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Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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On the approximate realization of continuous mappings by neural networks
K. I. Funahashi · 1989
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Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
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Approximation by ridge functions and neural networks with one hidden layer
C. K. Chui and X. Li · 1992
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Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
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The power of approximating: a comparison of activation functions
B. DasGupta and G. Schnitger · 1993
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Numerical methods for special functions
A. Gil, J. Segura, and N. M. Temme · 2007
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Learning deep architectures for ai
Y. Bengio · 2009
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Shallow vs. deep sum-product networks
O. Delalleau and Y. Bengio · 2011
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Imagenet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. E. Hinton · 2012
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Maxout networks
I. J. Goodfellow, D. Warde-Farley, M. Mirza, A. C. Courville, and Y. Bengio · 2013
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Regularization of neural networks using dropconnect
L. Wan, M. Zeiler, S. Zhang, Y. LeCun, and R. Fergus · 2013
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Learning polynomials with neural networks
A. Andoni, R. Panigrahy, G. Valiant, and L. Zhang · 2014
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On the number of linear regions of deep neural networks
G. F. Montufar, R. Pascanu, K. Cho, and Y. Bengio · 2014
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The power of depth for feedforward neural networks
R. Eldan and O. Shamir · 2015
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Notes on hierarchical splines, dclns and i-theory
T. Poggio, L. Rosasco, A. Shashua, N. Cohen, and F. Anselmi · 2015
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Benefits of depth in neural networks
M. Telgarsky · 2016
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D. Yarotsky · 2016
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