Fetching the paper…
Reading the bibliography…
We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks.
On Liouville’s theorem for biharmonic functions
R. R. Huilgol · 1971
Earlier work this paper cites.
Principles of mathematical analysis
W. Rudin · 1976
Earlier work this paper cites.
Holomorphic functions of several variables
L. Kaup and B. Kaup · 1983
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 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.
Polyanalytic functions
M. Balk · 1991
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
Earlier work this paper cites.
Functional analysis
W. Rudin · 1991
Earlier work this paper cites.
On the capability of neural networks with complex neurons in complex valued functions approximation
P. Arena, L. Fortuna, R. Re, and M. G. Xibilia · 1993
Earlier work this paper cites.
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
M. Leshno, V. Lin, A. Pinkus, and S. Schocken · 1993
Earlier work this paper cites.
Multilayer perceptrons to approximate complex valued functions
P. Arena, L. Fortuna, R. Re, and M. G. Xibilia · 1995
Earlier work this paper cites.
Neural networks for optimal approximation of smooth and analytic functions
H. N. Mhaskar · 1996
Earlier work this paper cites.
Neural networks in multidimensional domains: fundamentals and new trends in modelling and control
P. Arena, L. Fortuna, G. Muscato, and M. G. Xibilia · 1998
Earlier work this paper cites.
Real analysis
G. Folland · 1999
Earlier work this paper cites.
Topology
J. R. Munkres · 2000
Earlier work this paper cites.
Complex-valued neural networks: theories and applications
A. Hirose · 2003
Cited alongside, same era.
Approximation by fully complex multilayer perceptrons
T. Kim and T. Adalı · 2003
Cited alongside, same era.
Complex analysis
E. Stein and R. Shakarchi · 2003
Cited alongside, same era.
Universal approximation using incremental constructive feedforward networks with random hidden nodes
G.-B. Huang, L. Chen, and C. K. Siew · 2006
Cited alongside, same era.
Incremental extreme learning machine with fully complex hidden nodes
G.-B. Huang, M.-B. Li, L. Chen, and C.-K. Siew · 2007
Cited alongside, same era.
Weyl’s lemma, one of many
D. Stroock · 2008
Cited alongside, same era.
Better than real: Complex-valued neural nets for MRI fingerprinting
P. Virtue, S. X. Yu, and M. Lustig · 2017
Later among the works it cites.
Error bounds for approximations with deep ReLU networks
D. Yarotsky · 2017
Later among the works it cites.
ResNet with one-neuron hidden layers is a universal approximator
H. Lin and S. Jegelka · 2018
Later among the works it cites.
Optimal approximation of piecewise smooth functions using deep ReLU neural networks
P. Petersen and F. Voigtlaender · 2018
Later among the works it cites.
Deep complex networks
C. Trabelsi, O. Bilaniuk, Y. Zhang, D. Serdyuk, S. Subramanian, J. F. Santos, S. Mehri, N. Rostamzadeh, Y. Bengio, and C. J. Pal · 2018
Later among the works it cites.
Complex gated recurrent neural networks
M. Wolter and A. Yao · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
L. Evans · 2010
Cited alongside, same era.
Deep sparse rectifier neural networks
X. Glorot, A. Bordes, and Y. Bengio · 2011
Cited alongside, same era.
Sequence to sequence learning with neural networks
I. Sutskever, O. Vinyals, and Q. V. Le · 2014
Cited alongside, same era.
Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
Cited alongside, same era.
Linear functional analysis
H. W. Alt · 2016
Cited alongside, same era.
A mathematical motivation for complex-valued convolutional networks
M. Tygert, J. Bruna, S. Chintala, Y. LeCun, S. Piantino, and A. Szlam · 2016
Cited alongside, same era.
Universality of deep convolutional neural networks
D.-X. Zhou · 2019
Later among the works it cites.
Universal Approximation with Deep Narrow Networks
P. Kidger and T. Lyons · 2020
Closest in time.
Equivalence of approximation by convolutional neural networks and fully-connected networks
P. Petersen and F. Voigtlaender · 2020
Closest in time.
The phase diagram of approximation rates for deep neural networks
D. Yarotsky and A. Zhevnerchuk · 2020
Closest in time.
Theory of deep convolutional neural networks: Downsampling
D.-X. Zhou · 2020
Closest in time.
Deep Network Approximation for Smooth Functions
J. Lu, Z. Shen, H. Yang, and S. Zhang · 2021
Closest in time.
Approximation spaces of deep neural networks
R. Gribonval, G. Kutyniok, M. Nielsen, and F. Voigtlaender · 2022
Closest in time.
Universal approximations of invariant maps by neural networks
D. Yarotsky · 2022
Closest in time.