Retrieval properties of analog neural networks and the nonmonotonicity of transfer functions

Abstract

Characteristic properties of associative memory networks with continuous-time dynamics are extensively studied for a certain class of nonmonotonic transfer functions by means of the self-consistent signal-to-noise analysis (SCSNA) and numerical simulations. The conventional Hebb-type symmetric synaptic connections with unbiased random patterns are assumed. Although the occurrence of instability, including an oscillatory one, makes the storage capacity fall below the upper bound for storage ratio obtained by the SCSNA, the storage capacity remains as large as 0.4 in the optimal cases. It is also noted that noise in the local fields (i.e., the inputs to neurons) can vanish for certain cases of nonmonotonic transfer functions even with an extensive number of stored patterns. Implication of the present results is the possibility of improving the network performances by the achievement of errorless retrieval and enhancement of storage capacity with the use of nonmonotonic transfer functions.