Density and Approximation by Using Feed Forward Artificial Neural Networks
I n this paper ,we 'viii consider the density questions associC;lted with the single hidden layer feed forward model. We proved that a FFNN with one hidden layer can uniformly approximate any continuous function in C(k)(where k is a compact set in R11 ) to any requir...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2017-09-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/1335 |
| Summary: | I n this paper ,we 'viii consider the density questions associC;lted with the single hidden layer feed forward model. We proved that a FFNN with one hidden layer can uniformly approximate any continuous function in C(k)(where k is a compact set in R11 ) to any required accuracy.
However, if the set of basis function is dense then the ANN's can has al most one hidden layer. But if the set of basis function non-dense, then we need more hidden layers. Also, we have shown that there exist localized functions and that there is no theoretical lower bound on the degree of a pproximation common to all acti vation functions(contrary to the si tuation in the single hidden layer model).
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| ISSN: | 1609-4042 2521-3407 |