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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
35/1999

Hyperplane arrangements separating arbitrary vertex classes in n-cubes

Walter Wenzel, Nihat Ay and Frank Pasemann

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 in principle they can 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.

Received:
May 5, 1999
Published:
May 5, 1999
Keywords:
feedforward networks, binary units, classification problems, hypercube, separability, affine oriented hyperplane arrangements, linear codes

Related publications

inJournal
2000 Repository Open Access
Walter Wenzel, Nihat Ay and Frank Pasemann

Hyperplane arrangements separating arbitrary vertex classes in \(\mathscr n\)-cubes

In: Advances in applied mathematics, 25 (2000) 3, pp. 284-306