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DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training.
Measuring massive multitask language understanding
Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt · 2020
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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
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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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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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Generative ai for math: Abel
Ethan Chern, Haoyang Zou, Xuefeng Li, Jiewen Hu, Kehua Feng, Junlong Li, and Pengfei Liu · 2023
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Albert Q. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Florian Bressand, Gianna Lengyel, Guillaume Lample, Lucile Saulnier, Lélio Renard Lavaud, Marie-Anne Lachaux, Pierre Stock, Teven Le Scao, Thibaut Lavril, Thomas Wang, Timothée Lacroix, and William El Sayed · 2023
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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 · 2023
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Beyond human data: Scaling self-training for problem-solving with language models
Avi Singh, John D Co-Reyes, Rishabh Agarwal, Ankesh Anand, Piyush Patil, Xavier Garcia, Peter J Liu, James Harrison, Jaehoon Lee, Kelvin Xu, et al · 2023
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Math-shepherd: Verify and reinforce llms step-by-step without human annotations
Peiyi Wang, Lei Li, Zhihong Shao, RX Xu, Damai Dai, Yifei Li, Deli Chen, Yu Wu, and Zhifang Sui · 2023
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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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Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al · 2024
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Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, et al · 2024
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Aaron Hurst, Adam Lerer, Adam P Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, et al · 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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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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An empirical study on eliciting and improving r1-like reasoning models
Zhipeng Chen, Yingqian Min, Beichen Zhang, Jie Chen, Jinhao Jiang, Daixuan Cheng, Wayne Xin Zhao, Zheng Liu, Xu Miao, Yang Lu, et al · 2025
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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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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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Preserving diversity in supervised fine-tuning of large language models
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Understanding r1-zero-like training: A critical perspective
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Wei Liu, Junlong Li, Xiwen Zhang, Fan Zhou, Yu Cheng, and Junxian He · 2024
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Gpqa: A graduate-level google-proof q&a benchmark
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Deepseekmath: Pushing the limits of mathematical reasoning in open language models
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Hybridflow: A flexible and efficient rlhf framework
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Easy-to-hard generalization: Scalable alignment beyond human supervision
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Planning in natural language improves llm search for code generation
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LlamaFactory: Unified efficient fine-tuning of 100+ language models
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Instruction-following evaluation for large language models
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Deepscaler: Surpassing o1-preview with a 1.5b model by scaling rl, 2025
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