Effect of synaptic failure on the performance of sparsely encoded Hopfield associative memory

This paper investigates the fault-tolerance characteristic of sparsely encoded Hopfield associative memory with respect to synaptic disconnection. The effect of this fault on the network performance is evaluated in terms of capacity degradation. The optimum neuron´s threshold turns out to be depend on the failure-ratio β. Failure-ratio being an unknown, threshold is set to its optimum value corresponding to the case β=0. It then turns out that faulty-network is unable to store and retrieve patterns for at least β⩾1/2. Next, assuming that there exists an adaptive mechanism which estimates failure ratio and resets the threshold to its optimum value, it will be shown that network fault-tolerance is improved; network keeps its associative recall functionality for whole range of synaptic disconnectivity, showing only a graceful performance degradation. This degradation appears to be dependent on the sparsity of stored patterns