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 |
| _version_ | 1811308015275474944 |
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| author | R.S. Naoum L.N.M. Ta wfiq |
| author_facet | R.S. Naoum L.N.M. Ta wfiq |
| author_sort | R.S. Naoum |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-04-13T09:15:25Z |
| format | Article |
| id | doaj.art-7158ae65bd7f487a937ac0c219203ca4 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-13T09:15:25Z |
| publishDate | 2017-09-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-7158ae65bd7f487a937ac0c219203ca42022-12-22T02:52:45ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072017-09-01201Density and Approximation by Using Feed Forward Artificial Neural NetworksR.S. NaoumL.N.M. Ta wfiq 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). https://jih.uobaghdad.edu.iq/index.php/j/article/view/1335 |
| spellingShingle | R.S. Naoum L.N.M. Ta wfiq Density and Approximation by Using Feed Forward Artificial Neural Networks Ibn Al-Haitham Journal for Pure and Applied Sciences |
| title | Density and Approximation by Using Feed Forward Artificial Neural Networks |
| title_full | Density and Approximation by Using Feed Forward Artificial Neural Networks |
| title_fullStr | Density and Approximation by Using Feed Forward Artificial Neural Networks |
| title_full_unstemmed | Density and Approximation by Using Feed Forward Artificial Neural Networks |
| title_short | Density and Approximation by Using Feed Forward Artificial Neural Networks |
| title_sort | density and approximation by using feed forward artificial neural networks |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/1335 |
| work_keys_str_mv | AT rsnaoum densityandapproximationbyusingfeedforwardartificialneuralnetworks AT lnmtawfiq densityandapproximationbyusingfeedforwardartificialneuralnetworks |