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While forward reasoning (i.e., find the answer given the question) has been explored extensively in recent literature, backward reasoning is relatively unexplored.
Language models are few-shot learners
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Reversibility of thought: An instance in multiplicative tasks
Ajay Ramful and John Olive. 2008 · 2008
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On the pitfalls of abduction: Compolicities and complexities in patterning activity
FD Rivera. 2008 · 2008
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Automated theorem proving
Wolfgang Bibel. 2013 · 2013
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Learning to automatically solve algebra word problems
Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay. 2014 · 2014
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Sequence to sequence learning with neural networks
Ilya Sutskever, Oriol Vinyals, and Quoc V Le. 2014 · 2014
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Parsing algebraic word problems into equations
Rik Koncel-Kedziorski, Hannaneh Hajishirzi, Ashish Sabharwal, Oren Etzioni, and Siena Dumas Ang. 2015 · 2015
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Solving general arithmetic word problems
Subhro Roy and Dan Roth. 2015 · 2015
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Program induction by rationale generation: Learning to solve and explain algebraic word problems
Wang Ling, Dani Yogatama, Chris Dyer, and Phil Blunsom. 2017 · 2017
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Deep neural solver for math word problems
Yan Wang, Xiaojiang Liu, and Shuming Shi. 2017 · 2017
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Mapping to declarative knowledge for word problem solving
Subhro Roy and Dan Roth. 2018 · 2018
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Abductive commonsense reasoning
Chandra Bhagavatula, Ronan Le Bras, Chaitanya Malaviya, Keisuke Sakaguchi, Ari Holtzman, Hannah Rashkin, Doug Downey, Wen tau Yih, and Yejin Choi. 2020 · 2020
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Graph-to-tree neural networks for learning structured input-output translation with applications to semantic parsing and math word problem
Shucheng Li, Lingfei Wu, Shiwei Feng, Fangli Xu, Fengyuan Xu, and Sheng Zhong. 2020 · 2020
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Back to the future: Unsupervised backprop-based decoding for counterfactual and abductive commonsense reasoning
Lianhui Qin, Vered Shwartz, Peter West, Chandra Bhagavatula, Jena D. Hwang, Ronan Le Bras, Antoine Bosselut, and Yejin Choi. 2020 · 2020
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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 · 2021
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How can we know when language models know? on the calibration of language models for question answering
Zhengbao Jiang, Jun Araki, Haibo Ding, and Graham Neubig. 2021 · 2021
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Are NLP models really able to solve simple math word problems?
Arkil Patel, Satwik Bhattamishra, and Navin Goyal. 2021 · 2021
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Generate & rank: A multi-task framework for math word problems
Jianhao Shen, Yichun Yin, Lin Li, Lifeng Shang, Xin Jiang, Ming Zhang, and Qun Liu. 2021 · 2021
Large language models are better reasoners with self-verification
Yixuan Weng, Minjun Zhu, Fei Xia, Bin Li, Shizhu He, Kang Liu, and Jun Zhao. 2022 · 2022
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Palm 2 technical report
Rohan Anil, Andrew M. Dai, Orhan Firat, Melvin Johnson, Dmitry Lepikhin, Alexandre Passos, Siamak Shakeri, Emanuel Taropa, Paige Bailey, Zhifeng Chen, Eric Chu, Jonathan H. Clark, Laurent El Shafey, Yanping Huang, Kathy Meier-Hellstern, Gaurav Mishra, Erica Moreira, Mark Omernick, Kevin Robinson, Sebastian Ruder, Yi Tay, Kefan Xiao, Yuanzhong Xu, Yujing Zhang, Gustavo Hernandez Abrego, Junwhan Ahn, Jacob Austin, Paul Barham, Jan Botha, James Bradbury, Siddhartha Brahma, Kevin Brooks, Michele Catasta, Yong Cheng, Colin Cherry, Christopher A. Choquette-Choo, Aakanksha Chowdhery, Clément Crepy, Shachi Dave, Mostafa Dehghani, Sunipa Dev, Jacob Devlin, Mark Díaz, Nan Du, Ethan Dyer, Vlad Feinberg, Fangxiaoyu Feng, Vlad Fienber, Markus Freitag, Xavier Garcia, Sebastian Gehrmann, Lucas Gonzalez, Guy Gur-Ari, Steven Hand, Hadi Hashemi, Le