The construction and approximation of feedforward neural network with hyperbolic tangent function

被引:5
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
基金
中国国家自然科学基金;
关键词
UNIVERSAL APPROXIMATION; ACTIVATION FUNCTIONS; SIGMOIDAL FUNCTIONS; OPERATORS; SUPERPOSITIONS; CONVERGENCE; CAPABILITY;
D O I
10.1007/s11766-015-3000-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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.
引用
收藏
页码:151 / 162
页数:12
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