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Mathematical reasoning represents a critical frontier in advancing large language models (LLMs).
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
Earlier work this paper cites.
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
Earlier work this paper cites.
Efficient training of language models to fill in the middle
Mohammad Bavarian, Heewoo Jun, Nikolas Tezak, John Schulman, Christine McLeavey, Jerry Tworek, and Mark Chen. 2022 · 2022
Earlier work this paper cites.
Training compute-optimal large language models
Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, Tom Hennigan, Eric Noland, Katie Millican, George van den Driessche, Bogdan Damoc, Aurelia Guy, Simon Osindero, Karen Simonyan, Erich Elsen, Jack W. Rae, Oriol Vinyals, and Laurent Sifre. 2022 · 2022
Earlier work this paper cites.
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
Earlier work this paper cites.
Let’s verify step by step
Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. 2023 · 2023
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OpenAI. 2023 · 2023
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Openwebmath: An open dataset of high-quality mathematical web text
Keiran Paster, Marco Dos Santos, Zhangir Azerbayev, and Jimmy Ba. 2023 · 2023
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Chain-of-thought prompting elicits reasoning in large language models
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, and Denny Zhou. 2023 · 2023
Earlier work this paper cites.
Mammoth: Building math generalist models through hybrid instruction tuning
Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. 2023 · 2023
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Language agent tree search unifies reasoning acting and planning in language models
Andy Zhou, Kai Yan, Michal Shlapentokh-Rothman, Haohan Wang, and Yu-Xiong Wang. 2023 · 2023
Earlier work this paper cites.
The llama 3 herd of models
Meta AI. 2024 · 2024
Earlier work this paper cites.
Large language monkeys: Scaling inference compute with repeated sampling
Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V. Le, Christopher Ré, and Azalia Mirhoseini. 2024 · 2024
Earlier work this paper cites.
Alphamath almost zero: Process supervision without process
Guoxin Chen, Minpeng Liao, Chengxi Li, and Kai Fan. 2024 · 2024
Cited alongside, same era.
Unleashing reasoning capability of llms via scalable question synthesis from scratch
Yuyang Ding, Xinyu Shi, Xiaobo Liang, Juntao Li, Qiaoming Zhu, and Min Zhang. 2024 · 2024
Cited alongside, same era.
Mathodyssey: Benchmarking mathematical problem-solving skills in large language models using odyssey math data
Meng Fang, Xiangpeng Wan, Fei Lu, Fei Xing, and Kai Zou. 2024 · 2024
Cited alongside, same era.
Alphazero-like tree-search can guide large language model decoding and training
Xidong Feng, Ziyu Wan, Muning Wen, Stephen Marcus McAleer, Ying Wen, Weinan Zhang, and Jun Wang. 2024 · 2024
Cited alongside, same era.
Omni-math: A universal olympiad level mathematic benchmark for large language models
Bofei Gao, Feifan Song, Zhe Yang, Zefan Cai, Yibo Miao, Qingxiu Dong, Lei Li, Chenghao Ma, Liang Chen, Runxin Xu, et al. 2024 · 2024
Math-shepherd: Verify and reinforce llms step-by-step without human annotations
Peiyi Wang, Lei Li, Zhihong Shao, R. X. Xu, Damai Dai, Yifei Li, Deli Chen, Y. Wu, and Zhifang Sui. 2024 · 2024
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Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. 2024 · 2024
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S$^3$c-math: Spontaneous step-level self-correction makes large language models better mathematical reasoners
Yuchen Yan, Jin Jiang, Yang Liu, Yixin Cao, Xin Xu, Mengdi zhang, Xunliang Cai, and Jian Shao. 2024 · 2024
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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
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Internlm-math: Open math large language models toward verifiable reasoning
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Cited alongside, same era.
Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems
Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, Jie Liu, Lei Qi, Zhiyuan Liu, and Maosong Sun. 2024 · 2024
Cited alongside, same era.
The impact of reasoning step length on large language models
Mingyu Jin, Qinkai Yu, Dong Shu, Haiyan Zhao, Wenyue Hua, Yanda Meng, Yongfeng Zhang, and Mengnan Du. 2024 · 2024
Cited alongside, same era.
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, Bin Dong, Li Zhou, Yann Fleureau, Guillaume Lample, and Stanislas Polu. 2024 · 2024
Cited alongside, same era.
Don’t throw away your value model! generating more preferable text with value-guided monte-carlo tree search decoding
Jiacheng Liu, Andrew Cohen, Ramakanth Pasunuru, Yejin Choi, Hannaneh Hajishirzi, and Asli Celikyilmaz. 2024 · 2024
Cited alongside, same era.
Scaling llm test-time compute optimally can be more effective than scaling model parameters
Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. 2024 · 2024
Cited alongside, same era.
A survey of reasoning with foundation models
Jiankai Sun, Chuanyang Zheng, Enze Xie, Zhengying Liu, Ruihang Chu, Jianing Qiu, Jiaqi Xu, Mingyu Ding, Hongyang Li, Mengzhe Geng, Yue Wu, Wenhai Wang, Junsong Chen, Zhangyue Yin, Xiaozhe Ren, Jie Fu, Junxian He, Wu Yuan, Qi Liu, Xihui Liu, Yu Li, Hao Dong, Yu Cheng, Ming Zhang, Pheng Ann Heng, Jifeng Dai, Ping Luo, Jingdong Wang, Ji-Rong Wen, Xipeng Qiu, Yike Guo, Hui Xiong, Qun Liu, and Zhenguo Li. 2024 · 2024
Cited alongside, same era.
Openmathinstruct-2: Accelerating ai for math with massive open-source instruction data
Shubham Toshniwal, Wei Du, Ivan Moshkov, Branislav Kisacanin, Alexan Ayrapetyan, and Igor Gitman. 2024 · 2024
Cited alongside, same era.
Huaiyuan Ying, Shuo Zhang, Linyang Li, Zhejian Zhou, Yunfan Shao, Zhaoye Fei, Yichuan Ma, Jiawei Hong, Kuikun Liu, Ziyi Wang, Yudong Wang, Zijian Wu, Shuaibin Li, Fengzhe Zhou, Hongwei Liu, Songyang Zhang, Wenwei Zhang, Hang Yan, Xipeng Qiu, Jiayu Wang, Kai Chen, and Dahua Lin. 2024 · 2024
Later among the works it cites.
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. 2024 · 2024
Later among the works it cites.
Autonomous data selection with language models for mathematical texts
Yifan Zhang, Yifan Luo, Yang Yuan, and Andrew Chi-Chih Yao. 2024 · 2024
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Jiuzhang3.0: Efficiently improving mathematical reasoning by training small data synthesis models
Kun Zhou, Beichen Zhang, Jiapeng Wang, Zhipeng Chen, Wayne Xin Zhao, Jing Sha, Zhichao Sheng, Shijin Wang, and Ji-Rong Wen. 2024 · 2024
Later among the works it cites.
Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning
DeepSeek-AI. 2025 · 2025
Closest in time.
rstar-math: Small llms can master math reasoning with self-evolved deep thinking
Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang. 2025 · 2025
Closest in time.
Long Phan, Alice Gatti, Ziwen Han, Nathaniel Li, Josephina Hu, Hugh Zhang, Sean Shi, Michael Choi, Anish Agrawal, Arnav Chopra, et al. 2025 · 2025
Closest in time.
The lessons of developing process reward models in mathematical reasoning
Zhenru Zhang, Chujie Zheng, Yangzhen Wu, Beichen Zhang, Runji Lin, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin. 2025 · 2025
Closest in time.