Statistical mechanics of attractor neural networks and self-consistent signal-to-noise analysis : analog neural networks with nonmonotonic transfer functions and enhancement of the storage capacity(New Developments in Statistical Physics Similarities in Diversities,YITP Workshop)

Abstract

The self-consistent signal-to-noise analysis (SCSNA) we have recently deveoped is a systematic method to deal with the equilibrium properties of analog neural networks of associative memory with a general type of transfer functions. The method is based on a self-consistent treatment of the local fields of neurons to extract the self-interaction part and gaussian noise by means of a renormalization procedure. Applying the SCSNA to analog networks with nonmonotonic transfer functions in which the updating rule is given by continuous time dynamics and the synaptic couplings are formed by the Hebb learning rule with unbiased random patterns, we have found the networks 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 self-interaction part of the local field in combination with sufficiently steep negative slopes in the transfer functions.