ON THE STORAGE CAPACITY FOR TEMPORAL PATTERN SEQUENCES IN NETWORKS WITH DELAYS

We study the storage capacity for temporal sequences of random patterns in networks with arbitrary delays, evolving under parallel dynamics. For sequences with a common period T, made up of patterns which remain constant for DELTA-time steps, couplings with delays tau = DELTA.k - 1, where k is integer, are particularly important since they are tuned to the "rhythm" of the sequences. For networks with tuned delays only, we calculate the optimal storage capacity along the lines of Gardner [1] and find identical results to corresponding static cases, whereas untuned couplings induce several complications. For DELTA = 2, we consider networks with finite fractions 1 - a of untuned couplings, additionally weighted in strength by a parameter lambda with respect to the tuned couplings. For lambda-2(1 - a) << 1 we already find a pronounced decrease of the optimal storage capacity compared to the network where the fraction (1 - a) of untuned connections was cut. Thus for optimal error-free storage, the untuned couplings should be switched off. On the other hand, if errors are allowed and the couplings are chosen by a Hebbian prescription, the untuned couplings turn out to be useful, if the fraction a of tuned couplings exceeds a certain critical value, and the weight parameter lambda can then be optimized with respect to the storage capacity.