title: Multilayer perceptrons: approximation order and necessary number of hidden units.
abstract: 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 are 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.
authors.affiliation: Institute of Mathematics, Ilmenau University of Technology, Ilmenau 98684, Germany. stephan.trenn@tu-ilmenau.de
authors.forename: Stephan
authors.initials: S
authors.lastname: Trenn
mesh_terms: D000465:Algorithms; D001695:Biology; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics