In a landscape composed of N randomly distributed sites in Euclidean space, a walker (" tourist ") goes to the nearest one that has not been visited in the last τ steps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p. The tourist walk presents universal aspects with respect to τ and can be done in… (More)
In this article we study the effects of introducing structure in the input distribution of the data to be learnt by a simple perceptron. We determine the learning curves within the framework of Statistical Mechanics. Stepwise generalization occurs as a function of the number of examples when the distribution of patterns is highly anisotropic. Although… (More)
We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the… (More)
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the eeect of diierent normalizations of the features. If the normalization is adecuately chosen, there is a hierarchical learning of features of increasing order as a function of the training set size.