Representation properties of networks: Kolmogorov's theorem is irrelevant

Authors:
Federico Girosi;Tomaso Poggio
Affiliations:
Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA 02142 USA and Center for Biological Information Processing, Whitaker College, Cambridge, MA 02142 USA;Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA 02142 USA and Center for Biological Information Processing, Whitaker College, Cambridge, MA 02142 USA
Venue:
Neural Computation
Year:
1989

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Abstract

Many neural networks can be regarded as attempting to approximate a multivariate function in terms of one-input one-output units. This note considers the problem of an exact representation of nonlinear mappings in terms of simpler functions of fewer variables. We review Kolmogorov's theorem on the representation of functions of several variables in terms of functions of one variable and show that it is irrelevant in the context of networks for learning.