Provable approximation properties for deep neural networks

被引：159

作者：

Shaham, Uri ^{[1
]}

Cloninger, Alexander ^{[2
]}

Coifman, Ronald R. ^{[2
]}

机构：

[1] Yale Univ, Dept Stat, New Haven, CT 06520 USA

[2] Yale Univ, Program Appl Math, New Haven, CT 06520 USA

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2018年 / 44卷 / 03期

基金：

美国国家科学基金会;

关键词：

Neural nets; Function approximation; Wavelets;

D O I：

10.1016/j.acha.2016.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Gamma subset of R-m, we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Gamma, the complexity of f, in terms of its wavelet description, and only weakly on the ambient dimension m. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU). (c) 2016 Elsevier Inc. All rights reserved.

引用

页码：537 / 557

页数：21

共 21 条

[1]

[Anonymous], COMMUNICATION

[2]

[Anonymous], 2015, ARXIV150302406

[3]

Approximation and learning by greedy algorithms [J].