Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes

Authors: Wenzel W.¹; Ay N.²; Pasemann F.²

Source: Advances in Applied Mathematics, Volume 25, Number 3, October 2000 , pp. 284-306(23)

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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. With only one output neuron, they can in principle realize any Boolean function on n inputs. We address the problem of determining the necessary and sufficient numbers of hidden units for this task by using separability properties of affine oriented hyperplane arrangements. Copyright 2000 Academic Press.

Keywords: feedforward networks; binary units; classification problems; hypercube; separability; affine oriented hyperplane arrangements; linear codes

Language: English

Document Type: Research article

Affiliations: 1: Institute of Mathematics, Technical University of Chemnitz, Chemnitz, D-09107, Germany 2: Max-Planck-Institute for Mathematics in the Sciences, Leipzig, D-04103, Germany

Publication date: 2000-10-01