PERCEPTRONS ABOVE SATURATION

We study the storage of random patterns by a perceptron above its stor age capacity alpha(c), i.e. in the region where perfect storage become s impossible. We determine the minimal fraction of learning errors and the distribution of stabilities for different learning rules in onest ep replica symmetry breaking. Thereby we not only extend the known rep lica symmetric results to values of the storage capacity beyond the Ar line but also show that, depending on the learning rule, replica symm etry may be globally unstable already well below the AT line. As an ex ample for possible implications we compare the results for the typical basins of attraction of an extremely diluted attractor neural network as given by replica symmetry and one-step replica symmetry breaking.