Approximation of boolean functions by sigmoidal networks: Part i: xor and other two-variable functions

Authors:
E. K. Blum
Affiliations:
Mathematics Department, University of Southern California, Los Angeles, CA 90089 USA
Venue:
Neural Computation
Year:
1989

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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.