Characteristics of Hebbian-type associative memories having faulty interconnections

The performance of Hebbian-type associative memories (HAMs) in the presence of faulty (open- and short-circuit) synaptic interconnections is examined and equations for predicting network reliability are developed. The results show that a network with open-circuit interconnection faults has a higher probability of direct convergence than a network with short-circuit interconnection faults when the fraction of failed interconnections is small and the short-circuit signal is large. The results are extended to the case where network attraction radius is considered. Under certain assumptions, it is found that the expected numbers of neurons with b, b-1, b-2,. . .,1 input error bits in their state update are equal. Because of the capability of error correction, an asynchronous HAM is also found to have a higher probability of direct convergence than a synchronous HAM. Using these results, network reliability and generalization capability can be estimated when both the interconnection faults and the number of error bits in the probe vectors are taken into account.