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Intermediate token generation (ITG), where a model produces output before the solution, has been proposed as a method to improve the performance of language models on reasoning tasks.
On the shortest spanning subtree of a graph and the traveling salesman problem
Joseph B Kruskal · 1956
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Depth-first search and linear graph algorithms
Robert Tarjan · 1972
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Generating random spanning trees more quickly than the cover time
David Bruce Wilson · 1996
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Show your work: Scratchpads for intermediate computation with language models
Maxwell Nye, Anders Johan Andreassen, Guy Gur-Ari, Henryk Michalewski, Jacob Austin, David Bieber, David Dohan, Aitor Lewkowycz, Maarten Bosma, David Luan, et al · 2021
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Grokking: Generalization beyond overfitting on small algorithmic datasets
Alethea Power, Yuri Burda, Harri Edwards, Igor Babuschkin, and Vedant Misra · 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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Chain of thought imitation with procedure cloning
Mengjiao Sherry Yang, Dale Schuurmans, Pieter Abbeel, and Ofir Nachum · 2022
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Star: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman · 2022
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Automatic chain of thought prompting in large language models
Zhuosheng Zhang, Aston Zhang, Mu Li, and Alex Smola · 2022
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Sparks of artificial general intelligence: Early experiments with gpt-4, 2023
Sébastien Bubeck, Varun Chadrasekaran, Ronen Eldan, Johannes Gehrke, Eric Horvitz, Ece Kamar, Peter Lee, Yin Tat Lee, Yuanzhi Li, Scott Lundberg, et al · 2023
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Minillm: Knowledge distillation of large language models
Yuxian Gu, Li Dong, Furu Wei, and Minlie Huang · 2023
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Cheng-Yu Hsieh, Chun-Liang Li, Chih-Kuan Yeh, Hootan Nakhost, Yasuhisa Fujii, Alexander Ratner, Ranjay Krishna, Chen-Yu Lee, and Tomas Pfister · 2023
Earlier work this paper cites.
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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Hao Sun · 2023
Cited alongside, same era.
The clock and the pizza: Two stories in mechanistic explanation of neural networks
Ziqian Zhong, Ziming Liu, Max Tegmark, and Jacob Andreas · 2023
Cited alongside, same era.
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
Cited alongside, same era.
T \ \backslash " ulu 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, et al · 2024
Cited alongside, same era.
Beyond a*: Better planning with transformers via search dynamics bootstrapping
Verithinker: Learning to verify makes reasoning model efficient
Zigeng Chen, Xinyin Ma, Gongfan Fang, Ruonan Yu, and Xinchao Wang · 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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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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Don’t overthink it. preferring shorter thinking chains for improved llm reasoning
Michael Hassid, Gabriele Synnaeve, Yossi Adi, and Roy Schwartz · 2025
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Lucas Lehnert, Sainbayar Sukhbaatar, DiJia Su, Qinqing Zheng, Paul Mcvay, Michael Rabbat, and Yuandong Tian · 2024
Cited alongside, same era.
Can transformers reason logically? a study in sat solving
Leyan Pan, Vijay Ganesh, Jacob Abernethy, Chris Esposo, and Wenke Lee · 2024
Cited alongside, same era.
Let’s think dot by dot: Hidden computation in transformer language models
Jacob Pfau, William Merrill, and Samuel R Bowman · 2024
Cited alongside, same era.
Qwen Team · 2024
Cited alongside, same era.
Dualformer: Controllable fast and slow thinking by learning with randomized reasoning traces
DiJia Su, Sainbayar Sukhbaatar, Michael Rabbat, Yuandong Tian, and Qinqing Zheng · 2024
Cited alongside, same era.
Grokked transformers are implicit reasoners: A mechanistic journey to the edge of generalization
Boshi Wang, Xiang Yue, Yu Su, and Huan Sun · 2024
Cited alongside, same era.
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
Cited alongside, same era.
Training language models to reason efficiently, 2025
Daman Arora and Andrea Zanette · 2025
Cited alongside, same era.
Dacheng Li, Shiyi Cao, Tyler Griggs, Shu Liu, Xiangxi Mo, Eric Tang, Sumanth Hegde, Kourosh Hakhamaneshi, Shishir G Patil, Matei Zaharia, et al · 2025
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Aalc: Large language model efficient reasoning via adaptive accuracy-length control
Ruosen Li, Ziming Luo, Quan Zhang, Ruochen Li, Ben Zhou, Ali Payani, and Xinya Du · 2025
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Thought manipulation: External thought can be efficient for large reasoning models
Yule Liu, Jingyi Zheng, Zhen Sun, Zifan Peng, Wenhan Dong, Zeyang Sha, Shiwen Cui, Weiqiang Wang, and Xinlei He · 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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Sample more to think less: Group filtered policy optimization for concise reasoning, 2025
Vaishnavi Shrivastava, Ahmed Awadallah, Vidhisha Balachandran, Shivam Garg, Harkirat Behl, and Dimitris Papailiopoulos · 2025
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Understanding aha moments: from external observations to internal mechanisms
Shu Yang, Junchao Wu, Xin Chen, Yunze Xiao, Xinyi Yang, Derek F Wong, and Di Wang · 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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Efficient rl training for reasoning models via length-aware optimization
Danlong Yuan, Tian Xie, Shaohan Huang, Zhuocheng Gong, Huishuai Zhang, Chong Luo, Furu Wei, and Dongyan Zhao · 2025
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R1-zero’s" aha moment" in visual reasoning on a 2b non-sft model
Hengguang Zhou, Xirui Li, Ruochen Wang, Minhao Cheng, Tianyi Zhou, and Cho-Jui Hsieh · 2025
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