UNIVERSAL APPROXIMATION TO NONLINEAR OPERATORS BY NEURAL NETWORKS WITH ARBITRARY ACTIVATION FUNCTIONS AND ITS APPLICATION TO DYNAMICAL-SYSTEMS
UNIVERSAL APPROXIMATION TO NONLINEAR OPERATORS BY NEURAL NETWORKS WITH ARBITRARY ACTIVATION FUNCTIONS AND ITS APPLICATION TO DYNAMICAL-SYSTEMS
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DOI：
10.1109/72.392253
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发表时间：
1995-07-01
影响因子：
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通讯作者：
CHEN, H
中科院分区：
文献类型：
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作者：
CHEN, TP;CHEN, H
本文的目的是系统地研究神经网络的能力。主要结果如下：1）每个Tauber-Wiener函数都可作为三层神经网络隐层中的激活函数; 2）S'（R（1））中的连续函数是Tauber-Wiener函数的充要条件，它不是多项式; 3）证明了它逼近定义在Banach空间的某个紧集上的非线性泛函和非线性算子的能力，这意味着4）我们展示了通过神经计算来近似动力系统的整体输出（而不是在固定点处）的可能性，从而识别系统。
The purpose of this paper is to investigate neural network capability systematically. The main results are: 1) every Tauber-Wiener function is qualified as an activation function in the hidden layer of a three-layered neural network, 2) for a continuous function in S' (R(1)) to be a Tauber-Wiener function, the necessary and sufficient conditions that it is not a polynomial, 3) the capability of approximating nonlinear functionals defined on some compact set of a Banach space and nonlinear operators has been shown, which implies that 4) we show the possibility by neural computation to approximate the output as a whole (not at a fixed point) of a dynamical system, thus identifying the system.