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Existing methods to enhance the reasoning capability of large language models predominantly rely on supervised fine-tuning (SFT) followed by reinforcement learning (RL) on reasoning-specific data.
Semi-supervised learning by entropy minimization
Yves Grandvalet and Yoshua Bengio · 2004
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Tent: Fully test-time adaptation by entropy minimization
Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell · 2020
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Entropy minimization in emergent languages
Eugene Kharitonov, Rahma Chaabouni, Diane Bouchacourt, and Marco Baroni · 2020
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Trl: Transformer reinforcement learning
Leandro von Werra, Younes Belkada, Lewis Tunstall, Edward Beeching, Tristan Thrush, Nathan Lambert, Shengyi Huang, Kashif Rasul, and Quentin Gallouédec · 2020
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Large language models can self-improve
Jiaxin Huang, Shixiang Shane Gu, Le Hou, Yuexin Wu, Xuezhi Wang, Hongkun Yu, and Jiawei Han · 2022
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Prioritized training on points that are learnable, worth learning, and not yet learnt
Sören Mindermann, Jan M Brauner, Muhammed T Razzak, Mrinank Sharma, Andreas Kirsch, Winnie Xu, Benedikt Höltgen, Aidan N Gomez, Adrien Morisot, Sebastian Farquhar, et al · 2022
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Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar · 2023
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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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Deepseek-coder: When the large language model meets programming – the rise of code intelligence, 2024
Dejian Yang Daya Guo, Qihao Zhu · 2024
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Qwen2. 5-math technical report: Toward mathematical expert model via self-improvement
An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, et al · 2024
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Ai models collapse when trained on recursively generated data
Ilia Shumailov, Zakhar Shumaylov, Yiren Zhao, Nicolas Papernot, Ross Anderson, and Yarin Gal · 2024
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Preference optimization for reasoning with pseudo feedback
Fangkai Jiao, Geyang Guo, Xingxing Zhang, Nancy F Chen, Shafiq Joty, and Furu Wei · 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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Large language models can self-improve at web agent tasks
Ajay Patel, Markus Hofmarcher, Claudiu Leoveanu-Condrei, Marius-Constantin Dinu, Chris Callison-Burch, and Sepp Hochreiter · 2024
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Large language models can self-improve in long-context reasoning
Siheng Li, Cheng Yang, Zesen Cheng, Lemao Liu, Mo Yu, Yujiu Yang, and Wai Lam · 2024
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Self-rewarding language models, 2024
Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Xian Li, Sainbayar Sukhbaatar, Jing Xu, and Jason Weston · 2024
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Entropy-regularized token-level policy optimization for large language models
Muning Wen, Cheng Deng, Jun Wang, Weinan Zhang, and Ying Wen · 2024
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Training large language models for reasoning through reverse curriculum reinforcement learning
Zhiheng Xi, Wenxiang Chen, Boyang Hong, Senjie Jin, Rui Zheng, Wei He, Yiwen Ding, Shichun Liu, Xin Guo, Junzhe Wang, et al · 2024
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Come: Test-time adaption by conservatively minimizing entropy
rstar-math: Small llms can master math reasoning with self-evolved deep thinking
Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang · 2025
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Process reinforcement through implicit rewards
Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, et al · 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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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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Qingyang Zhang, Yatao Bian, Xinke Kong, Peilin Zhao, and Changqing Zhang · 2024
Cited alongside, same era.
Detecting hallucinations in large language models using semantic entropy
Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal · 2024
Cited alongside, same era.
The entropy enigma: Success and failure of entropy minimization
Ori Press, Ravid Shwartz-Ziv, Yann LeCun, and Matthias Bethge · 2024
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Numinamath
Jia LI, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Costa Huang, Kashif Rasul, Longhui Yu, Albert Jiang, Ziju Shen, Zihan Qin, Bin Dong, Li Zhou, Yann Fleureau, Guillaume Lample, and Stanislas Polu · 2024
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Do not think that much for 2+ 3=? on the overthinking of o1-like llms
Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, et al · 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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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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Tulu 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, Yuling Gu, Saumya Malik, Victoria Graf, Jena D. Hwang, Jiangjiang Yang, Ronan Le Bras, Oyvind Tafjord, Chris Wilhelm, Luca Soldaini, Noah A. Smith, Yizhong Wang, Pradeep Dasigi, and Hannaneh Hajishirzi · 2024
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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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CREAM: Consistency regularized self-rewarding language models
Zhaoyang Wang, Weilei He, Zhiyuan Liang, Xuchao Zhang, Chetan Bansal, Ying Wei, Weitong Zhang, and Huaxiu Yao · 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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Open r1: A fully open reproduction of deepseek-r1, January 2025
Hugging Face · 2025
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Online-dpo-r1: Unlocking effective reasoning without the ppo overhead, 2025
Hanning Zhang, Jiarui Yao, Chenlu Ye, Wei Xiong, and Tong Zhang · 2025
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Naturalreasoning: Reasoning in the wild with 2.8 m challenging questions
Weizhe Yuan, Jane Yu, Song Jiang, Karthik Padthe, Yang Li, Dong Wang, Ilia Kulikov, Kyunghyun Cho, Yuandong Tian, Jason E Weston, et al · 2025
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Estimating llm uncertainty with logits
Huan Ma, Jingdong Chen, Guangyu Wang, and Changqing Zhang · 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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Open-reasoner-zero: An open source approach to scaling reinforcement learning on the base model
Jingcheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, and Heung-Yeung Shum Xiangyu Zhang · 2025
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Does reinforcement learning really incentivize reasoning capacity in llms beyond the base model?
Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Shiji Song, and Gao Huang · 2025
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