Hyperplane arrangements separating arbitrary vertex classes in n-cubes
Walter Wenzel, Nihat Ay,and Frank Pasemann
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Submission date: 05. May. 1999
published in: Advances in applied mathematics, 25 (2000) 3, p. 284-306
DOI number (of the published article): 10.1006/aama.2000.0701
Keywords and phrases: feedforward networks, binary units, classification problems, hypercube, separability, affine oriented hyperplane arrangements, linear codes
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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 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.