@article{64021e19b1ec456abc606664f1f122e1,
title = "Exponential convergence of the deep neural network approximation for analytic functions",
abstract = "We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.",
keywords = "Primary 65D15, analytic functions, approximation theory, neural networks, secondary 41-04",
author = "E. Weinan and Qingcan Wang",
note = "Funding Information: This work was supported by Offce of Naval Research (ONR) (Grant No. N00014-13-1-0338) and Major Program of National Natural Science Foundation of China (Grant No. 91130005). The authors are grateful to Chao Ma for very helpful discussions during the early stage of this work. The authors are also grateful to Jinchao Xu for his interest, which motivated us to write up this paper. Funding Information: Acknowledgements This work was supported by Office of Naval Research (ONR) (Grant No. N00014-13-1-0338) and Major Program of National Natural Science Foundation of China (Grant No. 91130005). The authors are grateful to Chao Ma for very helpful discussions during the early stage of this work. The authors are also grateful to Jinchao Xu for his interest, which motivated us to write up this paper.",
year = "2018",
month = oct,
day = "1",
doi = "10.1007/s11425-018-9387-x",
language = "English (US)",
volume = "61",
pages = "1733--1740",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science in China Press",
number = "10",
}