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.