Fetching the paper…
Reading the bibliography…
We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results.
The theory of approximation
D. Jackson · 1930
Earlier work this paper cites.
ϵ \epsilon -entropy and ϵ \epsilon -capacity of sets in functional spaces
A.N. Kolmogorov and V.M. Tikhomirov · 1961
Earlier work this paper cites.
Optimal nonlinear approximation
Ronald A. DeVore, Ralph Howard, and Charles Micchelli · 1989
Earlier work this paper cites.
Fewnomials
A. G. Khovanskii · 1991
Earlier work this paper cites.
Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers
Paul W Goldberg and Mark R Jerrum · 1995
Earlier work this paper cites.
Constructive Approximation (Advanced Problems)
George G. Lorentz, Manfred v. Golitschek, and Yuly Makovoz · 1996
Earlier work this paper cites.
Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks
Marek Karpinski and Angus Macintyre · 1997
Earlier work this paper cites.
Almost linear VC-dimension bounds for piecewise polynomial networks
Peter L Bartlett, Vitaly Maiorov, and Ron Meir · 1998
Earlier work this paper cites.
Approximation theory of the MLP model in neural networks
Allan Pinkus · 1999
Earlier work this paper cites.
Lower bounds for approximation by mlp neural networks
Vitaly Maiorov and Allan Pinkus · 1999
Earlier work this paper cites.
A simple counterexample to Kouchnirenko’s conjecture
Bertrand Haas · 2002
Earlier work this paper cites.
Extremal real algebraic geometry and 𝒜 \mathcal{A} -discriminants
Alicia Dickenstein, J Maurice Rojas, Korben Rusek, and Justin Shih · 2007
Cited alongside, same era.
Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 2009
Cited alongside, same era.
benefits of depth in neural networks
Matus Telgarsky · 2016
Cited alongside, same era.
The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2016
Cited alongside, same era.
Error bounds for approximations with deep ReLU networks
Dmitry Yarotsky · 2017
Cited alongside, same era.
Why deep neural networks for function approximation?
Shiyu Liang and Rayadurgam Srikant · 2017
Cited alongside, same era.
Memory-optimal neural network approximation
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, and Philipp Petersen · 2017
Later among the works it cites.
Optimal approximation of piecewise smooth functions using deep ReLU neural networks
Philipp Petersen and Felix Voigtlaender · 2018
Later among the works it cites.
Optimal approximation of continuous functions by very deep ReLU networks
Dmitry Yarotsky · 2018
Later among the works it cites.
Provable approximation properties for deep neural networks
Uri Shaham, Alexander Cloninger, and Ronald R Coifman · 2018
Later among the works it cites.
The universal approximation power of finite-width deep ReLU networks
Dmytro Perekrestenko, Philipp Grohs, Dennis Elbrächter, and Helmut Bölcskei · 2018
Later among the works it cites.
Resnet with one-neuron hidden layers is a universal approximator
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Depth-width tradeoffs in approximating natural functions with neural networks
Itay Safran and Ohad Shamir · 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.
Approximating continuous functions by ReLU nets of minimal width
Boris Hanin and Mark Sellke · 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.
Neural networks and rational functions
Matus Telgarsky · 2017
Cited alongside, same era.
Hongzhou Lin and Stefanie Jegelka · 2018
Later among the works it cites.
Approximation in L p ( μ ) L^{p}(\mu) with deep ReLU neural networks
Felix Voigtlaender and Philipp Petersen · 2019
Closest in time.
New error bounds for deep ReLU networks using sparse grids
Hadrien Montanelli and Qiang Du · 2019
Closest in time.
Deep neural network approximation theory
Philipp Grohs, Dmytro Perekrestenko, Dennis Elbrächter, and Helmut Bölcskei · 2019
Closest in time.
Nearly-tight VC-dimension and Pseudodimension Bounds for Piecewise Linear Neural Networks
Peter L Bartlett, Nick Harvey, Christopher Liaw, and Abbas Mehrabian · 2019
Closest in time.
Nonparametric regression using deep neural networks with ReLU activation function
Johannes Schmidt-Hieber · 2020
Closest in time.