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Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling.
Coarse-to-fine n-best parsing and maxent discriminative reranking
Eugene Charniak and Mark Johnson · 2005
Earlier work this paper cites.
Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
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Training verifiers to solve math word problems
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman · 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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Lora: Low-rank adaptation of large language models
Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al · 2022
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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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Self-consistency improves chain of thought reasoning in language models
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, and Denny Zhou · 2022
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Star: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman · 2022
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Raft: Reward ranked finetuning for generative foundation model alignment
Hanze Dong, Wei Xiong, Deepanshu Goyal, Yihan Zhang, Winnie Chow, Rui Pan, Shizhe Diao, Jipeng Zhang, Kashun Shum, and Tong Zhang · 2023
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Large language models cannot self-correct reasoning yet
Jie Huang, Xinyun Chen, Swaroop Mishra, Huaixiu Steven Zheng, Adams Wei Yu, Xinying Song, and Denny Zhou · 2023
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GRACE: discriminator-guided chain-of-thought reasoning
Muhammad Khalifa, Lajanugen Logeswaran, Moontae Lee, Honglak Lee, and Lu Wang · 2023
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Prometheus: Inducing fine-grained evaluation capability in language models
Seungone Kim, Jamin Shin, Yejin Cho, Joel Jang, Shayne Longpre, Hwaran Lee, Sangdoo Yun, Seongjin Shin, Sungdong Kim, James Thorne, et al · 2023
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Making language models better reasoners with step-aware verifier
Yifei Li, Zeqi Lin, Shizhuo Zhang, Qiang Fu, Bei Chen, Jian-Guang Lou, and Weizhu Chen · 2023
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Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe · 2023
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Beyond human data: Scaling self-training for problem-solving with language models
Avi Singh, John D Co-Reyes, Rishabh Agarwal, Ankesh Anand, Piyush Patil, Xavier Garcia, Peter J Liu, James Harrison, Jaehoon Lee, Kelvin Xu, et al · 2023
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Gpt-4 doesn’t know it’s wrong: An analysis of iterative prompting for reasoning problems
Kaya Stechly, Matthew Marquez, and Subbarao Kambhampati · 2023
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Tree of thoughts: Deliberate problem solving with large language models
Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan · 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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Judgelm: Fine-tuned large language models are scalable judges
Lianghui Zhu, Xinggang Wang, and Xinlong Wang · 2023
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The surprising effectiveness of test-time training for abstract reasoning
Ekin Akyürek, Mehul Damani, Linlu Qiu, Han Guo, Yoon Kim, and Jacob Andreas · 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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Llms instead of human judges? a large scale empirical study across 20 nlp evaluation tasks
Anna Bavaresco, Raffaella Bernardi, Leonardo Bertolazzi, Desmond Elliott, Raquel Fernández, Albert Gatt, Esam Ghaleb, Mario Giulianelli, Michael Hanna, Alexander Koller, et al · 2024
Cited alongside, same era.
Large language monkeys: Scaling inference compute with repeated sampling
Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V Le, Christopher Ré, and Azalia Mirhoseini · 2024
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Alphazero-like tree-search can guide large language model decoding and training
Ziyu Wan, Xidong Feng, Muning Wen, Stephen Marcus McAleer, Ying Wen, Weinan Zhang, and Jun Wang · 2024
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Tianlu Wang, Ilia Kulikov, Olga Golovneva, Ping Yu, Weizhe Yuan, Jane Dwivedi-Yu, Richard Yuanzhe Pang, Maryam Fazel-Zarandi, Jason Weston, and Xian Li · 2024
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Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang · 2024
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An implementation of generative prm
Wei Xiong, Hanning Zhang, Nan Jiang, and Tong Zhang · 2024
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Physics of language models: Part 2.2, how to learn from mistakes on grade-school math problems
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Bofei Gao, Feifan Song, Zhe Yang, Zefan Cai, Yibo Miao, Qingxiu Dong, Lei Li, Chenghao Ma, Liang Chen, Runxin Xu, et al · 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
Cited alongside, same era.
Qwen2. 5-coder technical report
Binyuan Hui, Jian Yang, Zeyu Cui, Jiaxi Yang, Dayiheng Liu, Lei Zhang, Tianyu Liu, Jiajun Zhang, Bowen Yu, Kai Dang, 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.
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 · 2024
Cited alongside, same era.
C3ot: Generating shorter chain-of-thought without compromising effectiveness
Yu Kang, Xianghui Sun, Liangyu Chen, and Wei Zou · 2024
Cited alongside, same era.
Training language models to self-correct via reinforcement learning
Aviral Kumar, Vincent Zhuang, Rishabh Agarwal, Yi Su, John D Co-Reyes, Avi Singh, Kate Baumli, Shariq Iqbal, Colton Bishop, Rebecca Roelofs, et al · 2024
Cited alongside, same era.
Rewardbench: Evaluating reward models for language modeling
Nathan Lambert, Valentina Pyatkin, Jacob Morrison, LJ Miranda, Bill Yuchen Lin, Khyathi Chandu, Nouha Dziri, Sachin Kumar, Tom Zick, Yejin Choi, et al · 2024
Cited alongside, same era.
Tian Ye, Zicheng Xu, Yuanzhi Li, and Zeyuan Allen-Zhu · 2024
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Distilling system 2 into system 1
Ping Yu, Jing Xu, Jason Weston, and Ilia Kulikov · 2024
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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
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Small language models need strong verifiers to self-correct reasoning
Yunxiang Zhang, Muhammad Khalifa, Lajanugen Logeswaran, Jaekyeom Kim, Moontae Lee, Honglak Lee, and Lu Wang · 2024
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Processbench: Identifying process errors in mathematical reasoning
Chujie Zheng, Zhenru Zhang, Beichen Zhang, Runji Lin, Keming Lu, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin · 2024
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Relying on the unreliable: The impact of language models’ reluctance to express uncertainty
Kaitlyn Zhou, Jena D Hwang, Xiang Ren, and Maarten Sap · 2024
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The danger of overthinking: Examining the reasoning-action dilemma in agentic tasks
Alejandro Cuadron, Dacheng Li, Wenjie Ma, Xingyao Wang, Yichuan Wang, Siyuan Zhuang, Shu Liu, Luis Gaspar Schroeder, Tian Xia, Huanzhi Mao, et al · 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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Verdict: A library for scaling judge-time compute
Nimit Kalra and Leonard Tang · 2025
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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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Nishad Singhi, Hritik Bansal, Arian Hosseini, Aditya Grover, Kai-Wei Chang, Marcus Rohrbach, and Anna Rohrbach · 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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An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al · 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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