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Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge.
Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. 2020 · 1901
Earlier work this paper cites.
Transformer-xl: Attentive language models beyond a fixed-length context
Zihang Dai, Zhilin Yang, Yiming Yang, Jaime Carbonell, Quoc V Le, and Ruslan Salakhutdinov. 2019 · 1901
Earlier work this paper cites.
On the turing completeness of modern neural network architectures
Jorge Pérez, Javier Marinković, and Pablo Barceló. 2019 · 1901
Earlier work this paper cites.
Are transformers universal approximators of sequence-to-sequence functions?
Chulhee Yun, Srinadh Bhojanapalli, Ankit Singh Rawat, Sashank J Reddi, and Sanjiv Kumar. 2019 · 1912
Earlier work this paper cites.
Lower bounds for the size of circuits of bounded depth with basis fˆ; g
Alexander A Razborov. 1987 · 1987
Earlier work this paper cites.
Algebraic methods in the theory of lower bounds for boolean circuit complexity
Roman Smolensky. 1987 · 1987
Earlier work this paper cites.
Ieee standard 754 for binary floating-point arithmetic
William Kahan. 1996 · 1996
Earlier work this paper cites.
Latent dirichlet allocation
David M Blei, Andrew Y Ng, and Michael I Jordan. 2003 · 2003
Earlier work this paper cites.
Ieee standard for floating-point arithmetic
IEEE. 2019 · 2008
Earlier work this paper cites.
Computational complexity: a modern approach
Sanjeev Arora and Boaz Barak. 2009 · 2009
Earlier work this paper cites.
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Earlier work this paper cites.
Song Han, Huizi Mao, and William J Dally. 2015 · 2015
Earlier work this paper cites.
Gaussian error linear units (gelus)
Dan Hendrycks and Kevin Gimpel. 2016 · 2016
Earlier work this paper cites.
Language models are unsupervised multitask learners
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. 2019 · 2019
Earlier work this paper cites.
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David Saxton, Edward Grefenstette, Felix Hill, and Pushmeet Kohli. 2019 · 2019
Earlier work this paper cites.
Theoretical limitations of self-attention in neural sequence models
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Earlier work this paper cites.
O (n) connections are expressive enough: Universal approximability of sparse transformers
Chulhee Yun, Yin-Wen Chang, Srinadh Bhojanapalli, Ankit Singh Rawat, Sashank Reddi, and Sanjiv Kumar. 2020 · 2020
Earlier work this paper cites.
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Earlier work this paper cites.
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Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. 2021 · 2021
Earlier work this paper cites.
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Rodrigo Nogueira, Zhiying Jiang, and Jimmy Lin. 2021 · 2021
Earlier work this paper cites.
Attention is turing complete
Jorge Pérez, Pablo Barceló, and Javier Marinkovic. 2021 · 2021
Earlier work this paper cites.
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Gail Weiss, Yoav Goldberg, and Eran Yahav. 2021 · 2021
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Self-attention networks can process bounded hierarchical languages
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Your transformer may not be as powerful as you expect
Shengjie Luo, Shanda Li, Shuxin Zheng, Tie-Yan Liu, Liwei Wang, and Di He. 2022 · 2022
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Saturated transformers are constant-depth threshold circuits
William Merrill, Ashish Sabharwal, and Noah A Smith. 2022 · 2022
Earlier work this paper cites.
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Swaroop Mishra, Matthew Finlayson, Pan Lu, Leonard Tang, Sean Welleck, Chitta Baral, Tanmay Rajpurohit, Oyvind Tafjord, Ashish Sabharwal, Peter Clark, and Ashwin Kalyan. 2022 · 2022
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