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Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness.
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Deep reinforcement learning from human preferences
Paul F Christiano, Jan Leike, Tom Brown, Miljan Martic, Shane Legg, and Dario Amodei · 2017
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Attention is all you need
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Learning to summarize with human feedback
Nisan Stiennon, Long Ouyang, Jeffrey Wu, Daniel Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul F Christiano · 2020
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Language models are few-shot learners
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Approximating KL divergence
John Schulman · 2020
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Measuring mathematical problem solving with the math dataset
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Training language models to follow instructions with human feedback
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Chain-of-thought prompting elicits reasoning in large language models
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Solving quantitative reasoning problems with language models
Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, et al · 2022
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Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al · 2023
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LLaMA: Open and efficient foundation language models
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LLaMA 2: Open foundation and fine-tuned chat models
Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al · 2023
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Qwen-audio: Advancing universal audio understanding via unified large-scale audio-language models
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Gemini: a family of highly capable multimodal models
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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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Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al · 2024
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SimPO: Simple preference optimization with a reference-free reward
Yu Meng, Mengzhou Xia, and Danqi Chen · 2024
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On memorization of large language models in logical reasoning
Chulin Xie, Yangsibo Huang, Chiyuan Zhang, Da Yu, Xinyun Chen, Bill Yuchen Lin, Bo Li, Badih Ghazi, and Ravi Kumar · 2024
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Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems
Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, et al · 2024
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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
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Yuxi Xie, Anirudh Goyal, Wenyue Zheng, Min-Yen Kan, Timothy P Lillicrap, Kenji Kawaguchi, and Michael Shieh · 2024
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Alphamath almost zero: Process supervision without process
Guoxin Chen, Minpeng Liao, Chengxi Li, and Kai Fan · 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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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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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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Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al · 2024
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An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, et al · 2024
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Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context
Gemini Team, Petko Georgiev, Ving Ian Lei, Ryan Burnell, Libin Bai, Anmol Gulati, Garrett Tanzer, Damien Vincent, Zhufeng Pan, Shibo Wang, et al · 2024
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Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, et al · 2025
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DAPO: An open-source llm reinforcement learning system at scale
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A minimalist approach to llm reasoning: from rejection sampling to reinforce
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Learning dynamics of LLM finetuning
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Deepscaler: Surpassing o1-preview with a 1.5b model by scaling rl
Michael Luo, Sijun Tan, Justin Wong, Xiaoxiang Shi, William Y. Tang, Manan Roongta, Colin Cai, Jeffrey Luo, Li Erran Li, Raluca Ada Popa, and Ion Stoica · 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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Open-reasoner-zero: An open source approach to scaling up reinforcement learning on the base model
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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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VAPO: Efficient and reliable reinforcement learning for advanced reasoning tasks
Yufeng Yuan, Qiying Yu, Xiaochen Zuo, Ruofei Zhu, Wenyuan Xu, Jiaze Chen, Chengyi Wang, TianTian Fan, Zhengyin Du, Xiangpeng Wei, et al · 2025
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Efficient reinforcement finetuning via adaptive curriculum learning
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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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Reinforce++: A simple and efficient approach for aligning large language models
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