Fetching the paper…
Reading the bibliography…
In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
On the approximate realization of continuous mappings by neural networks
K.-I. Funahashi · 1989
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
Earlier work this paper cites.
Universality of fully connected recurrent neural networks
K. Doya · 1993
Earlier work this paper cites.
Approximation and estimation bounds for artificial neural networks
A. R. Barron · 1994
Earlier work this paper cites.
Networks of width one are universal classifiers
R. Rojas · 2003
Earlier work this paper cites.
Persistent homology-a survey
H. Edelsbrunner and J. Harer · 2008
Earlier work this paper cites.
Deep, narrow sigmoid belief networks are universal approximators
I. Sutskever and G. E. Hinton · 2008
Earlier work this paper cites.
Shallow vs. deep sum-product networks
O. Delalleau and Y. Bengio · 2011
Earlier work this paper cites.
Expressive power and approximation errors of restricted boltzmann machines
G. F. Montúfar, J. Rauh, and N. Ay · 2011
Earlier work this paper cites.
On the representational efficiency of restricted boltzmann machines
J. Martens, A. Chattopadhya, T. Pitassi, and R. Zemel · 2013
Earlier work this paper cites.
On the number of response regions of deep feed forward networks with piece-wise linear activations
R. Pascanu, G. Montufar, and Y. Bengio · 2013
Cited alongside, same era.
Do deep nets really need to be deep?
J. Ba and R. Caruana · 2014
Cited alongside, same era.
On the expressive efficiency of sum product networks
J. Martens and V. Medabalimi · 2014
Cited alongside, same era.
Universal approximation depth and errors of narrow belief networks with discrete units
G. F. Montúfar · 2014
Cited alongside, same era.
On the number of linear regions of deep neural networks
G. F. Montufar, R. Pascanu, K. Cho, and Y. Bengio · 2014
Cited alongside, same era.
Geometry and expressive power of conditional restricted boltzmann machines
Benefits of depth in neural networks
M. Telgarsky · 2016
Later among the works it cites.
Nearly-tight vc-dimension bounds for piecewise linear neural networks
N. Harvey, C. Liaw, and A. Mehrabian · 2017
Later among the works it cites.
Expressive power of recurrent neural networks
V. Khrulkov, A. Novikov, and I. Oseledets · 2017
Later among the works it cites.
Why does deep and cheap learning work so well?
H. W. Lin, M. Tegmark, and D. Rolnick · 2017
Later among the works it cites.
The expressive power of neural networks: A view from the width
Z. Lu, H. Pu, F. Wang, Z. Hu, and L. Wang · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
G. Montúfar, N. Ay, and K. Ghazi-Zahedi · 2015
Cited alongside, same era.
On the expressive power of deep learning: A tensor analysis
N. Cohen, O. Sharir, and A. Shashua · 2016
Cited alongside, same era.
Capacity and trainability in recurrent neural networks
J. Collins, J. Sohl-Dickstein, and D. Sussillo · 2016
Cited alongside, same era.
The power of depth for feedforward neural networks
R. Eldan and O. Shamir · 2016
Cited alongside, same era.
Why deep neural networks for function approximation?
S. Liang and R. Srikant · 2016
Cited alongside, same era.
Deep vs. shallow networks: An approximation theory perspective
H. N. Mhaskar and T. Poggio · 2016
Cited alongside, same era.
Q. Nguyen and M. Hein · 2017
Later among the works it cites.
The power of deeper networks for expressing natural functions
D. Rolnick and M. Tegmark · 2017
Later among the works it cites.
Error bounds for approximations with deep relu networks
D. Yarotsky · 2017
Later among the works it cites.
https://playground.tensorflow.org/
Tensorflow neural network playground · 2018
Closest in time.
Neural networks should be wide enough to learn disconnected decision regions
Q. Nguyen, M. Mukkamala, and M. Hein · 2018
Closest in time.