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The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks.
Certification of algorithm 112: position of point relative to polygon
Richard Hacker · 1962
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Algorithm 112: position of point relative to polygon
Moshe Shimrat · 1962
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A proof of the Jordan curve theorem
Helge Tverberg · 1980
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On the capabilities of multilayer perceptrons
Eric B. Baum · 1988
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, Halbert White, et al · 1989
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The Jordan-Schönflies theorem and the classification of surfaces
Carsten Thomassen · 1992
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Moshe Leshno, Vladimir Ya Lin, Allan Pinkus, and Shimon Schocken · 1993
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Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions
Guang-Bin Huang and Haroon A Babri · 1998
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Approximation theory of the MLP model in neural networks
Allan Pinkus · 1999
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Learning capability and storage capacity of two-hidden-layer feedforward networks
Guang-Bin Huang · 2003
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Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2016
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Benefits of depth in neural networks
Matus Telgarsky · 2016
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Approximating continuous functions by ReLU nets of minimal width
Boris Hanin and Mark Sellke · 2017
Cited alongside, same era.
Automatic chemical design using a data-driven continuous representation of molecules
Rafael Gómez-Bombarelli, Jennifer N Wei, David Duvenaud, José Miguel Hernández-Lobato, Benjamín Sánchez-Lengeling, Dennis Sheberla, Jorge Aguilera-Iparraguirre, Timothy D Hirzel, Ryan P Adams, and Alán Aspuru-Guzik · 2018
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Junction tree variational autoencoder for molecular graph generation
Wengong Jin, Regina Barzilay, and Tommi Jaakkola · 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
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Deep, skinny neural networks are not universal approximators
Jesse Johnson · 2019
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RoBERTa: A robustly optimized BERT pretraining approach
Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov · 2019
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Why does deep and cheap learning work so well?
Henry W Lin, Max Tegmark, and David Rolnick · 2017
Cited alongside, same era.
The expressive power of neural networks: A view from the width
Zhou Lu, Hongming Pu, Feicheng Wang, Zhiqiang Hu, and Liwei Wang · 2017
Cited alongside, same era.
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, and Qianli Liao · 2017
Cited alongside, same era.
Approximation capabilities of neural networks on unbounded domains
Yang Qu and Ming-Xi Wang · 2019
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Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity
Chulhee Yun, Suvrit Sra, and Ali Jadbabaie · 2019
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Universal approximation with deep narrow networks
Patrick Kidger and Terry Lyons · 2020
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Memory capacity of neural networks with threshold and ReLU activations
Roman Vershynin · 2020
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