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Process Reward Models (PRMs) have recently emerged as a powerful framework for supervising intermediate reasoning steps in large language models (LLMs).
Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Not all samples are created equal: Deep learning with importance sampling
Angelos Katharopoulos and François Fleuret · 2018
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Measuring mathematical problem solving with the math dataset, 2021
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt · 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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Solving math word problems with process- and outcome-based feedback, 2022
Jonathan Uesato, Nate Kushman, Ramana Kumar, Francis Song, Noah Siegel, Lisa Wang, Antonia Creswell, Geoffrey Irving, and Irina Higgins · 2022
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Competition-level code generation with alphacode
Yujia Li, David Choi, Junyoung Chung, Nate Kushman, Julian Schrittwieser, Rémi Leblond, Tom Eccles, James Keeling, Felix Gimeno, Agustin Dal Lago, Thomas Hubert, Peter Choy, Cyprien de Masson d’Autume, Igor Babuschkin, Xinyun Chen, Po-Sen Huang, Johannes Welbl, Sven Gowal, Alexey Cherepanov, James Molloy, Daniel Mankowitz, Esme Sutherland Robson, Pushmeet Kohli, Nando de Freitas, Koray Kavukcuoglu, and Oriol Vinyals · 2022
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Gpqa: A graduate-level google-proof q&a benchmark, 2023
David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman · 2023
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Judging llm-as-a-judge with mt-bench and chatbot arena
Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al · 2023
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Scaling data-constrained language models
Niklas Muennighoff, Alexander Rush, Boaz Barak, Teven Le Scao, Nouamane Tazi, Aleksandra Piktus, Sampo Pyysalo, Thomas Wolf, and Colin A Raffel · 2023
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Doremi: Optimizing data mixtures speeds up language model pretraining
Sang Michael Xie, Hieu Pham, Xuanyi Dong, Nan Du, Hanxiao Liu, Yifeng Lu, Percy S Liang, Quoc V Le, Tengyu Ma, and Adams Wei Yu · 2023
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Camel: Communicative agents for "mind" exploration of large scale language model society, 2023
Guohao Li, Hasan Abed Al Kader Hammoud, Hani Itani, Dmitrii Khizbullin, and Bernard Ghanem · 2023
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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
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Improve mathematical reasoning in language models by automated process supervision
Liangchen Luo, Yinxiao Liu, Rosanne Liu, Samrat Phatale, Meiqi Guo, Harsh Lara, Yunxuan Li, Lei Shu, Yun Zhu, Lei Meng, 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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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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Deepseekmath: Pushing the limits of mathematical reasoning in open language models, 2024
Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, and Daya Guo · 2024
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Skywork-o1 open series
Jujie He, Tianwen Wei, Rui Yan, Jiacai Liu, Chaojie Wang, Yimeng Gan, Shiwen Tu, Chris Yuhao Liu, Liang Zeng, Xiaokun Wang, Boyang Wang, Yongcong Li, Fuxiang Zhang, Jiacheng Xu, Bo An, Yang Liu, and Yahui Zhou · 2024
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Critique-out-loud reward models
Zachary Ankner, Mansheej Paul, Brandon Cui, Jonathan D Chang, and Prithviraj Ammanabrolu · 2024
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Buffer of thoughts: Thought-augmented reasoning with large language models
Ling Yang, Zhaochen Yu, Tianjun Zhang, Shiyi Cao, Minkai Xu, Wentao Zhang, Joseph E Gonzalez, and Bin Cui · 2024
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Qwen2.5: A party of foundation models, September 2024
