Mean-field dynamics of sequence processing neural networks with finite connectivity

A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type is extended and analyzed here for a symmetrically diluted network with finite connectivity near saturation. Equations for the dynamics and the stationary states are obtained for the macroscopic observables and the precise equivalence is established with the single-pattern retrieval problem in a layered feed-forward network with finite connectivity.