Hou, Joshua Howland, Andrea Hu, Jeffrey Hui, Jeremy Hurwitz, Michael Isard, Abe Ittycheriah, Matthew Jagielski, Wenhao Jia, Kathleen Kenealy, Maxim Krikun, Sneha Kudugunta, Chang Lan, Katherine Lee, Benjamin Lee, Eric Li, Music Li, Wei Li, YaGuang Li, Jian Li, Hyeontaek Lim, Hanzhao Lin, Zhongtao Liu, Frederick Liu, Marcello Maggioni, Aroma Mahendru, Joshua Maynez, Vedant Misra, Maysam Moussalem, Zachary Nado, John Nham, Eric Ni, Andrew Nystrom, Alicia Parrish, Marie Pellat, Martin Polacek, Alex Polozov, Reiner Pope, Siyuan Qiao, Emily Reif, Bryan Richter, Parker Riley, Alex Castro Ros, Aurko Roy, Brennan Saeta, Rajkumar Samuel, Renee Shelby, Ambrose Slone, Daniel Smilkov, David R. So, Daniel Sohn, Simon Tokumine, Dasha Valter, Vijay Vasudevan, Kiran Vodrahalli, Xuezhi Wang, Pidong Wang, Zirui Wang, Tao Wang, John Wieting, Yuhuai Wu, Kelvin Xu, Yunhan Xu, Linting Xue, Pengcheng Yin, Jiahui Yu, Qiao Zhang, Steven Zheng, Ce Zheng, Weikang Zhou, Denny Zhou, Slav Petrov, and Yonghui Wu. 2023 · 2023
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Calibrate before use: Improving few-shot performance of language models
Zihao Zhao, Eric Wallace, Shi Feng, Dan Klein, and Sameer Singh. 2021 · 2021
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Aojun Zhou, Ke Wang, Zimu Lu, Weikang Shi, Sichun Luo, Zipeng Qin, Shaoqing Lu, Anya Jia, Linqi Song, Mingjie Zhan, and Hongsheng Li. 2023 · 2021
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Optq: Accurate quantization for generative pre-trained transformers
Elias Frantar, Saleh Ashkboos, Torsten Hoefler, and Dan Alistarh. 2022 · 2022
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Learning to reason deductively: Math word problem solving as complex relation extraction
Zhanming Jie, Jierui Li, and Wei Lu. 2022 · 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. 2022 · 2022
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COLD decoding: Energy-based constrained text generation with langevin dynamics
Lianhui Qin, Sean Welleck, Daniel Khashabi, and Yejin Choi. 2022 · 2022
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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 V Le, and Denny Zhou. 2022 · 2022
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Pal: Program-aided language models
Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. 2023 · 2023
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Solving math word problems by combining language models with symbolic solvers
Joy He-Yueya, Gabriel Poesia, Rose E. Wang, and Noah D. Goodman. 2023 · 2023
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Self-refine: Iterative refinement with self-feedback
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Llama 2: Open foundation and fine-tuned chat models
Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, Dan Bikel, Lukas Blecher, Cristian Canton Ferrer, Moya Chen, Guillem Cucurull, David Esiobu, Jude Fernandes, Jeremy Fu, Wenyin Fu, Brian Fuller, Cynthia Gao, Vedanuj Goswami, Naman Goyal, Anthony Hartshorn, Saghar Hosseini, Rui Hou, Hakan Inan, Marcin Kardas, Viktor Kerkez, Madian Khabsa, Isabel Kloumann, Artem Korenev, Punit Singh Koura, Marie-Anne Lachaux, Thibaut Lavril, Jenya Lee, Diana Liskovich, Yinghai Lu, Yuning Mao, Xavier Martinet, Todor Mihaylov, Pushkar Mishra, Igor Molybog, Yixin Nie, Andrew Poulton, Jeremy Reizenstein, Rashi Rungta, Kalyan Saladi, Alan Schelten, Ruan Silva, Eric Michael Smith, Ranjan Subramanian, Xiaoqing Ellen Tan, Binh Tang, Ross Taylor, Adina Williams, Jian Xiang Kuan, Puxin Xu, Zheng Yan, Iliyan Zarov, Yuchen Zhang, Angela Fan, Melanie Kambadur, Sharan Narang, Aurelien Rodriguez, Robert Stojnic, Sergey Edunov, and Thomas Scialom. 2023 · 2023
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Self-consistency improves chain of thought reasoning in language models
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V. Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023 · 2023
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Generating sequences by learning to self-correct
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Progressive-hint prompting improves reasoning in large language models
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Leandojo: Theorem proving with retrieval-augmented language models
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Metamath: Bootstrap your own mathematical questions for large language models
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