Arena P, Fortuna L, Re R, Xibilia M G
Dipartimento Elettrico, Elettronico e Sistemistico University of Cantania, Italy.
Int J Neural Syst. 1995 Dec;6(4):435-46. doi: 10.1142/s0129065795000299.
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.
本文对文献中报道的不同结构的复数前馈神经网络的逼近能力进行了理论分析。特别地，证明了具有复值非解析Sigmoid激活函数的复数多层感知器的一个新的密度定理。这一结果使得具有复值神经元的多层感知器成为连续复值函数的通用插值器。此外，还研究了解析激活函数叠加的逼近性质，证明了这种组合在连续复值函数集中不是稠密的。还给出了几个数值例子，以展示复数多层感知器相对于经典实值多层感知器在计算复杂度方面的优势。
