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Mathematical reasoning tasks have become prominent benchmarks for assessing the reasoning capabilities of LLMs, especially with reinforcement learning (RL) methods such as GRPO showing significant performance gains.
MathQA: Towards interpretable math word problem solving with operation-based formalisms
Aida Amini, Saadia Gabriel, Peter Lin, Rik Koncel-Kedziorski, Yejin Choi, and Hannaneh Hajishirzi · 1905
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Huggingface’s transformers: State-of-the-art natural language processing, 2020
Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush · 1910
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Natural language input computer problem solving system
Daniel Bobrow · 1964
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Why g matters: The complexity of everyday life
Linda S Gottfredson · 1997
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High-stakes testing and curricular control: A qualitative metasynthesis
Wayne Au · 2007
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High stakes testing in higher education and employment: appraising the evidence for validity and fairness
Paul R Sackett, Matthew J Borneman, and Brian S Connelly · 2008
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Learning to summarize from human feedback
Nisan Stiennon, Long Ouyang, Jeff Wu, Daniel M Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul Christiano · 2009
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Homo heuristicus: Why biased minds make better inferences
Gerd Gigerenzer and Henry Brighton · 2011
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Thinking, Fast and Slow
Daniel Kahneman · 2011
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MAWPS: A math word problem repository
Rik Koncel-Kedziorski, Subhro Roy, Aida Amini, Nate Kushman, and Hannaneh Hajishirzi · 2016
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Deep neural solver for math word problems
Yan Wang, Xiaojiang Liu, and Shuming Shi · 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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Mastering chess and shogi by self-play with a general reinforcement learning algorithm, 2017
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
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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, Christopher Hesse, and John Schulman · 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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MiniF2F: a cross-system benchmark for formal olympiad-level mathematics
Kunhao Zheng, Jesse Michael Han, and Stanislas Polu · 2021
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NaturalProofs: Mathematical theorem proving in natural language
Sean Welleck, Jiacheng Liu, Ronan Le Bras, Hannaneh Hajishirzi, Yejin Choi, and Kyunghyun Cho · 2021
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GeoQA: A geometric question answering benchmark towards multimodal numerical reasoning
Jiaqi Chen, Jianheng Tang, Jinghui Qin, Xiaodan Liang, Lingbo Liu, Eric P Xing, and Liang Lin · 2021
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Learn to explain: Multimodal reasoning via thought chains for science question answering
Pan Lu, Swaroop Mishra, Tony Xia, Liang Qiu, Kai-Wei Chang, Song-Chun Zhu, Oyvind Tafjord, Peter Clark, and Ashwin Kalyan · 2022
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Training language models to follow instructions with human feedback
Long Ouyang, Jeff Wu, Xu Jiang, Diogo Almeida, Carroll L Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul Christiano, Jan Leike, and Ryan Lowe · 2022
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STaR: Bootstrapping reasoning with reasoning
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah D Goodman · 2022
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Self-consistency improves chain of thought reasoning in language models
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou · 2022
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A survey of deep learning for mathematical reasoning
Pan Lu, Liang Qiu, Wenhao Yu, Sean Welleck, and Kai-Wei Chang · 2023
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MMMU: A massive multi-discipline multimodal understanding and reasoning benchmark for expert AGI
Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Yuxuan Sun, Cong Wei, Botao Yu, Ruibin Yuan, Renliang Sun, Ming Yin, Boyuan Zheng, Zhenzhu Yang, Yibo Liu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen · 2023
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GLoRe: When, where, and how to improve LLM reasoning via global and local refinements
Alex Havrilla, Sharath Raparthy, Christoforus Nalmpantis, Jane Dwivedi-Yu, Maksym Zhuravinskyi, Eric Hambro, and Roberta Raileanu · 2024
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Maya Okawa, Ekdeep Singh Lubana, Robert P. Dick, and Hidenori Tanaka · 2024
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Emergence of hidden capabilities: Exploring learning dynamics in concept space, 2024
Core Francisco Park, Maya Okawa, Andrew Lee, Hidenori Tanaka, and Ekdeep Singh Lubana · 2024
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Physics of language models: Part 3.2, knowledge manipulation, 2024
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Reinforced self-training (ReST) for language modeling
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Attention is all you need, 2023
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DeepSeekMath: Pushing the limits of mathematical reasoning in open language models
Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, Y K Li, Y Wu, and Daya Guo · 2024
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PutnamBench: Evaluating neural theorem-provers on the putnam mathematical competition
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The quantization model of neural scaling, 2024
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D1: Scaling reasoning in diffusion large language models via reinforcement learning
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Assessing diversity collapse in reasoning
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Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective STaRs
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To backtrack or not to backtrack: When sequential search limits model reasoning, 2025
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