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Neural Computation

Winter 1989, Vol. 1, No. 4, Pages 532-540
(doi: 10.1162/neco.1989.1.4.532)
© 1989 Massachusetts Institute of Technology
Approximation of Boolean Functions by Sigmoidal Networks: Part I: XOR and Other Two-Variable Functions
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Abstract

We prove the existence of a manifold of exact solutions (mean-square error E = 0) of weights and thresholds for sigmoidal networks for XOR and other 2-variable Boolean functions. We also prove the existence of a manifold of local minima of E where E ≠ 0.