

Zhenda Xie

Z

Zhengyan Zhang

Z

Zhewen Hao

Z

Zhicheng Ma

Z

Zhigang Yan

Z

Zhiyu Wu

Z

Zihui Gu

Z

Zijia Zhu

Z

Zijun Liu

Z

Zilin Li

Z

Ziwei Xie

Z

Ziyang Song

Z

Zizheng Pan

Z

Zhen Huang

Z

Zhipeng Xu

Z

Zhongyu Zhang

Z

Zhen Zhang

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