Walter Wenzel; Nihat Ay; Frank Pasemann : Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes

Author(s) :

Walter Wenzel; Nihat Ay; Frank Pasemann

Title :

Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-6, 1999

Mathematics Subject Classification :

05B25 [ Finite geometries (combinatorics) ]

51D20 [ Combinatorial geometries ]

52B30 [ Arrangements of hyperplanes (convex geometry) ]

54A20 [ Convergence in general topology ]

92B20 [ General theory of neural networks ]

Abstract :

Strictly layered feedforward networks with binary neurons are viewed as maps from the vertex set of an n-cube to the vertex set of an l-cube; these maps are induced by hyperplane arrangements consisting of l hyperplanes and separating some given vertex set of the n-cube in some sense. We prove that l grows exponentially with n.

Keywords :

Feedforward Networks, Binary Units, Classification Problems, Hypercube, Separability, Affine Oriented Hyperplane Arrangements, Linear Codes

Language :

english

Publication time :

5/1999