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Recent advancements in long chain-of-thought (CoT) reasoning, particularly through the Group Relative Policy Optimization algorithm used by DeepSeek-R1, have led to significant interest in the potential of Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Models (LLMs).
Policy gradient methods for reinforcement learning with function approximation
Richard S Sutton, David McAllester, Satinder Singh, and Yishay Mansour · 1999
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Mastering the game of Go without human knowledge
David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, et al · 2017
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Scaling laws for neural language models
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei · 2020
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Evaluating large language models trained on code
Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde De Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, et al · 2021
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Solving math word problems with process-and outcome-based feedback
Jonathan Uesato, Nate Kushman, Ramana Kumar, Francis Song, Noah Siegel, Lisa Wang, Antonia Creswell, Geoffrey Irving, and Irina Higgins · 2022
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Direct preference optimization: Your language model is secretly a reward model
Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn · 2023
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Introducing Gemini 2.0: our new AI model for the agentic era
Team Gemini · 2024
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Tulu 3: Pushing frontiers in open language model post-training
Nathan Lambert, Jacob Morrison, Valentina Pyatkin, Shengyi Huang, Hamish Ivison, Faeze Brahman, Lester James V Miranda, Alisa Liu, Nouha Dziri, Shane Lyu, et al · 2024
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Let’s verify step by step
Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe · 2024
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Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al · 2024
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Learning to reason with LLMs
Team OpenAI · 2024
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Team Qwen · 2024
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DeepSeekMath: Pushing the limits of mathematical reasoning in open language models
Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al · 2024
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Math-Shepherd: Verify and reinforce LLMs step-by-step without human annotations
Peiyi Wang, Lei Li, Zhihong Shao, Runxin Xu, Damai Dai, Yifei Li, Deli Chen, Yu Wu, and Zhifang Sui · 2024
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Introducing Claude 4
Team Anthropic · 2025
Cited alongside, same era.
Chain-of-thought reasoning in the wild is not always faithful
Iván Arcuschin, Jett Janiak, Robert Krzyzanowski, Senthooran Rajamanoharan, Neel Nanda, and Arthur Conmy · 2025
Cited alongside, same era.
SkyRL-v0: Train real-world long-horizon agents via reinforcement learning
Shiyi Cao, Sumanth Hegde, Dacheng Li, Tyler Griggs, Shu Liu, Eric Tang, Jiayi Pan, Xingyao Wang, Akshay Malik, Graham Neubig, Kourosh Hakhamaneshi, Richard Liaw, Philipp Moritz, Matei Zaharia, Joseph E. Gonzalez, and Ion Stoica · 2025
Cited alongside, same era.
Process reinforcement through implicit rewards
Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, et al · 2025
Cited alongside, same era.
DeepSeek-R1-0528 release
Team DeepSeek · 2025
Cited alongside, same era.
HybridFlow: A flexible and efficient RLHF framework
Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu · 2025
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Parshin Shojaee, Iman Mirzadeh, Keivan Alizadeh, Maxwell Horton, Samy Bengio, and Mehrdad Farajtabar · 2025
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Welcome to the era of experience
David Silver and Richard S Sutton · 2025
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Xuerui Su, Shufang Xie, Guoqing Liu, Yingce Xia, Renqian Luo, Peiran Jin, Zhiming Ma, Yue Wang, Zun Wang, and Yuting Liu · 2025
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Light-R1: Curriculum SFT, DPO and RL for long CoT from scratch and beyond
Liang Wen, Yunke Cai, Fenrui Xiao, Xin He, Qi An, Zhenyu Duan, Yimin Du, Junchen Liu, Lifu Tang, Xiaowei Lv, et al · 2025
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Gemini 2.5: Our most intelligent models are getting even better
Team Gemini · 2025
Cited alongside, same era.
Grok 3 Beta — The age of reasoning agents
Team Grok · 2025
Cited alongside, same era.
DeepSeek-R1: Incentivizing reasoning capability in LLMs via reinforcement learning
Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al · 2025
Cited alongside, same era.
Skywork open reasoner 1 technical report
Jujie He, Jiacai Liu, Chris Yuhao Liu, Rui Yan, Chaojie Wang, Peng Cheng, Xiaoyu Zhang, Fuxiang Zhang, Jiacheng Xu, Wei Shen, et al · 2025
Cited alongside, same era.
Open-Reasoner-Zero: An open source approach to scaling up reinforcement learning on the base model
Jingcheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, Xiangyu Zhang, and Heung-Yeung Shum · 2025
Cited alongside, same era.
LiveCodeBench: Holistic and contamination free evaluation of large language models for code
Naman Jain, King Han, Alex Gu, Wen-Ding Li, Fanjia Yan, Tianjun Zhang, Sida Wang, Armando Solar-Lezama, Koushik Sen, and Ion Stoica · 2025
Cited alongside, same era.
Large language models’ reasoning stalls: An investigation into the capabilities of frontier models
Lachlan McGinness and Peter Baumgartner · 2025
Cited alongside, same era.
Closest in time.
LiveBench: A challenging, contamination-limited LLM benchmark
Colin White, Samuel Dooley, Manley Roberts, Arka Pal, Ben Feuer, Siddhartha Jain, Ravid Shwartz-Ziv, Neel Jain, Khalid Saifullah, Sreemanti Dey, Shubh-Agrawal, Sandeep Singh Sandha, Siddartha Naidu, Chinmay Hegde, Yann LeCun, Tom Goldstein, Willie Neiswanger, and Micah Goldblum · 2025
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Logic-RL: Unleashing LLM reasoning with rule-based reinforcement learning
Tian Xie, Zitian Gao, Qingnan Ren, Haoming Luo, Yuqian Hong, Bryan Dai, Joey Zhou, Kai Qiu, Zhirong Wu, and Chong Luo · 2025
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The second half
Shunyu Yao · 2025
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EvalHub: All-in-one benchmarking platform for evaluating large language models (LLMs) with comprehensive metrics and standardized testing frameworks
Shengyu Ye · 2025
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DAPO: An open-source LLM reinforcement learning system at scale
Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Tiantian Fan, Gaohong Liu, Lingjun Liu, Xin Liu, et al · 2025
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Does reinforcement learning really incentivize reasoning capacity in LLMs beyond the base model?
Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Shiji Song, and Gao Huang · 2025
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SimpleRL-Zoo: Investigating and taming zero reinforcement learning for open base models in the wild
Weihao Zeng, Yuzhen Huang, Qian Liu, Wei Liu, Keqing He, Zejun Ma, and Junxian He · 2025
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Right question is already half the answer: Fully unsupervised LLM reasoning incentivization
Qingyang Zhang, Haitao Wu, Changqing Zhang, Peilin Zhao, and Yatao Bian · 2025
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The surprising effectiveness of negative reinforcement in LLM reasoning
Xinyu Zhu, Mengzhou Xia, Zhepei Wei, Wei-Lin Chen, Danqi Chen, and Yu Meng · 2025
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