The Minimum Number of Errors in the N-Parity and its Solution with an Incremental Neural Network |
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| Authors: | Torres-Moreno J Manuel Aguilar Julio C Gordon Mirta B |
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| Affiliation: | (1) Département de Génie informatique, CP, École Polytechnique de Montréal, 6079 Succ. Centre-ville, H3C3A7 Montréal, (Québec), Canada;(2) Laboratorio Nacional de Informática Avanzada (LANIA), Rébsamen, 80-91090 Xalapa, México;(3) Laboratoire Leibniz – IMAG (CNRS), 46, Avenue Félix Viallet, 38031 Grenoble Cedex, France |
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| Abstract: | The N-dimensional parity problem is frequently a difficult classification task for Neural Networks. We found an expression for the minimum number of errors  f as function of N for this problem, performed by a perceptron. We verified this quantity experimentally for N=1,...,15 using an optimal train perceptron. With a constructive approach we solved the full N-dimensional parity problem using a minimal feedforward neural network with a single hidden layer of h=N units. |
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| Keywords: | classification tasks minimerror monoplan parity problem perceptrons supervised learning |
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