PMID: 8963472Dec 1, 1995Paper

Multilayer perceptrons to approximate complex valued functions

International Journal of Neural Systems
P ArenaM G. Xibilia

Abstract

In this paper the approximation capabilities of different structures of complex feedforward neural networks, reported in the literature, have been theoretically analyzed. In particular a new density theorem for Complex Multilayer Perceptrons with complex valued non-analytical sigmoidal activation functions has been proven. Such a result makes Multilayer Perceptrons with complex valued neurons universal interpolators of continuous complex valued functions. Moreover the approximation properties of superpositions of analytic activation functions have been investigated, proving that such combinations are not dense in the set of continuous complex valued functions. Several numerical examples have also been reported in order to show the advantages introduced by Complex Multilayer Perceptrons in terms of computational complexity with respect to the classical real MLP.

Citations

Mar 1, 1997·Neural Networks : the Official Journal of the International Neural Network Society·M G. XibiliaP Arena
May 3, 2008·International Journal of Neural Systems·Sven Buchholz, Nicolas LE Bihan
Jun 3, 2008·Neural Networks : the Official Journal of the International Neural Network Society·Sven Buchholz, Gerald Sommer

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