Separating the Vertices of N-Cubes by Hyperplanes and its Application to Artificial Neural Networks
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Abstract
We obtain a new sufficient condition that a region be classifiable by a 2-layer
feed-forward net using threshold activation functions. Briefly, it is either a convex
polytope, or that minus the removal of convex polytope from its interior, or that
minus a convex polytope from its interior, or ... recursively. We refer to these
sets as convex recursive deletion regions. Our proof of implementability exploits
the equivalence of this problem with that of characterizing two set partitions of
the vertices of a hypercube which are separable by a hyperplane for which we also
obtain a new result.
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1994-02
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