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We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning.
Generating correctness proofs with neural networks
Alex Sanchez-Stern, Yousef Alhessi, Lawrence Saul, and Sorin Lerner · 1907
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Exploring the limits of transfer learning with a unified text-to-text transformer
Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu · 1910
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PEGASUS: pre-training with extracted gap-sentences for abstractive summarization
Jingqing Zhang, Yao Zhao, Mohammad Saleh, and Peter J. Liu · 1912
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HOL Light: A tutorial introduction
John Harrison · 1996
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Teaching temporal logics to neural networks
Bernd Finkbeiner, Christopher Hahn, Markus N. Rabe, and Frederik Schmitt · 2003
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ROUGE: A package for automatic evaluation of summaries
Chin-Yew Lin · 2004
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Informalising formal mathematics: Searching the mizar library with latent semantics
Paul Cairns · 2004
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Mptp–motivation, implementation, first experiments
Josef Urban · 2004
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Language models are few-shot learners, 2020
Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei · 2005
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Learning-assisted automated reasoning with flyspeck
Cezary Kaliszyk and Josef Urban · 2014
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Initial experiments with statistical conjecturing over large formal corpora
Thibault Gauthier, Cezary Kaliszyk, and Josef Urban · 2016
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin · 2017
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TacticToe: Learning to reason with HOL4 tactics
Thibault Gauthier, Cezary Kaliszyk, and Josef Urban · 2017
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Language models are unsupervised multitask learners
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever · 2018
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First experiments with neural translation of informal to formal mathematics
Qingxiang Wang, Cezary Kaliszyk, and Josef Urban · 2018
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Unsupervised machine translation using monolingual corpora only
Guillaume Lample, Alexis Conneau, Ludovic Denoyer, and Marc’Aurelio Ranzato · 2018
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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
GamePad: A learning environment for theorem proving
Daniel Huang, Prafulla Dhariwal, Dawn Song, and Ilya Sutskever · 2019
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Learning to prove theorems via interacting with proof assistants
Kaiyu Yang and Jia Deng · 2019
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Can neural networks learn symbolic rewriting?
Bartosz Piotrowski, Josef Urban, Chad E Brown, and Cezary Kaliszyk · 2019
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Novel positional encodings to enable tree-based transformers
Vighnesh Leonardo Shiv and Chris Quirk · 2019
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Spanbert: Improving pre-training by representing and predicting spans
Mandar Joshi, Danqi Chen, Yinhan Liu, Daniel S. Weld, Luke Zettlemoyer, and Omer Levy · 2020
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Deep learning for symbolic mathematics
Guillaume Lample and François Charton · 2020
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HOList: An environment for machine learning of higher-order theorem proving
Kshitij Bansal, Sarah M Loos, Markus N Rabe, Christian Szegedy, and Stewart Wilcox · 2019
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MASS: masked sequence to sequence pre-training for language generation
Kaitao Song, Xu Tan, Tao Qin, Jianfeng Lu, and Tie-Yan Liu · 2019
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Unified language model pre-training for natural language understanding and generation
Li Dong, Nan Yang, Wenhui Wang, Furu Wei, Xiaodong Liu, Yu Wang, Jianfeng Gao, Ming Zhou, and Hsiao-Wuen Hon · 2019
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Cross-lingual language model pretraining
Alexis Conneau and Guillaume Lample · 2019
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Exploration of neural machine translation in autoformalization of mathematics in Mizar
Qingxiang Wang, Chad Brown, Cezary Kaliszyk, and Josef Urban · 2020
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First neural conjecturing datasets and experiments
Josef Urban and Jan Jakubův · 2020
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Modelling high-level mathematical reasoning in mechanised declarative proofs
Wenda Li, Lei Yu, Yuhuai Wu, and Lawrence C. Paulson · 2020
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Global relational models of source code
Vincent J. Hellendoorn, Charles Sutton, Rishabh Singh, Petros Maniatis, and David Bieber · 2020
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