I. Kocher
Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, (Unite Propre de Recherche du CNRS, associée à l’Ecole Normale Supérieure et à l’Université de Paris-Sud.) 24 rue Lhomond, 75231 Paris Cedex 05, France
R. Monasson
Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, (Unite Propre de Recherche du CNRS, associée à l’Ecole Normale Supérieure et à l’Université de Paris-Sud.) 24 rue Lhomond, 75231 Paris Cedex 05, France

Received 25 January 1991
Revised 26 April 1991

We study the supervised learning of a two-dimensional patches detector. We compute the generalization error of the network with the annealed approximation; a first-order phase transition appears at all temperatures on the generalization error curve as a function of the size of the training set.

We show that the system is subject to dynamical effects: the earlier story of presentation of the patterns to the system can be relevant, and a hysteresis appears on the generalization error curve.

We show Monte Carlo simulations which agree with the theoretical predictions.