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Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities.
Isabelle: A Generic Theorem Prover
Lawrence C. Paulson. 1994 · 1994
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Generative language modeling for automated theorem proving
Stanislas Polu and Ilya Sutskever. 2020 · 2009
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The lean theorem prover (system description)
Leonardo Mendonça de Moura, Soonho Kong, Jeremy Avigad, Floris van Doorn, and Jakob von Raumer. 2015 · 2015
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Thinking fast and slow with deep learning and tree search
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017 · 2017
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Mastering chess and shogi by self-play with a general reinforcement learning algorithm
David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. 2017 · 2017
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Minif2f: a cross-system benchmark for formal olympiad-level mathematics
Kunhao Zheng, Jesse Michael Han, and Stanislas Polu. 2021 · 2021
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Hypertree proof search for neural theorem proving
Guillaume Lample, Marie-Anne Lachaux, Thibaut Lavril, Xavier Martinet, Amaury Hayat, Gabriel Ebner, Aurélien Rodriguez, and Timothée Lacroix. 2022 · 2022
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Formal mathematics statement curriculum learning
Stanislas Polu, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Igor Babuschkin, and Ilya Sutskever. 2022 · 2022
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Draft, sketch, and prove: Guiding formal theorem provers with informal proofs
Albert Q. Jiang, Sean Welleck, Jin Peng Zhou, Wenda Li, Jiacheng Liu, Mateja Jamnik, Timothée Lacroix, Yuhuai Wu, and Guillaume Lample. 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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Inference-aware fine-tuning for best-of-n sampling in large language models
Yinlam Chow, Guy Tennenholtz, Izzeddin Gur, Vincent Zhuang, Bo Dai, Sridhar Thiagarajan, Craig Boutilier, Rishabh Agarwal, Aviral Kumar, and Aleksandra Faust. 2024 · 2024
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ABEL: Sample efficient online reinforcement learning for neural theorem proving
Fabian Gloeckle, Jannis Limperg, Gabriel Synnaeve, and Amaury Hayat. 2024 · 2024
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minictx: Neural theorem proving with (long-) contexts
Jiewen Hu, Thomas Zhu, and Sean Welleck. 2024 · 2024
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OpenAI, :, Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, Alex Iftimie, Alex Karpenko, Alex Tachard Passos, Alexander Neitz, Alexander Prokofiev, Alexander Wei, Allison Tam, and 244 others. 2024 · 2024
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Weight ensembling improves reasoning in language models
Xingyu Dang, Christina Baek, Kaiyue Wen, Zico Kolter, and Aditi Raghunathan. 2025 · 2025
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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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Z. Z. Ren, Zhihong Shao, Junxiao Song, Huajian Xin, Haocheng Wang, Wanjia Zhao, Liyue Zhang, Zhe Fu, Qihao Zhu, Dejian Yang, Z. F. Wu, Zhibin Gou, Shirong Ma, Hongxuan Tang, Yuxuan Liu, Wenjun Gao, Daya Guo, and Chong Ruan. 2025 · 2025
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Optimizing language models for inference time objectives using reinforcement learning
Yunhao Tang, Kunhao Zheng, Gabriel Synnaeve, and Rémi Munos. 2025 · 2025
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Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, and Daya Guo. 2024 · 2024
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Hybridflow: A flexible and efficient rlhf framework
Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang, Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. 2024 · 2024
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Gpt-accelera: Simple and efficient pytorch-native transformer training and inference (batched)
Zhiqing Sun. 2024 · 2024
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Zijian Wu, Suozhi Huang, Zhejian Zhou, Huaiyuan Ying, Jiayu Wang, Dahua Lin, and Kai Chen. 2024 · 2024
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Huajian Xin, Z. Z. Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du, Wenjun Gao, Qihao Zhu, Dejian Yang, Zhibin Gou, Z. F. Wu, Fuli Luo, and Chong Ruan. 2024 · 2024
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Formal mathematical reasoning: A new frontier in ai
Kaiyu Yang, Gabriel Poesia, Jingxuan He, Wenda Li, Kristin Lauter, Swarat Chaudhuri, and Dawn Song. 2024 · 2024
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Lean workbook: A large-scale lean problem set formalized from natural language math problems
Huaiyuan Ying, Zijian Wu, Yihan Geng, Jiayu Wang, Dahua Lin, and Kai Chen. 2024 · 2024
Cited alongside, same era.
Lean-star: Learning to interleave thinking and proving
Haohan Lin, Zhiqing Sun, Sean Welleck, and Yiming Yang. 2025a
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Machine-assisted proof
Terence Tao. 2025 · 2025
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Kimina-prover preview: Towards large formal reasoning models with reinforcement learning
Haiming Wang, Mert Unsal, Xiaohan Lin, Mantas Baksys, Junqi Liu, Marco Dos Santos, Flood Sung, Marina Vinyes, Zhenzhe Ying, Zekai Zhu, Jianqiao Lu, Hugues de Saxcé, Bolton Bailey, Chendong Song, Chenjun Xiao, Dehao Zhang, Ebony Zhang, Frederick Pu, Han Zhu, and 21 others. 2025 · 2025
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Bfs-prover: Scalable best-first tree search for llm-based automatic theorem proving
Ran Xin, Chenguang Xi, Jie Yang, Feng Chen, Hang Wu, Xia Xiao, Yifan Sun, Shen Zheng, and Kai Shen. 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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Does reinforcement learning really incentivize reasoning capacity in llms beyond the base model?
Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, and Gao Huang. 2025 · 2025
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Leanabell-prover: Posttraining scaling in formal reasoning
Jingyuan Zhang, Qi Wang, Xingguang Ji, Yahui Liu, Yang Yue, Fuzheng Zhang, Di Zhang, Guorui Zhou, and Kun Gai. 2025 · 2025
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