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 - <p style="text-align: justify;">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.</p>