Retrieval dynamics of neural networks for sparsely coded sequential patterns

It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In this work, we study the dynamical properties of a neural network designed to store sparsely coded sequential patterns rather than static ones. Applying the theory of statistical neurodynamics, we derive the dynamical equations governing the retrieval process which are described by some macroscopic order parameters such as the overlap. It is found that our theory provides good predictions for the storage capacity and the basin of attraction obtained through numerical simulations. The results indicate that the nature of the basin of attraction depends on the methods of activity control employed. Furthermore, it is found that robustness against random synaptic dilution slightly deteriorates with the degree of sparseness.