%0 Journal Article %1 392253 %A Tianping Chen, %A Hong Chen, %D 1995 %J IEEE Transactions on Neural Networks %K approximate deep-learning readings theory %N 4 %P 911-917 %R 10.1109/72.392253 %T Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems %U https://ieeexplore.ieee.org/document/392253 %V 6 %X 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/sup 1/) 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.<>

@article{392253, abstract = {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/sup 1/) 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.<>}, added-at = {2020-06-09T18:58:33.000+0200}, author = {{Tianping Chen} and {Hong Chen}}, biburl = {https://www.bibsonomy.org/bibtex/28c23373629a50e901de5401535c9be10/kirk86}, description = {Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems - IEEE Journals & Magazine}, doi = {10.1109/72.392253}, interhash = {a4469adfce7087b2808b056d6c034f3e}, intrahash = {8c23373629a50e901de5401535c9be10}, issn = {1941-0093}, journal = {IEEE Transactions on Neural Networks}, keywords = {approximate deep-learning readings theory}, month = {July}, number = 4, pages = {911-917}, timestamp = {2020-06-09T18:58:33.000+0200}, title = {Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems}, url = {https://ieeexplore.ieee.org/document/392253}, volume = 6, year = 1995 }