Quantitative study of attractor neural networks retrieving at low spike rates: II. Low-rate retrieval in symmetric networks

A network of current-rate dynamics with a symmetric synaptic matrix is analysed and simulated for its low-rate attractor structure. The dynamics is deterministic, with the noise included in a realistic current-rate transduction function (discussed in part I)The analysis is carried out in mean-field theory. It is shown that at low loading the network retrieves without errors, with uniform low rates, that there are no simple spurious states and that the low-rate attractors, retrieving single patterns, are stable to the admixture of additional patterns. The analysis of the attractors in a network with an extensive number of patterns is carried out in the replica symmetric approximations. The results for the dependence of the retrieval rates on loading level; for the distribution of rates among neurons, as well as for the storage capacity are compared with simulations. Simulations also show that retriewal performance is very robust to random elimination of synapses. Moreover, errors in the stimulus, relative to the stored patterns, are very rapidly corrected.It is shown that memory saturation expresses itself either in a drift toward a quiescent state, or in the freezing of rates in the two classes of neurons in a pattern in the foreground and in the background. Freezing means that in each class a subset of neurons are active at high rates and the others are quiescent. The two activity distributions become indistinguishable