Analysis of the error surface of the XOR network with two hidden nodes

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Abstract

The exclusive-or learning task in a feed-forward neural network with two hidden nodes is investigated. Constraint equations are derived which fully describe the finite stationary points of the error surface. It is shown that the stationary points occur in a single connected union of eighteen manifolds. A Taylor series expansion is applied to the network error surface and it is shown that all points within the enumerated manifolds are arbitrarily close to points of lower error. It follows that the finite stationary points of the exclusive-or task are not relative minima. This result is surprising in view of the commonly held belief that the exclusive-or task exhibits local minima. The present result complements a recent result of the author's which proves the absence of regional local minima in the exclusive-or task.
Original languageEnglish
Title of host publicationProceedings of the Seventh Australian Conference on Neural Networks : ACNN'96, Canberra, 10-12 April 1996
EditorsP Bartlett, A Burkitt, R Williamson
Place of PublicationCanberra
PublisherANU
Pages179-183
Number of pages5
ISBN (Print)0731524292
Publication statusPublished - 1996
EventAustralian Conference on Neural Networks (7th : 1996) - Canberra, Australia
Duration: 10 Apr 199612 Apr 1996

Conference

ConferenceAustralian Conference on Neural Networks (7th : 1996)
CountryAustralia
CityCanberra
Period10/04/9612/04/96

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  • Cite this

    Hamey, L. (1996). Analysis of the error surface of the XOR network with two hidden nodes. In P. Bartlett, A. Burkitt, & R. Williamson (Eds.), Proceedings of the Seventh Australian Conference on Neural Networks : ACNN'96, Canberra, 10-12 April 1996 (pp. 179-183). Canberra: ANU.