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We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference.
Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2013
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Reweighted wake-sleep
Jörg Bornschein and Yoshua Bengio · 2015
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Importance weighted autoencoders
Yuri Burda, Roger Grosse, and Ruslan Salakhutdinov · 2015
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Decoupled weight decay regularization
Ilya Loshchilov and Frank Hutter · 2019
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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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Gflownet foundations
Yoshua Bengio, Salem Lahlou, Tristan Deleu, Edward J. Hu, Mo Tiwari, and Emmanuel Bengio · 2023
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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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Training chain-of-thought via latent-variable inference
Matthew Douglas Hoffman, Du Phan, david dohan, Sholto Douglas, Tuan Anh Le, Aaron T Parisi, Pavel Sountsov, Charles Sutton, Sharad Vikram, and Rif A. Saurous · 2023
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Efficient memory management for large language model serving with pagedattention
Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and Ion Stoica · 2023
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Taco: Topics in algorithmic code generation dataset
Rongao Li, Jie Fu, Bo-Wen Zhang, Tao Huang, Zhihong Sun, Chen Lyu, Guang Liu, Zhi Jin, and Ge Li · 2023
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Eureka: Human-level reward design via coding large language models
Yecheng Jason Ma, William Liang, Guanzhi Wang, De-An Huang, Osbert Bastani, Dinesh Jayaraman, Yuke Zhu, Linxi Fan, and Anima Anandkumar · 2023
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American mathematics competitions - amc
MAA · 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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Language models are hidden reasoners: Unlocking latent reasoning capabilities via self-rewarding
Haolin Chen, Yihao Feng, Zuxin Liu, Weiran Yao, Akshara Prabhakar, Shelby Heinecke, Ricky Ho, Phil Mui, Silvio Savarese, Caiming Xiong, et al · 2024
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On designing effective rl reward at training time for llm reasoning
Jiaxuan Gao, Shusheng Xu, Wenjie Ye, Weilin Liu, Chuyi He, Wei Fu, Zhiyu Mei, Guangju Wang, and Yi Wu · 2024
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Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems, 2024
Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, Jie Liu, Lei Qi, Zhiyuan Liu, and Maosong Sun · 2024
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Amortizing intractable inference in large language models
Edward J Hu, Moksh Jain, Eric Elmoznino, Younesse Kaddar, Guillaume Lajoie, Yoshua Bengio, and Nikolay Malkin · 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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Vineppo: Unlocking rl potential for llm reasoning through refined credit assignment
Amirhossein Kazemnejad, Milad Aghajohari, Eva Portelance, Alessandro Sordoni, Siva Reddy, Aaron Courville, and Nicolas Le Roux · 2024
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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
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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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Gpqa: A graduate-level google-proof q&a benchmark
David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R Bowman · 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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Qwq: Reflect deeply on the boundaries of the unknown
Qwen Team · 2024
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Mmlu-pro: A more robust and challenging multi-task language understanding benchmark
Yubo Wang, Xueguang Ma, Ge Zhang, Yuansheng Ni, Abhranil Chandra, Shiguang Guo, Weiming Ren, Aaran Arulraj, Xuan He, Ziyan Jiang, et al · 2024
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An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu · 2024
Cited alongside, same era.
General-reasoner: Advancing llm reasoning across all domains
Xueguang Ma, Qian Liu, Dongfu Jiang, Ge Zhang, Zejun Ma, and Wenhu Chen · 2025
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American invitational mathematics examination - aime
MAA · 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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Optimizing anytime reasoning via budget relative policy optimization
Penghui Qi, Zichen Liu, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin · 2025
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Reasoning to learn from latent thoughts
Yangjun Ruan, Neil Band, Chris J Maddison, and Tatsunori Hashimoto · 2025
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Yaowei Zheng, Richong Zhang, Junhao Zhang, Yanhan Ye, Zheyan Luo, Zhangchi Feng, and Yongqiang Ma · 2024
Cited alongside, same era.
Reinforcement learning teachers of test time scaling
Edoardo Cetin, Tianyu Zhao, and Yujin Tang · 2025
Cited alongside, same era.
Acereason-nemotron: Advancing math and code reasoning through reinforcement learning
Yang Chen, Zhuolin Yang, Zihan Liu, Chankyu Lee, Peng Xu, Mohammad Shoeybi, Bryan Catanzaro, and Wei Ping · 2025
Cited alongside, same era.
