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We solve an open question from Lu et al.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken · 1993
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Minimum width for universal approximation
S. Park, C. Yun, J. Lee, and J. Shin · 2006
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Provable memorization via deep neural networks using sub-linear parameters
S. Park, J. Lee, C. Yun, and J. Shin · 2010
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On the representational efficiency of restricted boltzmann machines
J. Martens, A. Chattopadhya, T. Pitassi, and R. Zemel · 2013
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The power of depth for feedforward neural networks
R. Eldan and O. Shamir · 2016
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Why deep neural networks for function approximation?
S. Liang and R. Srikant · 2016
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Benefits of depth in neural networks
M. Telgarsky · 2016
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Depth separation for neural networks
A. Daniely · 2017
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Approximating continuous functions by relu nets of minimal width
B. Hanin and M. Sellke · 2017
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The expressive power of neural networks: A view from the width
Z. Lu, H. Pu, F. Wang, Z. Hu, and L. Wang · 2017
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Depth-width tradeoffs in approximating natural functions with neural networks
I. Safran and O. Shamir · 2017
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Error bounds for approximations with deep relu networks
D. Yarotsky · 2017
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Deep, skinny neural networks are not universal approximators
J. Johnson · 2018
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Efficient and accurate estimation of lipschitz constants for deep neural networks
M. Fazlyab, A. Robey, H. Hassani, M. Morari, and G. J. Pappas · 2019
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Depth separations in neural networks: What is actually being separated?
I. Safran, R. Eldan, and O. Shamir · 2019
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Sharp representation theorems for relu networks with precise dependence on depth
G. Bresler and D. Nagaraj · 2020
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Universal approximation with deep narrow networks
P. Kidger and T. Lyons · 2020
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Lipschitz constant estimation of neural networks via sparse polynomial optimization
F. Latorre, P. Rolland, and V. Cevher · 2020
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
K. Scaman and A. Virmaux · 2018
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Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks
P. L. Bartlett, N. Harvey, C. Liaw, and A. Mehrabian · 2019
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Depth-width trade-offs for relu networks via sharkovsky’s theorem
V. Chatziafratis, S. G. Nagarajan, I. Panageas, and X. Wang · 2019
Cited alongside, same era.
Size and depth separation in approximating natural functions with neural networks
G. Vardi, D. Reichman, T. Pitassi, and O. Shamir
Cited in the paper.
On the optimal memorization power of relu neural networks
G. Vardi, G. Yehudai, and O. Shamir
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Neural networks with small weights and depth-separation barriers
G. Vardi and O. Shamir · 2020
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The connection between approximation, depth separation and learnability in neural networks
E. Malach, G. Yehudai, S. Shalev-Shwartz, and O. Shamir · 2021
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Depth separation beyond radial functions
L. Venturi, S. Jelassi, T. Ozuch, and J. Bruna · 2021
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