Qwen Team · 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, Guanting Dong, Haoran Wei, Huan Lin, Jialong Tang, Jialin Wang, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Ma, Jin Xu, Jingren Zhou, Jinze Bai, Jinzheng He, Junyang Lin, Kai Dang, Keming Lu, Keqin Chen, Kexin Yang, Mei Li, Mingfeng Xue, Na Ni, Pei Zhang, Peng Wang, Ru Peng, Rui Men, Ruize Gao, Runji Lin, Shijie Wang, Shuai Bai, Sinan Tan, Tianhang Zhu, Tianhao Li, Tianyu Liu, Wenbin Ge, Xiaodong Deng, Xiaohuan Zhou, Xingzhang Ren, Xinyu Zhang, Xipin Wei, Xuancheng Ren, Yang Fan, Yang Yao, Yichang Zhang, Yu Wan, Yunfei Chu, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zhihao Fan · 2024
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When scaling meets llm finetuning: The effect of data, model and finetuning method
Biao Zhang, Zhongtao Liu, Colin Cherry, and Orhan Firat · 2024
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Ziche Liu, Rui Ke, Yajiao Liu, Feng Jiang, and Haizhou Li · 2024
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A survey on data selection for language models
Alon Albalak, Yanai Elazar, Sang Michael Xie, Shayne Longpre, Nathan Lambert, Xinyi Wang, Niklas Muennighoff, Bairu Hou, Liangming Pan, Haewon Jeong, et al · 2024
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Greats: Online selection of high-quality data for llm training in every iteration
Jiachen Tianhao Wang, Tong Wu, Dawn Song, Prateek Mittal, and Ruoxi Jia · 2024
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Less: Selecting influential data for targeted instruction tuning
Mengzhou Xia, Sadhika Malladi, Suchin Gururangan, Sanjeev Arora, and Danqi Chen · 2024
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Instruction mining: Instruction data selection for tuning large language models, 2024
Yihan Cao, Yanbin Kang, Chi Wang, and Lichao Sun · 2024
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The best of both worlds: Bridging quality and diversity in data selection with bipartite graph, 2024
Minghao Wu, Thuy-Trang Vu, Lizhen Qu, and Gholamreza Haffari · 2024
Process reward models that think, 2025
Muhammad Khalifa, Rishabh Agarwal, Lajanugen Logeswaran, Jaekyeom Kim, Hao Peng, Moontae Lee, Honglak Lee, and Lu Wang · 2025
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Genprm: Scaling test-time compute of process reward models via generative reasoning, 2025
Jian Zhao, Runze Liu, Kaiyan Zhang, Zhimu Zhou, Junqi Gao, Dong Li, Jiafei Lyu, Zhouyi Qian, Biqing Qi, Xiu Li, and Bowen Zhou · 2025
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Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025
DeepSeek-AI · 2025
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s1: Simple test-time scaling, 2025
Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, and Tatsunori Hashimoto · 2025
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Limo: Less is more for reasoning
Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu · 2025
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Cited alongside, same era.
Jiaru Zou, Mengyu Zhou, Tao Li, Shi Han, and Dongmei Zhang · 2024
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Synthetic data (almost) from scratch: Generalized instruction tuning for language models
Haoran Li, Qingxiu Dong, Zhengyang Tang, Chaojun Wang, Xingxing Zhang, Haoyang Huang, Shaohan Huang, Xiaolong Huang, Zeqiang Huang, Dongdong Zhang, et al · 2024
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A survey on knowledge distillation of large language models
Xiaohan Xu, Ming Li, Chongyang Tao, Tao Shen, Reynold Cheng, Jinyang Li, Can Xu, Dacheng Tao, and Tianyi Zhou · 2024
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Dots: Learning to reason dynamically in llms via optimal reasoning trajectories search
Murong Yue, Wenlin Yao, Haitao Mi, Dian Yu, Ziyu Yao, and Dong Yu · 2024
Cited alongside, same era.
Rest-mcts*: Llm self-training via process reward guided tree search
Dan Zhang, Sining Zhoubian, Ziniu Hu, Yisong Yue, Yuxiao Dong, and Jie Tang · 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.
Math-shepherd: Verify and reinforce llms step-by-step without human annotations, 2024
Peiyi Wang, Lei Li, Zhihong Shao, R. X. Xu, Damai Dai, Yifei Li, Deli Chen, Y. Wu, and Zhifang Sui · 2024
Cited alongside, same era.
