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Training large language models (LLMs) for complex reasoning via Reinforcement Learning with Verifiable Rewards (RLVR) is effective but limited by reliance on costly, domain-specific supervision.
Simple statistical gradient-following algorithms for connectionist reinforcement learning
Ronald J Williams · 1992
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What is intrinsic motivation? a typology of computational approaches
Pierre-Yves Oudeyer and Frederic Kaplan · 2007
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Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix
Nicolas De Condorcet et al · 2014
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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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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Fine-tuning language models from human preferences
Daniel M Ziegler, Nisan Stiennon, Jeffrey Wu, Tom B Brown, Alec Radford, Dario Amodei, Paul Christiano, and Geoffrey Irving · 2019
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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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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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Star: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman · 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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Scaling laws for reward model overoptimization
Leo Gao, John Schulman, and Jacob Hilton · 2023
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Is your code generated by chatgpt really correct? rigorous evaluation of large language models for code generation
Jiawei Liu, Chunqiu Steven Xia, Yuyao Wang, and Lingming Zhang · 2023
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Weak-to-strong generalization: Eliciting strong capabilities with weak supervision
Collin Burns, Pavel Izmailov, Jan Hendrik Kirchner, Bowen Baker, Leo Gao, Leopold Aschenbrenner, Yining Chen, Adrien Ecoffet, Manas Joglekar, Jan Leike, et al · 2023
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Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar · 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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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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Lighteval: A lightweight framework for llm evaluation, 2023
Nathan Habib, Clémentine Fourrier, Hynek Kydlíček, Thomas Wolf, and Lewis Tunstall · 2023
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T \ \backslash "ulu 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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Detecting hallucinations in large language models using semantic entropy
Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal · 2024
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Unfamiliar finetuning examples control how language models hallucinate
Katie Kang, Eric Wallace, Claire Tomlin, Aviral Kumar, and Sergey Levine · 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
Cited alongside, same era.
Livecodebench: Holistic and contamination free evaluation of large language models for code
Code-r1: Reproducing r1 for code with reliable rewards
Jiawei Liu and Lingming Zhang · 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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Mimo: Unlocking the reasoning potential of language model – from pretraining to posttraining, 2025
Xiaomi LLM-Core Team · 2025
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Scalable best-of-n selection for large language models via self-certainty
Zhewei Kang, Xuandong Zhao, and Dawn Song · 2025
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Reasoning models can be effective without thinking
Wenjie Ma, Jingxuan He, Charlie Snell, Tyler Griggs, Sewon Min, and Matei Zaharia · 2025
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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.
Cruxeval: A benchmark for code reasoning, understanding and execution
Alex Gu, Baptiste Rozière, Hugh Leather, Armando Solar-Lezama, Gabriel Synnaeve, and Sida I Wang · 2024
Cited alongside, same era.
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.
Self-play fine-tuning converts weak language models to strong language models
Zixiang Chen, Yihe Deng, Huizhuo Yuan, Kaixuan Ji, and Quanquan Gu · 2024
Cited alongside, same era.
Self-rewarding language models
Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Xian Li, Sainbayar Sukhbaatar, Jing Xu, and Jason E. Weston · 2024
Cited alongside, same era.
Learning formal mathematics from intrinsic motivation
Gabriel Poesia, David Broman, Nick Haber, and Noah Goodman · 2024
Cited alongside, same era.
Self-playing adversarial language game enhances llm reasoning
Pengyu Cheng, Yong Dai, Tianhao Hu, Han Xu, Zhisong Zhang, Lei Han, Nan Du, and Xiaolong Li · 2024
Cited alongside, same era.
What is wrong with perplexity for long-context language modeling?
Lizhe Fang, Yifei Wang, Zhaoyang Liu, Chenheng Zhang, Stefanie Jegelka, Jinyang Gao, Bolin Ding, and Yisen Wang · 2024
Cited alongside, same era.
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Deepcoder: A fully open-source 14b coder at o3-mini level
Michael Luo, Sijun Tan, Roy Huang, Xiaoxiang Shi, Rachel Xin, Colin Cai, Ameen Patel, Alpay Ariyak, Qingyang Wu, Ce Zhang, Li Erran Li, Raluca Ada Popa, and Ion Stoica · 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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Genius: A generalizable and purely unsupervised self-training framework for advanced reasoning
Fangzhi Xu, Hang Yan, Chang Ma, Haiteng Zhao, Qiushi Sun, Kanzhi Cheng, Junxian He, Jun Liu, and Zhiyong Wu · 2025
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Ttrl: Test-time reinforcement learning
Yuxin Zuo, Kaiyan Zhang, Shang Qu, Li Sheng, Xuekai Zhu, Biqing Qi, Youbang Sun, Ganqu Cui, Ning Ding, and Bowen Zhou · 2025
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Absolute zero: Reinforced self-play reasoning with zero data
Andrew Zhao, Yiran Wu, Yang Yue, Tong Wu, Quentin Xu, Matthieu Lin, Shenzhi Wang, Qingyun Wu, Zilong Zheng, and Gao Huang · 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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Seed-grpo: Semantic entropy enhanced grpo for uncertainty-aware policy optimization
Minghan Chen, Guikun Chen, Wenguan Wang, and Yi Yang · 2025
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The unreasonable effectiveness of entropy minimization in llm reasoning
Shivam Agarwal, Zimin Zhang, Lifan Yuan, Jiawei Han, and Hao Peng · 2025
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Open r1: A fully open reproduction of deepseek-r1, January 2025
Hugging Face · 2025
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Introducing GPT -
OpenAI · 2025
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Llama 3.2: Revolutionizing edge ai and vision with open, customizable models
Meta AI · 2025
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