文献类型：期刊文献

中文题名：The construction and approximation of feedforward neural network with hyperbolic tangent function

英文题名：The construction and approximation of feedforward neural network with hyperbolic tangent function

作者：Chen Zhi-xiang[1];Cao Fei-long[2]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing 312000, Peoples R China;[2]China Jiliang Univ, Dept Math, Hangzhou 310018, Peoples R China

年份：2015

卷号：0

期号：2

起止页码：151

中文期刊名：高校应用数学学报：英文版（B辑）

外文期刊名：APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B

收录：SCI-EXPANDED(收录号：WOS:000355859700003)、、CSCD2015_2016、Scopus(收录号：2-s2.0-84930615590)、WOS、CSCD

基金：Supported by the National Natural Science Foundation of China (61179041, 61272023, and 11401388).

语种：英文

中文关键词：双曲正切函数;前馈神经网络;逼近误差;网络运营商;误差估计;函数分析;激活功能;二元函数

外文关键词：approximation; Hyperbolic tangent function; modulus of continuity; neural networks

中文摘要：In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.

外文摘要：In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.