Recall Time in Densely Encoded Hopfield Network: Results from KFS Theory and Computer Simulation
Recall time in Hopfield attractor neural network with parallel dynamics is investigated analytically and by computer simulation. The method of the recall time estimation is based on calculation of overlaps between successive patterns of network dynamics. Recall time is estimated as the time when the overlap reaches the value 1 — Δm where Δm is the minimal increment of overlap for the network of a given size. It is shown, first, that this time actually gives rather accurate estimation for the recall time and, second, that the overlap between successive patterns of network dynamics can be rather accurately estimated by the theory recently developed by . It is shown that recall process has three very different phases: the search of the recalled prototype by large steps with low convergence rate, fast convergence to the attractor in the vicinity of the recalled prototype and again slow convergence to the attractor when it is almost reached. If recall process ends at two first phases then point attractors dominate. If it ends at the third phase then cyclic at tractors of the length 2 dominate. Transition to the third phase can be revealed by computer simulation of networks of extremely large size (up to the number of neurons in the order 105). Special algorithm is used to avoid storing in the computer memory both connection matrix and the set of stored prototypes.
KeywordsNetwork Dynamic Associative Memory Convergence Time Successive Pattern Point Attractor
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