Separating the vertices of N-cubes by hyperplanes and itsapplication to artificial neural networks

A new sufficient condition that a region be classifiable by a two-layer feedforward network using threshold activation functions is found. Briefly, it is either a convex polytope, or that minus the removal of convex polytope from its interior, or. . .recursively. The author refers to these sets as convex recursive deletion regions. The 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 a new result is obtained.