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Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions
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@Article{JCM-39-801,
author = {Montanelli , HadrienYang , Haizhao and Du , Qiang},
title = {Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions},
journal = {Journal of Computational Mathematics},
year = {2021},
volume = {39},
number = {6},
pages = {801--815},
abstract = {
We prove a theorem concerning the approximation of generalized bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is based on a result by Maurey and on the ability of deep ReLU networks to approximate Chebyshev polynomials and analytic functions efficiently.
}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2007-m2019-0239}, url = {http://global-sci.org/intro/article_detail/jcm/19912.html} }
TY - JOUR
T1 - Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions
AU - Montanelli , Hadrien
AU - Yang , Haizhao
AU - Du , Qiang
JO - Journal of Computational Mathematics
VL - 6
SP - 801
EP - 815
PY - 2021
DA - 2021/10
SN - 39
DO - http://doi.org/10.4208/jcm.2007-m2019-0239
UR - https://global-sci.org/intro/article_detail/jcm/19912.html
KW - Machine learning, Deep ReLU networks, Curse of dimensionality, Approximation theory, Bandlimited functions, Chebyshev polynomials.
AB -
We prove a theorem concerning the approximation of generalized bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is based on a result by Maurey and on the ability of deep ReLU networks to approximate Chebyshev polynomials and analytic functions efficiently.
Montanelli , HadrienYang , Haizhao and Du , Qiang. (2021). Deep ReLU Networks Overcome the Curse of Dimensionality for Generalized Bandlimited Functions.
Journal of Computational Mathematics. 39 (6).
801-815.
doi:10.4208/jcm.2007-m2019-0239
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