Associative Memory of Analog Networks without the Energy Concept Using Biased Patterns and Positive-Valued Transfer Functions

Abstract

Associative memory of analog neural networks for which the concept of energy functions is lost is studied by means of the SCSNA (Self-Consistent Signal-to-Noise Analysis). Asymmetric synaptic couplings with biased random patterns are assumed together with positive-valued transfer functions which allow nonmonotonicity resulting from an appropriate cut off of output activity. Phase diagrams are given in terms of several parameters of the networks, showing the occurrence of enhancement of the storage capacity due to nonmonotonic transfer functions. Super retrieval states ensuring errorless memory retrieval under the loading of extensively many patterns are allowed to remain in existence in the presence of asymmetric synaptic couplings with biased patterns. A sample-dependent component in the local fields of neurons, which arises from the assumed asymmetric couplings, is discussed and shown to become of no effect in the super retrieval phase.