The Minimum Number of Errors in the N-Parity and its Solution with an Incremental Neural Network

  • Authors:
  • J. Manuel Torres-Moreno;Julio C. Aguilar;Mirta B. Gordon

  • Affiliations:
  • École Polytechnique de Montréal, Département de Génie informatique, CP 6079 Succ. Centre-ville, H3C3A7 Montréal (Québec) Canada. E-mail: juan-manuel.torres@po ...;Laboratorio Nacional de Informática Avanzada (LANIA), Rébsamen 80-91090 Xalapa, México;Laboratoire Leibniz – IMAG (CNRS), 46, Avenue Félix Viallet, 38031 Grenoble Cedex, France

  • Venue:
  • Neural Processing Letters
  • Year:
  • 2002

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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 νf 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.