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Recent large language models (LLMs) have demonstrated strong reasoning capabilities that benefits from online reinforcement learning (RL).
Simple statistical gradient-following algorithms for connectionist reinforcement learning
Ronald J Williams · 1992
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Decoupled weight decay regularization
Ilya Loshchilov and Frank Hutter · 2017
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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BERT: Pre-training of deep bidirectional transformers for language understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2019
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Denoising diffusion probabilistic models
Jonathan Ho, Ajay Jain, and Pieter Abbeel · 2020
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Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2020
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Trl: Transformer reinforcement learning
Leandro von Werra, Younes Belkada, Lewis Tunstall, Edward Beeching, Tristan Thrush, Nathan Lambert, Shengyi Huang, Kashif Rasul, and Quentin Gallouédec · 2020
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Evaluating large language models trained on code
Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde De Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, et al · 2021
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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
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt · 2021
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Training a helpful and harmless assistant with reinforcement learning from human feedback
Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, et al · 2022
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Training language models to follow instructions with human feedback
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al · 2022
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Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al · 2023
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Likelihood-based diffusion language models
Ishaan Gulrajani and Tatsunori B Hashimoto · 2023
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Ziniu Li, Tian Xu, Yushun Zhang, Zhihang Lin, Yang Yu, Ruoyu Sun, and Zhi-Quan Luo · 2023
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Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe · 2023
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Openwebmath: An open dataset of high-quality mathematical web text, 2023
Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba · 2023
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Metamath: Bootstrap your own mathematical questions for large language models
Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu · 2023
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Lima: less is more for alignment
Chunting Zhou, Pengfei Liu, Puxin Xu, Srini Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, et al · 2023
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Back to basics: Revisiting reinforce style optimization for learning from human feedback in llms
Arash Ahmadian, Chris Cremer, Matthias Gallé, Marzieh Fadaee, Julia Kreutzer, Olivier Pietquin, Ahmet Üstün, and Sara Hooker · 2024
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FlashAttention-2: Faster attention with better parallelism and work partitioning
Tri Dao · 2024
Block diffusion: Interpolating between autoregressive and diffusion language models
Marianne Arriola, Aaron Gokaslan, Justin T Chiu, Zhihan Yang, Zhixuan Qi, Jiaqi Han, Subham Sekhar Sahoo, and Volodymyr Kuleshov · 2025
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Sft memorizes, rl generalizes: A comparative study of foundation model post-training
Tianzhe Chu, Yuexiang Zhai, Jihan Yang, Shengbang Tong, Saining Xie, Dale Schuurmans, Quoc V Le, Sergey Levine, and Yi Ma · 2025
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Scaling diffusion language models via adaptation from autoregressive models
Shansan Gong, Shivam Agarwal, Yizhe Zhang, Jiacheng Ye, Lin Zheng, Mukai Li, Chenxin An, Peilin Zhao, Wei Bi, Jiawei Han, Hao Peng, and Lingpeng Kong · 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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The llama 3 herd of models, 2024
Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, Archie Sravankumar, Artem Korenev, Arthur Hinsvark, Arun Rao, Aston Zhang, Aurelien Rodriguez, Austen Gregerson, et al · 2024
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Rlef: Grounding code llms in execution feedback with reinforcement learning
Jonas Gehring, Kunhao Zheng, Jade Copet, Vegard Mella, Quentin Carbonneaux, Taco Cohen, and Gabriel Synnaeve · 2024
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Numinamath
Jia LI, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Costa Huang, Kashif Rasul, Longhui Yu, Albert Jiang, Ziju Shen, Zihan Qin, Bin Dong, Li Zhou, Yann Fleureau, Guillaume Lample, and Stanislas Polu · 2024
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Scaling up masked diffusion models on text
Shen Nie, Fengqi Zhu, Chao Du, Tianyu Pang, Qian Liu, Guangtao Zeng, Min Lin, and Chongxuan Li · 2024
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Learning to reason with llms, September 2024
OpenAI · 2024
Cited alongside, same era.
Your absorbing discrete diffusion secretly models the conditional distributions of clean data
Jingyang Ou, Shen Nie, Kaiwen Xue, Fengqi Zhu, Jiacheng Sun, Zhenguo Li, and Chongxuan Li · 2024
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Simple and effective masked diffusion language models
Subham Sekhar Sahoo, Marianne Arriola, Aaron Gokaslan, Edgar Mariano Marroquin, Alexander M Rush, Yair Schiff, Justin T Chiu, and Volodymyr Kuleshov · 2024
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Mercury: Ultra-fast language models based on diffusion
Inception Labs, Samar Khanna, Siddhant Kharbanda, Shufan Li, Harshit Varma, Eric Wang, Sawyer Birnbaum, Ziyang Luo, Yanis Miraoui, Akash Palrecha, Stefano Ermon, Aditya Grover, and Volodymyr Kuleshov · 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
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Dynamic scaling of unit tests for code reward modeling
Zeyao Ma, Xiaokang Zhang, Jing Zhang, Jifan Yu, Sijia Luo, and Jie Tang · 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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Large language diffusion models, 2025
Shen Nie, Fengqi Zhu, Zebin You, Xiaolu Zhang, Jingyang Ou, Jun Hu, Jun Zhou, Yankai Lin, Ji-Rong Wen, and Chongxuan Li · 2025
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Tinyzero
Jiayi Pan, Junjie Zhang, Xingyao Wang, Lifan Yuan, Hao Peng, and Alane Suhr · 2025
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Kimi k1. 5: Scaling reinforcement learning with llms
Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, et al · 2025
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Open Thoughts
OpenThoughts Team · 2025
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Kodcode: A diverse, challenging, and verifiable synthetic dataset for coding
Zhangchen Xu, Yang Liu, Yueqin Yin, Mingyuan Zhou, and Radha Poovendran · 2025
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Dream 7b, 2025a
Jiacheng Ye, Zhihui Xie, Lin Zheng, Jiahui Gao, Zirui Wu, Xin Jiang, Zhenguo Li, and Lingpeng Kong · 2025
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Fine-tuning discrete diffusion models with policy gradient methods
Oussama Zekri and Nicolas Boullé · 2025
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