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

• 作 者: Hadrien Montanelli Haizhao Yang Qiang Du
• 机 构: Centre de Mathématiques Appliquées,(E)cole Polytechnique,Palaiseau,France;Department of Mathematics,
• 出 处: 计算数学（英文版）
• 发表日期: 2021年6期
• 关键词: Machine learning Deep ReLU networks Curse of dimensionality Approxima-tion theor

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.