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Recent research on Reasoning of Large Language Models (LLMs) has sought to further enhance their performance by integrating meta-thinking -- enabling models to monitor, evaluate, and control their reasoning processes for more adaptive and effective problem-solving.
Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry
John H Flavell · 1979
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Hierarchical skills and cognitive architectures
Pat Langley, Kirstin Cummings, and Daniel Shapiro · 2004
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Sequence transduction with recurrent neural networks
Alex Graves · 2012
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Trust region policy optimization
John Schulman, Sergey Levine, Pieter Abbeel, Michael I. Jordan, and Philipp Moritz · 2015
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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A survey of cognitive architectures in the past 20 years
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The bitter lesson
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Language models are few-shot learners
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Learning to give checkable answers with prover-verifier games
Cem Anil, Guodong Zhang, Yuhuai Wu, and Roger B. Grosse · 2021
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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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Red teaming language models with language models
Ethan Perez, Saffron Huang, Francis Song, Trevor Cai, Roman Ring, John Aslanides, Amelia Glaese, Nat McAleese, and Geoffrey Irving · 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, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou · 2022
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Chain-of-thought prompting elicits reasoning in large language models
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al · 2022
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Generating sequences by learning to self-correct
Sean Welleck, Ximing Lu, Peter West, Faeze Brahman, Tianxiao Shen, Daniel Khashabi, and Yejin Choi · 2022
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Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al · 2023
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Playing repeated games with large language models
Elif Akata, Lion Schulz, Julian Coda-Forno, Seong Joon Oh, Matthias Bethge, and Eric Schulz · 2023
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Gemini: A family of highly capable multimodal models
Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, Katie Millican, et al · 2023
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Agentverse: Facilitating multi-agent collaboration and exploring emergent behaviors
Weize Chen, Yusheng Su, Jingwei Zuo, Cheng Yang, Chenfei Yuan, Chi-Min Chan, Heyang Yu, Yaxi Lu, Yi-Hsin Hung, Chen Qian, et al · 2023
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Palm: Scaling language modeling with pathways
Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al · 2023
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Improving factuality and reasoning in language models through multiagent debate
Yilun Du, Shuang Li, Antonio Torralba, Joshua B Tenenbaum, and Igor Mordatch · 2023
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Metagpt: Meta programming for multi-agent collaborative framework
Sirui Hong, Xiawu Zheng, Jonathan Chen, Yuheng Cheng, Jinlin Wang, Ceyao Zhang, Zili Wang, Steven Ka Shing Yau, Zijuan Lin, Liyang Zhou, et al · 2023
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Encouraging divergent thinking in large language models through multi-agent debate
Tian Liang, Zhiwei He, Wenxiang Jiao, Xing Wang, Yan Wang, Rui Wang, Yujiu Yang, Shuming Shi, and Zhaopeng Tu · 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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Red teaming game: A game-theoretic framework for red teaming language models
Chengdong Ma, Ziran Yang, Minquan Gao, Hai Ci, Jun Gao, Xuehai Pan, and Yaodong Yang · 2023
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Self-refine: Iterative refinement with self-feedback
Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye, Yiming Yang, 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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Sayplan: Grounding large language models using 3d scene graphs for scalable robot task planning
Krishan Rana, Jesse Haviland, Sourav Garg, Jad Abou-Chakra, Ian Reid, and Niko Suenderhauf · 2023
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Llm-planner: Few-shot grounded planning for embodied agents with large language models
Chan Hee Song, Jiaman Wu, Clayton Washington, Brian M Sadler, Wei-Lun Chao, and Yu Su · 2023
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Medagents: Large language models as collaborators for zero-shot medical reasoning
Xiangru Tang, Anni Zou, Zhuosheng Zhang, Ziming Li, Yilun Zhao, Xingyao Zhang, Arman Cohan, and Mark Gerstein · 2023
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Metacognitive prompting improves understanding in large language models
Yuqing Wang and Yun Zhao · 2023
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Zhenhailong Wang, Shaoguang Mao, Wenshan Wu, Tao Ge, Furu Wei, and Heng Ji · 2023
Cited alongside, same era.
Xue Yan, Yan Song, Xinyu Cui, Filippos Christianos, Haifeng Zhang, David Henry Mguni, and Jun Wang · 2023
Cited alongside, same era.
Evaluating the performance of large language models on gaokao benchmark
Xiaotian Zhang, Chunyang Li, Yi Zong, Zhengyu Ying, Liang He, and Xipeng Qiu · 2023
Cited alongside, same era.
Mindstorms in natural language-based societies of mind
Mingchen Zhuge, Haozhe Liu, Francesco Faccio, Dylan R Ashley, Róbert Csordás, Anand Gopalakrishnan, Abdullah Hamdi, Hasan Abed Al Kader Hammoud, Vincent Herrmann, Kazuki Irie, et al · 2023
Cited alongside, same era.
