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We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute.
On the density of families of sets
Norbert Sauer · 1972
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Some extensions of w. gautschi’s inequalities for the gamma function
D. Kershaw · 1983
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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A comparison of the computational power of sigmoid and Boolean threshold circuits
Wolfgang Maass, Georg Schnitger, and Eduardo D Sontag · 1994
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Almost linear vc-dimension bounds for piecewise polynomial networks
Peter L Bartlett, Vitaly Maiorov, and Ron Meir · 1998
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Hyperplane arrangements
Richard Stanley · 2011
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2012
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On the number of response regions of deep feed forward networks with piece-wise linear activations
Razvan Pascanu, Guido Montufar, and Yoshua Bengio · 2013
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On the representational efficiency of restricted boltzmann machines
James Martens, Arkadev Chattopadhya, Toni Pitassi, and Richard Zemel · 2013
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On some inequalities for the gamma function
Andrea Laforgia and Pierpaolo Natalini · 2013
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On the number of linear regions of deep neural networks
Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio · 2014
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On the complexity of neural network classifiers: A comparison between shallow and deep architectures
Deep knowledge tracing
Chris Piech, Jonathan Bassen, Jonathan Huang, Surya Ganguli, Mehran Sahami, Leonidas J Guibas, and Jascha Sohl-Dickstein · 2015
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The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2015
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Representation benefits of deep feedforward networks
Matus Telgarsky · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
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Mastering the game of go with deep neural networks and tree search
David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al · 2016
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Monica Bianchini and Franco Scarselli · 2014
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Explaining and harnessing adversarial examples
Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
Cited alongside, same era.
Exponential expressivity in deep neural networks through transient chaos
Ben Poole, Subhaneil Lahiri, Maithra Raghu, Jascha Sohl-Dickstein, and Surya Ganguli · 2016
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