Reliability characteristics of quadratic Hebbian-type associative memories in optical and electronic network implementations

The performance capability of quadratic Hebbian type associative memories (QHAM´s) in the presence of interconnection faults is examined, and equations for predicting the probability of direct convergence P_dc given a fraction of interconnection faults are developed. The interconnection faults considered are the equivalent of open circuit and short circuit synaptic interconnections in electronic implementations. Our results show that a network with open circuit interconnection faults has a higher probability of direct convergence P _dc than a network with short circuit interconnection faults, when the fraction of failed interconnections p is small and the short circuit signal G is large. Certain values of G are found to have only mild effects on network performance degradation. Network reliability characteristics taking the generalization capability into account are also analyzed. All of these results are compared with those of Hebbian type associative memories (HAM´s), which have linear association network models. Our results indicate that QHAM´s have much higher network capacity and fault tolerance capability in the presence of interconnection faults. However, the fault tolerance to input errors in QHAM´s is much less than that of HAM´s