Self-consistent signal-to-noise analysis of analog neural networks with nonmonotonic transfer functions and enhancement of the storage capacity

Analog neural networks of associative memory with nonmonotonic transfer functions are studied using the self-consistent signal-to-noise analysis. It is assumed that the networks are governed by continuous time dynamics and the synaptic couplings are formed by the Hebb learning rule with unbiased random patterns. The networks of nonmonotonic neurons are shown to exhibit remarkable properties leading to an improvement of network performances under the local learning rule ; enhancement of the storage capacity and occurrence of errorless memory retrieval with an extensive number of memory patterns . The latter is due to the vanishing of noise in the local fields of neurons which is caused by the functioning of the output proportional term in the local field in combination with sufficiently steep negative slopes in the transfer functions.