Complex Systems

Basins of Attraction in a Perceptron-Like Neural Network Download PDF

Werner Krauth
Marc Mézard
Jean-Pierre Nadal
Laboratoire de Physique Statistique,
Laboratoire de Physique Théorique de l'E.N.S.,
24 rue Lhomond, 75231 Paris Cedex 05, France


We study the performance of a neural network of the perceptron type. We isolate two important sets of parameters which render the network fault tolerant (existence of large basins of attraction) in both hetero-associative and auto-associative systems and study the size of the basins of attraction (the maximal allowable noise level still ensuring recognition) for sets of random patterns. The relevance of our results to the perceptron's ability to generalize are pointed out, as is the role of diagonal couplings in the fully connected Hopfield model.