Ling Yang, Zhaochen Yu, Bin Cui, and Mengdi Wang · 2025
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Demystifying long chain-of-thought reasoning in llms
Edward Yeo, Yuxuan Tong, Morry Niu, Graham Neubig, and Xiang Yue · 2025
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AIME 2024 dataset
Maxwell-Jia · 2025
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AIME 2025 dataset
math ai · 2025
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Gemini Flash Thinking API
Google · 2025
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Learning to plan & reason for evaluation with thinking-llm-as-a-judge
Swarnadeep Saha, Xian Li, Marjan Ghazvininejad, Jason Weston, and Tianlu Wang · 2025
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Reinforce++: A simple and efficient approach for aligning large language models
Jian Hu · 2025
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Open Thoughts
OpenThoughts Team · 2025
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Take the essence and discard the dross: A rethinking on data selection for fine-tuning large language models, 2025
Ziche Liu, Rui Ke, Yajiao Liu, Feng Jiang, and Haizhou Li · 2025
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Openthoughts: Data recipes for reasoning models, 2025
Etash Guha, Ryan Marten, Sedrick Keh, Negin Raoof, Georgios Smyrnis, Hritik Bansal, Marianna Nezhurina, Jean Mercat, Trung Vu, Zayne Sprague, Ashima Suvarna, Benjamin Feuer, Liangyu Chen, Zaid Khan, Eric Frankel, Sachin Grover, Caroline Choi, Niklas Muennighoff, Shiye Su, Wanjia Zhao, John Yang, Shreyas Pimpalgaonkar, Kartik Sharma, Charlie Cheng-Jie Ji, Yichuan Deng, Sarah Pratt, Vivek Ramanujan, Jon Saad-Falcon, Jeffrey Li, Achal Dave, Alon Albalak, Kushal Arora, Blake Wulfe, Chinmay Hegde, Greg Durrett, Sewoong Oh, Mohit Bansal, Saadia Gabriel, Aditya Grover, Kai-Wei Chang, Vaishaal Shankar, Aaron Gokaslan, Mike A. Merrill, Tatsunori Hashimoto, Yejin Choi, Jenia Jitsev, Reinhard Heckel, Maheswaran Sathiamoorthy, Alexandros G. Dimakis, and Ludwig Schmidt · 2025
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Exploring the limit of outcome reward for learning mathematical reasoning
Chengqi Lyu, Songyang Gao, Yuzhe Gu, Wenwei Zhang, Jianfei Gao, Kuikun Liu, Ziyi Wang, Shuaibin Li, Qian Zhao, Haian Huang, et al · 2025
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Co-evolving llm coder and unit tester via reinforcement learning
Yinjie Wang, Ling Yang, Ye Tian, Ke Shen, and Mengdi Wang · 2025
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Rm-r1: Reward modeling as reasoning, 2025
Xiusi Chen, Gaotang Li, Ziqi Wang, Bowen Jin, Cheng Qian, Yu Wang, Hongru Wang, Yu Zhang, Denghui Zhang, Tong Zhang, Hanghang Tong, and Heng Ji · 2025
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Wizardmath: Empowering mathematical reasoning for large language models via reinforced evol-instruct, 2025
Haipeng Luo, Qingfeng Sun, Can Xu, Pu Zhao, Jianguang Lou, Chongyang Tao, Xiubo Geng, Qingwei Lin, Shifeng Chen, Yansong Tang, and Dongmei Zhang · 2025
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Towards thinking-optimal scaling of test-time compute for llm reasoning
Wenkai Yang, Shuming Ma, Yankai Lin, and Furu Wei · 2025
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Can 1b llm surpass 405b llm? rethinking compute-optimal test-time scaling
Runze Liu, Junqi Gao, Jian Zhao, Kaiyan Zhang, Xiu Li, Biqing Qi, Wanli Ouyang, and Bowen Zhou · 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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