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Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks.
Steps toward artificial intelligence
Marvin Minsky · 2007
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Hindsight experience replay
Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, OpenAI Pieter Abbeel, and Wojciech Zaremba · 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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Reinforcement learning: An introduction
Richard S Sutton and Andrew G Barto · 2018
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Training verifiers to solve math word problems
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al · 2021
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Measuring mathematical problem solving with the math dataset
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt · 2021
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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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Training language models to follow instructions with human feedback
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al · 2022
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Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al · 2023
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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 · 2023
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A survey of temporal credit assignment in deep reinforcement learning
Eduardo Pignatelli, Johan Ferret, Matthieu Geist, Thomas Mesnard, Hado van Hasselt, Olivier Pietquin, and Laura Toni · 2023
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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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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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Math-shepherd: Verify and reinforce llms step-by-step without human annotations
Peiyi Wang, Lei Li, Zhihong Shao, RX Xu, Damai Dai, Yifei Li, Deli Chen, Yu Wu, and Zhifang Sui · 2023
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Back to basics: Revisiting reinforce style optimization for learning from human feedback in llms
Arash Ahmadian, Chris Cremer, Matthias Gallé, Marzieh Fadaee, Julia Kreutzer, Olivier Pietquin, Ahmet Üstün, and Sara Hooker · 2024
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RIME: Robust preference-based reinforcement learning with noisy preferences
Jie Cheng, Gang Xiong, Xingyuan Dai, Qinghai Miao, Yisheng Lv, and Fei-Yue Wang · 2024
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Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, et al · 2024
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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
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
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Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars
Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D Goodman · 2025
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rstar-math: Small llms can master math reasoning with self-evolved deep thinking, 2025
Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang · 2025
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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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Reinforce++: A simple and efficient approach for aligning large language models
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Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions
Jia Li, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Huang, Kashif Rasul, Longhui Yu, Albert Q Jiang, Ziju Shen, et al · 2024
Cited alongside, same era.
Rewarding progress: Scaling automated process verifiers for llm reasoning
Amrith Setlur, Chirag Nagpal, Adam Fisch, Xinyang Geng, Jacob Eisenstein, Rishabh Agarwal, Alekh Agarwal, Jonathan Berant, and Aviral Kumar · 2024
Cited alongside, same era.
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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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 · 2024
Cited alongside, same era.
Reward hacking in reinforcement learning
Lilian Weng · 2024
Cited alongside, same era.
An implementation of generative prm
Wei Xiong, Hanning Zhang, Nan Jiang, and Tong Zhang · 2024
Cited alongside, same era.
Free process rewards without process labels
Lifan Yuan, Wendi Li, Huayu Chen, Ganqu Cui, Ning Ding, Kaiyan Zhang, Bowen Zhou, Zhiyuan Liu, and Hao Peng · 2024
Cited alongside, same era.
Sc-tune: Unleashing self-consistent referential comprehension in large vision language models
Tongtian Yue, Jie Cheng, Longteng Guo, Xingyuan Dai, Zijia Zhao, Xingjian He, Gang Xiong, Yisheng Lv, and Jing Liu · 2024
Cited alongside, same era.
Jian Hu · 2025
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Jingcheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, Xiangyu Zhang, and Heung-Yeung Shum · 2025
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Understanding r1-zero-like training: A critical perspective
Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin · 2025
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Prmbench: A fine-grained and challenging benchmark for process-level reward models
Mingyang Song, Zhaochen Su, Xiaoye Qu, Jiawei Zhou, and Yu Cheng · 2025
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Kimi k1. 5: Scaling reinforcement learning with llms
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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Step-3 is large yet affordable: Model-system co-design for cost-effective decoding
Bin Wang, Bojun Wang, Changyi Wan, Guanzhe Huang, Hanpeng Hu, Haonan Jia, Hao Nie, Mingliang Li, Nuo Chen, Siyu Chen, et al · 2025
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Swe-rl: Advancing llm reasoning via reinforcement learning on open software evolution
Yuxiang Wei, Olivier Duchenne, Jade Copet, Quentin Carbonneaux, Lingming Zhang, Daniel Fried, Gabriel Synnaeve, Rishabh Singh, and Sida I Wang · 2025
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Self-rewarding correction for mathematical reasoning
Wei Xiong, Hanning Zhang, Chenlu Ye, Lichang Chen, Nan Jiang, and Tong Zhang · 2025
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The lessons of developing process reward models in mathematical reasoning
Zhenru Zhang, Chujie Zheng, Yangzhen Wu, Beichen Zhang, Runji Lin, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin · 2025
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