The Universal Approximation Capabilities of Cylindrical Approximate Identity Neural Networks

被引：7

作者：

Zainuddin, Zarita ^{[1
]}

Fard, Saeed Panahian ^{[1
]}

机构：

[1] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

来源：

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING | 2016年 / 41卷 / 08期

关键词：

Cylindrical approximate identity; Cylindrical convolution; Cylindrical approximate identity neural networks; Epsilon-net; Uniform convergence; Universal approximation; MULTILAYER FEEDFORWARD NETWORKS; CIRCULAR-CIRCULAR DATA; DISTRIBUTIONS; OPERATORS;

D O I：

10.1007/s13369-016-2067-9

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Universal approximation capability of feedforward neural networks is one of the important theoretical concepts in artificial neural networks. In this study, a type of single-hidden-layer feedforward neural networks is presented. The networks is called feedforward cylindrical approximate identity neural networks. Then, universal approximation capabilities of the networks are investigated in two function spaces. Whereby the notions of cylindrical approximate identity and cylindrical convolution are introduced. The analyses are divided into two cases: In the first case, universal approximation capability of a single-hidden-layer feedforward cylindrical approximate identity neural networks to continuous bivariate functions on the infinite cylinder is investigated. In the latter case, universal approximation capability of the networks is extended to the pth-order Lebesgue integrable bivariate functions on the infinite cylinder.

引用

页码：3027 / 3034

页数：8

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