Reinforcing language agents via policy optimization with action decomposition
Muning Wen, Ziyu Wan, Weinan Zhang, Jun Wang, and Ying Wen · 2024
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Enhancing llm reasoning via critique models with test-time and training-time supervision
Zhiheng Xi, Dingwen Yang, Jixuan Huang, Jiafu Tang, Guanyu Li, Yiwen Ding, Wei He, Boyang Hong, Shihan Do, Wenyu Zhan, et al · 2024
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Cellagent: An llm-driven multi-agent framework for automated single-cell data analysis
Yihang Xiao, Jinyi Liu, Yan Zheng, Xiaohan Xie, Jianye Hao, Mingzhi Li, Ruitao Wang, Fei Ni, Yuxiao Li, Jintian Luo, et al · 2024
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What matters for model merging at scale?
Prateek Yadav, Tu Vu, Jonathan Lai, Alexandra Chronopoulou, Manaal Faruqui, Mohit Bansal, and Tsendsuren Munkhdalai · 2024
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Autotamp: Autoregressive task and motion planning with llms as translators and checkers
Yongchao Chen, Jacob Arkin, Charles Dawson, Yang Zhang, Nicholas Roy, and Chuchu Fan · 2024
Cited alongside, same era.
Metacognitive capabilities of llms: An exploration in mathematical problem solving
Aniket Didolkar, Anirudh Goyal, Nan Rosemary Ke, Siyuan Guo, Michal Valko, Timothy Lillicrap, Danilo Rezende, Yoshua Bengio, Michael Mozer, and Sanjeev Arora · 2024
Cited alongside, same era.
Hybrid llm: Cost-efficient and quality-aware query routing
Dujian Ding, Ankur Mallick, Chi Wang, Robert Sim, Subhabrata Mukherjee, Victor Ruhle, Laks VS Lakshmanan, and Ahmed Hassan Awadallah · 2024
Cited alongside, same era.
Xgrammar: Flexible and efficient structured generation engine for large language models
Yixin Dong, Charlie F Ruan, Yaxing Cai, Ruihang Lai, Ziyi Xu, Yilong Zhao, and Tianqi Chen · 2024
Cited alongside, same era.
Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al · 2024
Cited alongside, same era.
Acc-debate: An actor-critic approach to multi-agent debate, 2024
Andrew Estornell, Jean-Francois Ton, Yuanshun Yao, and Yang Liu · 2024
Cited alongside, same era.
Meta reasoning for large language models
Peizhong Gao, Ao Xie, Shaoguang Mao, Wenshan Wu, Yan Xia, Haipeng Mi, and Furu Wei · 2024
Cited alongside, same era.
Improving llm reasoning with multi-agent tree-of-thought validator agent, 2024
Fatemeh Haji, Mazal Bethany, Maryam Tabar, Jason Chiang, Anthony Rios, and Peyman Najafirad · 2024
Cited alongside, same era.
An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, and Zhenru Zhang · 2024
Later among the works it cites.
Language models are super mario: Absorbing abilities from homologous models as a free lunch
Le Yu, Bowen Yu, Haiyang Yu, Fei Huang, and Yongbin Li · 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
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Marco-o1: Towards open reasoning models for open-ended solutions, 2024
Yu Zhao, Huifeng Yin, Bo Zeng, Hao Wang, Tianqi Shi, Chenyang Lyu, Longyue Wang, Weihua Luo, and Kaifu Zhang · 2024
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Archer: Training language model agents via hierarchical multi-turn rl, 2024
Yifei Zhou, Andrea Zanette, Jiayi Pan, Sergey Levine, and Aviral Kumar · 2024
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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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Gemini flash thinking, 2025
Google DeepMind · 2025
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Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025
DeepSeek-AI, Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Han Bao, Hanwei Xu, Haocheng Wang, Honghui Ding, Huajian Xin, Huazuo Gao, Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jiawei Wang, Jingchang Chen, Jingyang Yuan, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang, Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpan Huang, Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang, Shuiping Yu, Shunfeng Zhou, Shuting Pan, S. S. Li, Shuang Zhou, Shaoqing Wu, Shengfeng Ye, Tao Yun, Tian Pei, Tianyu Sun, T. Wang, Wangding Zeng, Wanjia Zhao, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, W. L. Xiao, Wei An, Xiaodong Liu, Xiaohan Wang, Xiaokang Chen, Xiaotao Nie, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, X. Q. Li, Xiangyue Jin, Xiaojin Shen, Xiaosha Chen, Xiaowen Sun, Xiaoxiang Wang, Xinnan Song, Xinyi Zhou, Xianzu Wang, Xinxia Shan, Y. K. Li, Y. Q. Wang, Y. X. Wei, Yang Zhang, Yanhong Xu, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Wang, Yi Yu, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Yishi Piao, Yisong Wang, Yixuan Tan, Yiyang Ma, Yiyuan Liu, Yongqiang Guo, Yuan Ou, Yuduan Wang, Yue Gong, Yuheng Zou, Yujia He, Yunfan Xiong, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Y. X. Zhu, Yanhong Xu, Yanping Huang, Yaohui Li, Yi Zheng, Yuchen Zhu, Yunxian Ma, Ying Tang, Yukun Zha, Yuting Yan, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhenda Xie, Zhengyan Zhang, Zhewen Hao, Zhicheng Ma, Zhigang Yan, Zhiyu Wu, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, Zizheng Pan, Zhen Huang, Zhipeng Xu, Zhongyu Zhang, and Zhen Zhang · 2025
Closest in time.
