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Self-taught reasoners (STaRs) enhance the mathematical reasoning abilities of large language models (LLMs) by leveraging self-generated responses for self-training.
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, Christopher Hesse, and John Schulman. 2021 · 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 · 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, Yuhuai Wu, Behnam Neyshabur, Guy Gur-Ari, and Vedant Misra. 2022 · 2022
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STar: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. 2022 · 2022
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Reinforced self-training (rest) for language modeling
Caglar Gulcehre, Tom Le Paine, Srivatsan Srinivasan, Ksenia Konyushkova, Lotte Weerts, Abhishek Sharma, Aditya Siddhant, Alex Ahern, Miaosen Wang, Chenjie Gu, Wolfgang Macherey, Arnaud Doucet, Orhan Firat, and Nando de Freitas. 2023 · 2023
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Large language models can self-improve
Jiaxin Huang, Shixiang Gu, Le Hou, Yuexin Wu, Xuezhi Wang, Hongkun Yu, and Jiawei Han. 2023 · 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 · 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 · 2023
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Scaling relationship on learning mathematical reasoning with large language models
Zheng Yuan, Hongyi Yuan, Chengpeng Li, Guanting Dong, Keming Lu, Chuanqi Tan, Chang Zhou, and Jingren Zhou. 2023 · 2023
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Phi-3 technical report: A highly capable language model locally on your phone
Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, Alon Benhaim, Misha Bilenko, Johan Bjorck, Sébastien Bubeck, Martin Cai, Qin Cai, Vishrav Chaudhary, Dong Chen, Dongdong Chen, and 110 others. 2024 · 2024
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V-STar: Training verifiers for self-taught reasoners
Arian Hosseini, Xingdi Yuan, Nikolay Malkin, Aaron Courville, Alessandro Sordoni, and Rishabh Agarwal. 2024 · 2024
Earlier work this paper cites.
Selective reflection-tuning: Student-selected data recycling for LLM instruction-tuning
Ming Li, Lichang Chen, Jiuhai Chen, Shwai He, Jiuxiang Gu, and Tianyi Zhou. 2024c · 2024
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From quantity to quality: Boosting LLM performance with self-guided data selection for instruction tuning
Ming Li, Yong Zhang, Zhitao Li, Jiuhai Chen, Lichang Chen, Ning Cheng, Jianzong Wang, Tianyi Zhou, and Jing Xiao. 2024d · 2024
Earlier work this paper cites.
SelectIT: Selective instruction tuning for LLMs via uncertainty-aware self-reflection
Liangxin Liu, Xuebo Liu, Derek F. Wong, Dongfang Li, Ziyi Wang, Baotian Hu, and Min Zhang. 2024 · 2024
Cited alongside, same era.
Iterative reasoning preference optimization
Richard Yuanzhe Pang, Weizhe Yuan, He He, Kyunghyun Cho, Sainbayar Sukhbaatar, and Jason Weston. 2024 · 2024
Cited alongside, same era.
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, Aaron T Parisi, Abhishek Kumar, Alexander A Alemi, Alex Rizkowsky, Azade Nova, Ben Adlam, Bernd Bohnet, Gamaleldin Fathy Elsayed, Hanie Sedghi, and 21 others. 2024 · 2024
Cited alongside, same era.
Mathscale: scaling instruction tuning for mathematical reasoning
Zhengyang Tang, Xingxing Zhang, Benyou Wang, and Furu Wei. 2024 · 2024
Cited alongside, same era.
Toward self-improvement of llms via imagination, searching, and criticizing
Ye Tian, Baolin Peng, Linfeng Song, Lifeng Jin, Dian Yu, Lei Han, Haitao Mi, and Dong Yu. 2024 · 2024
Cited alongside, same era.
Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning
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, and 181 others. 2025 · 2025
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Mitigating tail narrowing in LLM self-improvement via socratic-guided sampling
Yiwen Ding, Zhiheng Xi, Wei He, Lizhuoyuan Lizhuoyuan, Yitao Zhai, Shi Xiaowei, Xunliang Cai, Tao Gui, Qi Zhang, and Xuanjing Huang. 2025 · 2025
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Rlae: Reinforcement learning-assisted ensemble for llms
Yuqian Fu, Yuanheng Zhu, Jiajun Chai, Guojun Yin, Wei Lin, Qichao Zhang, and Dongbin Zhao. 2025 · 2025
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From system 1 to system 2: A survey of reasoning large language models
Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi Chen, Yingying Zhang, Fei Yin, Jiahua Dong, Zhiwei Li, Bao-Long Bi, Ling-Rui Mei, Junfeng Fang, Zhijiang Guo, Le Song, and Cheng-Lin Liu. 2025 · 2025
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Dart-math: Difficulty-aware rejection tuning for mathematical problem-solving
Yuxuan Tong, Xiwen Zhang, Rui Wang, Ruidong Wu, and Junxian He. 2024 · 2024
Cited alongside, same era.
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, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, and Zhenru Zhang. 2024 · 2024
Cited alongside, same era.
Self-rewarding language models
Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Xian Li, Sainbayar Sukhbaatar, Jing Xu, and Jason Weston. 2024 · 2024
Cited alongside, same era.
ReST-MCTS*: LLM self-training via process reward guided tree search
Dan Zhang, Sining Zhoubian, Ziniu Hu, Yisong Yue, Yuxiao Dong, and Jie Tang. 2024 · 2024
Cited alongside, same era.
Exploring the learning difficulty of data: Theory and measure
Weiyao Zhu, Ou Wu, Fengguang Su, and Yingjun Deng. 2024 · 2024
Cited alongside, same era.
Online difficulty filtering for reasoning oriented reinforcement learning
Sanghwan Bae, Jiwoo Hong, Min Young Lee, Hanbyul Kim, JeongYeon Nam, and Donghyun Kwak. 2025 · 2025
Cited alongside, same era.
Stop summation: Min-form credit assignment is all process reward model needs for reasoning
Jie Cheng, Ruixi Qiao, Lijun Li, Chao Guo, Junle Wang, Gang Xiong, Yisheng Lv, and Fei-Yue Wang. 2025 · 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 · 2025
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Qwen, :, 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, and 25 others. 2025 · 2025
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Scaling LLM test-time compute optimally can be more effective than scaling parameters for reasoning
Charlie Victor Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. 2025 · 2025
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Enhancing llm reasoning with iterative dpo: A comprehensive empirical investigation
Songjun Tu, Jiahao Lin, Xiangyu Tian, Qichao Zhang, Linjing Li, Yuqian Fu, Nan Xu, Wei He, Xiangyuan Lan, Dongmei Jiang, and Dongbin Zhao. 2025 · 2025
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Progress or regress? self-improvement reversal in post-training
Ting Wu, Xuefeng Li, and Pengfei Liu. 2025 · 2025
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Dast: Difficulty-aware self-training on large language models
Boyang Xue, Qi Zhu, Hongru Wang, Rui Wang, Sheng Wang, Hongling Xu, Fei Mi, Yasheng Wang, Lifeng Shang, Qun Liu, and Kam-Fai Wong. 2025 · 2025
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How is llm reasoning distracted by irrelevant context? an analysis using a controlled benchmark
Minglai Yang, Ethan Huang, Liang Zhang, Mihai Surdeanu, William Wang, and Liangming Pan. 2025 · 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, Haibin Lin, Zhiqi Lin, Bole Ma, Guangming Sheng, Yuxuan Tong, Chi Zhang, Mofan Zhang, Wang Zhang, Hang Zhu, and 16 others. 2025 · 2025
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