Multilayer perceptrons : approximation order and necessary number of hidden units

Trenn, Stephan GND

This paper considers the approximation of sufficiently smooth multivariable functions with a multilayer perceptron (MLP). For a given approximation order explicit formulas for the necessary number of hidden units and its distributions to the hidden layers of the MLP is derived. These formulas depend only on the number of input variables and on the desired approximation order. The concept of approximation order encompasses Kolmogorov-Gabor polynomials or discrete Volterra series which are widely used in static and dynamic models of nonlinear systems. The results are obtained by considering structural properties of the Taylor polynomials of the function in question and of the MLP function.

Cite

Citation style:
Trenn Dr. rer. nat., S., 2007. Multilayer perceptrons: approximation order and necessary number of hidden units. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 07–27.
Could not load citation form. Default citation form is displayed.

Rights

Use and reproduction:
All rights reserved

Export