Random and systematic dilutions of synaptic connections in a neural network with a nonmonotonic response function

It has been observed that the dilution of synaptic connections in neural networks has relevance to biology and applicability to engineering. From this viewpoint, the effects of synaptic dilution on the retrieval performance of an associative memory model with a nonmonotonic response function are investigated through the self-consistent signal-to-noise analysis. Compared with a fully connected neural network, for which a nonmonotonic response function is known to achieve a large enhancement of storage capacity and the occurrence of the superretrieval phase leads to an errorless memory retrieval, the nonmonotonic neural network with a random synaptic dilution undergoes a considerable decrease in storage capacity. It is shown, however, that by employing a systematic dilution technique characterized by a nonlinear learning rule, in which larger connections are retained, it is possible to significantly reverse the undesirable rapid reduction in storage capacity. It is also proved that the superretrieval phase is structurally unstable against the dilution of synapses.