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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems

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2 Author(s)
Tianping Chen ; Dept. of Math., Fudan Univ., Shanghai, China ; Hong Chen

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'(R1 ) to be a Tauber-Wiener function, the necessary and sufficient condition is 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; and 4) 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

Published in:

IEEE Transactions on Neural Networks  (Volume:6 ,  Issue: 4 )