Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday  

作　　者：Weinan E Qingcan Wang 

机构地区：[1]Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544, USA [2]Center for Big Data Research, Peking University, Beijing 100871, China [3]Beijing Institute of Big Data Research, Beijing 100871, China [4]Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA

出　　处：《Science China Mathematics》2018年第10期1733-1740,共8页中国科学：数学（英文版）

基　　金：supported by Office of Naval Research(ONR)(Grant No.N00014-13-1-0338);Major Program of National Natural Science Foundation of China(Grant No.91130005)

摘　　要：We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

关 键 词：neural networks approximation theory analytic functions 

分 类 号：O174.41[理学—数学]