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.
|Title of host publication||Proceedings of the Seventh Australian Conference on Neural Networks : ACNN'96, Canberra, 10-12 April 1996|
|Editors||P Bartlett, A Burkitt, R Williamson|
|Place of Publication||Canberra|
|Number of pages||5|
|Publication status||Published - 1996|
|Event||Australian Conference on Neural Networks (7th : 1996) - Canberra, Australia|
Duration: 10 Apr 1996 → 12 Apr 1996
|Conference||Australian Conference on Neural Networks (7th : 1996)|
|Period||10/04/96 → 12/04/96|
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.