DEEP RELU NETWORKS OVERCOME THE CURSE OF DIMENSIONALITY FOR GENERALIZED BANDLIMITED FUNCTIONS

• 作者: Hadrien Montanelli Haizhao Yang Qiang Du
• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（6）
• 页码范围: 801-815
• 页数: 15页
• 语种: 英文
• DOI: 10.4208/jcm.2007-m2019-0239

摘要

We prove a theorem concerning the approximation of generalized bandlimited mul-tivariate 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.