title: Estimates of the Number of Hidden Units and Variation with Respect to Half-Spaces.
abstract: We estimate variation with respect to half-spaces in terms of "flows through hyperplanes". Our estimate is derived from an integral representation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequently we obtain conditions which guarantee approximation error rate of order O by one-hidden-layer networks with n sigmoidal perceptrons. Copyright 1997 Elsevier Science Ltd.
authors.affiliation: Department of Computer Science, University of Texas at, El Paso, USA
authors.forename: Vladik
authors.initials: V
authors.lastname: Kreinovich
authors.forename: Paul C.
authors.initials: PC
authors.lastname: Kainen
authors.forename: Vera
authors.lastname: Kůrková