GENERALIZATION ERROR AND DYNAMICAL EFFECTS IN A TWO-DIMENSIONAL PATCHES DETECTOR

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Abstract
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.