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Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks.
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
Earlier work this paper cites.
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
Earlier work this paper cites.
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
Earlier work this paper cites.
Star: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman · 2022
Earlier work this paper cites.
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
Earlier work this paper cites.
Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe · 2023
Earlier work this paper cites.
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 · 2023
Earlier work this paper cites.
Code llama: Open foundation models for code
Baptiste Roziere, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Romain Sauvestre, Tal Remez, et al · 2023
Earlier work this paper cites.
Self-consistency improves chain of thought reasoning in language models
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou · 2023
Earlier work this paper cites.
Tree of thoughts: Deliberate problem solving with large language models
Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik R Narasimhan · 2023
Earlier work this paper cites.
Automatic chain of thought prompting in large language models
Zhuosheng Zhang, Aston Zhang, Mu Li, and Alex Smola · 2023
Earlier work this paper cites.
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
Earlier work this paper cites.
Stream of search (sos): Learning to search in language
Kanishk Gandhi, Denise Lee, Gabriel Grand, Muxin Liu, Winson Cheng, Archit Sharma, and Noah D Goodman · 2024
Earlier work this paper cites.
Omni-math: A universal olympiad level mathematic benchmark for large language models
Bofei Gao, Feifan Song, Zhe Yang, Zefan Cai, Yibo Miao, Qingxiu Dong, Lei Li, Chenghao Ma, Liang Chen, Runxin Xu, et al · 2024
Earlier work this paper cites.
Frontiermath: A benchmark for evaluating advanced mathematical reasoning in ai
Elliot Glazer, Ege Erdil, Tamay Besiroglu, Diego Chicharro, Evan Chen, Alex Gunning, Caroline Falkman Olsson, Jean-Stanislas Denain, Anson Ho, Emily de Oliveira Santos, et al · 2024
Earlier work this paper cites.
Zhen Huang, Haoyang Zou, Xuefeng Li, Yixiu Liu, Yuxiang Zheng, Ethan Chern, Shijie Xia, Yiwei Qin, Weizhe Yuan, and Pengfei Liu · 2024
Cited alongside, same era.
Step-dpo: Step-wise preference optimization for long-chain reasoning of llms
Xin Lai, Zhuotao Tian, Yukang Chen, Senqiao Yang, Xiangru Peng, and Jiaya Jia · 2024
Cited alongside, same era.
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
Cited alongside, same era.
Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al · 2024
Cited alongside, same era.
Di Zhang, Xiaoshui Huang, Dongzhan Zhou, Yuqiang Li, and Wanli Ouyang · 2024
Later among the works it cites.
Marco-o1: Towards open reasoning models for open-ended solutions
Yu Zhao, Huifeng Yin, Bo Zeng, Hao Wang, Tianqi Shi, Chenyang Lyu, Longyue Wang, Weihua Luo, and Kaifu Zhang · 2024
Later among the works it cites.
Process reinforcement through implicit rewards, 2025
Ganqu Cui, Lifan Yuan, Zefan Wang, Hanbin Wang, Wendi Li, Bingxiang He, Yuchen Fan, Tianyu Yu, Qixin Xu, Weize Chen, Jiarui Yuan, Huayu Chen, Kaiyan Zhang, Xingtai Lv, Shuo Wang, Yuan Yao, Hao Peng, Yu Cheng, Zhiyuan Liu, Maosong Sun, Bowen Zhou, and Ning Ding · 2025
Closest in time.
Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 1 2025
DeepSeek · 2025
Closest in time.
rstar-math: Small llms can master math reasoning with self-evolved deep thinking
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Introducing llama 3.1: Our most capable models to date
MetaAI · 2024
Cited alongside, same era.
Imitate, explore, and self-improve: A reproduction report on slow-thinking reasoning systems
Yingqian Min, Zhipeng Chen, Jinhao Jiang, Jie Chen, Jia Deng, Yiwen Hu, Yiru Tang, Jiapeng Wang, Xiaoxue Cheng, Huatong Song, et al · 2024
Cited alongside, same era.
Qwen2. 5: A party of foundation models
Qwen Team · 2024
Cited alongside, same era.
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 · 2024
Cited alongside, same era.
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.
Skywork-o1 open series
Skywork-o1 · 2024
Cited alongside, same era.
Scaling llm test-time compute optimally can be more effective than scaling model parameters
Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar · 2024
Cited alongside, same era.
An empirical analysis of compute-optimal inference for problem-solving with language models
Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang · 2024
Cited alongside, same era.
Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang · 2025
Closest in time.
Kimi k1.5: Scaling reinforcement learning with llms, 1 2025
Kimi Team · 2025
Closest in time.
Star-r1: Spatial transformation reasoning by reinforcing multimodal llms
Zongzhao Li, Zongyang Ma, Mingze Li, Songyou Li, Yu Rong, Tingyang Xu, Ziqi Zhang, Deli Zhao, and Wenbing Huang · 2025
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O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning
Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao · 2025
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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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Sky-t1: Train your own o1 preview model within $450
NovaSky Team · 2025
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Qwq-32b: Embracing the power of reinforcement learning, November 2025
Qwen Team · 2025
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Tinyr1-32b-preview: Boosting accuracy with branch-merge distillation
Lin Sun, Guangxiang Zhao, Xiaoqi Jian, Yuhan Wu, Weihong Lin, Yongfu Zhu, Linglin Zhang, Jinzhu Wu, Junfeng Ran, Sai-er Hu, et al · 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
Closest in time.
Deepcritic: Deliberate critique with large language models
Wenkai Yang, Jingwen Chen, Yankai Lin, and Ji-Rong Wen · 2025
Closest in time.