Reasoning with exploration: An entropy perspective
Daixuan Cheng, Shaohan Huang, Xuekai Zhu, Bo Dai, Wayne Xin Zhao, Zhenliang Zhang, and Furu Wei · 2025
Cited alongside, same era.
Sft memorizes, rl generalizes: A comparative study of foundation model post-training
Tianzhe Chu, Yuexiang Zhai, Jihan Yang, Shengbang Tong, Saining Xie, Dale Schuurmans, Quoc V Le, Sergey Levine, and Yi Ma · 2025
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Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, et al · 2025
Cited alongside, same era.
Openthoughts: Data recipes for reasoning models
Etash Guha, Ryan Marten, Sedrick Keh, Negin Raoof, Georgios Smyrnis, Hritik Bansal, Marianna Nezhurina, Jean Mercat, Trung Vu, Zayne Sprague, et al · 2025
Cited alongside, same era.
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
Cited alongside, same era.
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Rl’s razor: Why online reinforcement learning forgets less
Idan Shenfeld, Jyothish Pari, and Pulkit Agrawal · 2025
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Learning to chain-of-thought with jensen’s evidence lower bound
Yunhao Tang, Sid Wang, and Rémi Munos · 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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Sky-t1: Train your own o1 preview model within $450
NovaSky Team · 2025
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Ragen: Understanding self-evolution in llm agents via multi-turn reinforcement learning
Zihan Wang, Kangrui Wang, Qineng Wang, Pingyue Zhang, Linjie Li, Zhengyuan Yang, Xing Jin, Kefan Yu, Minh Nhat Nguyen, Licheng Liu, 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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Light-r1: Curriculum sft, dpo and rl for long cot from scratch and beyond
Liang Wen, Yunke Cai, Fenrui Xiao, Xin He, Qi An, Zhenyu Duan, Yimin Du, Junchen Liu, Lifu Tang, Xiaowei Lv, et al · 2025
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On the generalization of sft: A reinforcement learning perspective with reward rectification
Yongliang Wu, Yizhou Zhou, Zhou Ziheng, Yingzhe Peng, Xinyu Ye, Xinting Hu, Wenbo Zhu, Lu Qi, Ming-Hsuan Yang, and Xu Yang · 2025
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Towards system 2 reasoning in llms: Learning how to think with meta chain-of-thought
Violet Xiang, Charlie Snell, Kanishk Gandhi, Alon Albalak, Anikait Singh, Chase Blagden, Duy Phung, Rafael Rafailov, Nathan Lile, Dakota Mahan, et al · 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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Direct reasoning optimization: Llms can reward and refine their own reasoning for open-ended tasks
Yifei Xu, Tusher Chakraborty, Srinagesh Sharma, Leonardo Nunes, Emre Kıcıman, Songwu Lu, and Ranveer Chandra · 2025
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Simpletir: End-to-end reinforcement learning for multi-turn tool-integrated reasoning
Zhenghai Xue, Longtao Zheng, Qian Liu, Yingru Li, Xiaosen Zheng, Zejun Ma, and Bo An · 2025
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Swe-smith: Scaling data for software engineering agents
John Yang, Kilian Lieret, Carlos E Jimenez, Alexander Wettig, Kabir Khandpur, Yanzhe Zhang, Binyuan Hui, Ofir Press, Ludwig Schmidt, and Diyi Yang · 2025
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7b model and 8k examples: Emerging reasoning with reinforcement learning is both effective and efficient
Weihao Zeng, Yuzhen Huang, Wei Liu, Keqing He, Qian Liu, Zejun Ma, and Junxian He · 2025
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Group sequence policy optimization
Chujie Zheng, Shixuan Liu, Mingze Li, Xiong-Hui Chen, Bowen Yu, Chang Gao, Kai Dang, Yuqiong Liu, Rui Men, An Yang, et al · 2025
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Brite: Bootstrapping reinforced thinking process to enhance language model reasoning
Han Zhong, Yutong Yin, Shenao Zhang, Xiaojun Xu, Yuanxin Liu, Yifei Zuo, Zhihan Liu, Boyi Liu, Sirui Zheng, Hongyi Guo, et al · 2025
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Reinforcing general reasoning without verifiers
Xiangxin Zhou, Zichen Liu, Anya Sims, Haonan Wang, Tianyu Pang, Chongxuan Li, Liang Wang, Min Lin, and Chao Du · 2025
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