Given a multilayer perceptron (MLP), there are functions that can be approximated up to any degree of accuracy by the MLP without having to increase the number of the hidden nodes. Those functions belong to the closure F̄ of the set F of the maps realizable by the MLP. In the paper, we give a list of maps with this property. In particular, it is proven that rationales belongs to F̄ for networks with arctangent activation function and exponentials belongs to F̄ for networks with sigmoid activation function. Moreover, for a restricted class of MLPs, we prove that the list is complete and give an analytic definition of F̄.

Gori, M., Scarselli, F., Tsoi, A.C. (1996). Which classes of functions can a given multilayer perceptron approximate?. In Proceedings of International Conference on Neural Networks (ICNN'96) (pp.2226-2231). IEEE [10.1109/ICNN.1996.549247].

Which classes of functions can a given multilayer perceptron approximate?

GORI, MARCO;SCARSELLI, FRANCO;
1996-01-01

Abstract

Given a multilayer perceptron (MLP), there are functions that can be approximated up to any degree of accuracy by the MLP without having to increase the number of the hidden nodes. Those functions belong to the closure F̄ of the set F of the maps realizable by the MLP. In the paper, we give a list of maps with this property. In particular, it is proven that rationales belongs to F̄ for networks with arctangent activation function and exponentials belongs to F̄ for networks with sigmoid activation function. Moreover, for a restricted class of MLPs, we prove that the list is complete and give an analytic definition of F̄.
1996
0780332113
Gori, M., Scarselli, F., Tsoi, A.C. (1996). Which classes of functions can a given multilayer perceptron approximate?. In Proceedings of International Conference on Neural Networks (ICNN'96) (pp.2226-2231). IEEE [10.1109/ICNN.1996.549247].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/36862
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