Multiplicity of metastable retrieval phases in networks of multistate neurons

Abstract

It is demonstrated that networks of multistate neurons storing an ensemble of multistate patterns exhibit a multiplicity of metastable retrieval phases. These phases are described by solutions of fixed-point equations with characteristic retrieval errors. They emerge if the gain of the neural input-output relation is varied. The number of these phases increases asQ ² with the numberQ of gray levels available to each neuron. Implications for the optimal gain function and basins of attraction are briefly discussed. Again, networks endowed with pseudoinverse couplings are found to perform better than networks with Hebbian couplings: at moderate loading levels phases with retrieval errors are destabilized, whereas the error-free phase remains stable up to the theoretically possible maximum, if the gain parameter is properly chosen.