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Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes

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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.

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

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: October 1, 2000

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