Separating the Vertices of N-Cubes by Hyperplanes and its Application to Artificial Neural Networks
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.