Stp: Self-play llm theorem provers with iterative conjecturing and proving, 2025
Kefan Dong and Tengyu Ma · 2025
Closest in time.
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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Chatllm network: More brains, more intelligence
Rui Hao, Linmei Hu, Weijian Qi, Qingliu Wu, Yirui Zhang, and Liqiang Nie · 2025
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Reinforce++: A simple and efficient approach for aligning large language models
Jian Hu · 2025
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Search-r1: Training llms to reason and leverage search engines with reinforcement learning, 2025
Bowen Jin, Hansi Zeng, Zhenrui Yue, Jinsung Yoon, Sercan Arik, Dong Wang, Hamed Zamani, and Jiawei Han · 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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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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Chanwoo Park, Seungju Han, Xingzhi Guo, Asuman Ozdaglar, Kaiqing Zhang, and Joo-Kyung Kim · 2025
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A roadmap to guide the integration of llms in hierarchical planning
Israel Puerta-Merino, Carlos Núñez-Molina, Pablo Mesejo, and Juan Fernández-Olivares · 2025
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Raise: Reinforenced adaptive instruction selection for large language models, 2025
Lv Qingsong, Yangning Li, Zihua Lan, Zishan Xu, Jiwei Tang, Yinghui Li, Wenhao Jiang, Hai-Tao Zheng, and Philip S. Yu · 2025
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Maohao Shen, Guangtao Zeng, Zhenting Qi, Zhang-Wei Hong, Zhenfang Chen, Wei Lu, Gregory Wornell, Subhro Das, David Cox, and Chuang Gan · 2025
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Multiagent finetuning: Self improvement with diverse reasoning chains, 2025
Vighnesh Subramaniam, Yilun Du, Joshua B. Tenenbaum, Antonio Torralba, Shuang Li, and Igor Mordatch · 2025
Closest in time.
Ragen: Understanding self-evolution in llm agents via multi-turn reinforcement learning, 2025
Zihan Wang, Kangrui Wang, Qineng Wang, Pingyue Zhang, Linjie Li, Zhengyuan Yang, Kefan Yu, Minh Nhat Nguyen, Licheng Liu, Eli Gottlieb, Monica Lam, Yiping Lu, Kyunghyun Cho, Jiajun Wu, Li Fei-Fei, Lijuan Wang, Yejin Choi, and Manling Li · 2025
Closest in time.
Towards system 2 reasoning in llms: Learning how to think with meta chain-of-though
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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Towards large reasoning models: A survey of reinforced reasoning with large language models
Fengli Xu, Qianyue Hao, Zefang Zong, Jingwei Wang, Yunke Zhang, Jingyi Wang, Xiaochong Lan, Jiahui Gong, Tianjian Ouyang, Fanjin Meng, et al · 2025
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Reasonflux: Hierarchical llm reasoning via scaling thought templates
Ling Yang, Zhaochen Yu, Bin Cui, and Mengdi Wang · 2025
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Dapo: An open-source llm reinforcement learning system at scale, 2025
Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Tiantian Fan, Gaohong Liu, Lingjun Liu, Xin Liu, Haibin Lin, Zhiqi Lin, Bole Ma, Guangming Sheng, Yuxuan Tong, Chi Zhang, Mofan Zhang, Wang Zhang, Hang Zhu, Jinhua Zhu, Jiaze Chen, Jiangjie Chen, Chengyi Wang, Hongli Yu, Weinan Dai, Yuxuan Song, Xiangpeng Wei, Hao Zhou, Jingjing Liu, Wei-Ying Ma, Ya-Qin Zhang, Lin Yan, Mu Qiao, Yonghui Wu, and Mingxuan Wang · 2025
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Simplerl-zoo: Investigating and taming zero reinforcement learning for open base models in the wild, 2025
Weihao Zeng, Yuzhen Huang, Qian Liu, Wei Liu, Keqing He, Zejun Ma, and Junxian He · 2025
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Echo chamber: Rl post-training amplifies behaviors learned in pretraining, 2025
Rosie Zhao, Alexandru Meterez, Sham Kakade, Cengiz Pehlevan, Samy Jelassi, and Eran Malach · 2025
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