Effect of the learning procedure on local stabilities in neural networks

The role of learning algorithms is to find a synaptic matrix Jij for which a set of given configurations are fixed points of the network dynamics. Below critical storage there are many matrices which satisfy this condition, but differ in several of their properties, in particular, in the distribution of the local stabilities. It is common to quote the typical distribution of local stabilities obtained by averaging over the space of all the possible solutions to the learning problem. We show that the learning algorithms, in general, lead to a restricted subspace of these solutions, which are determined by the initial conditions, and characterized by distributions of stabilities which are significantly different from the typical ones. These differences are reflected in the retrieval properties of the network, in particular by their effect on the size of the basins of attraction.