Storing an extensive number of grey-toned patterns in a neural network using multistate neurons
Heiko Rieger · Journal of Physics A Mathematical and General · 1990
Grey-toned patterns are pictures composed of pixels of several shades of grey. The ability of neural networks using multistate neurons to store such patterns is systematically investigated. If conventional generalizations of Hopfield networks using analogue or soft neurons are considered, it is impossible to stabilize these grey tones. Nevertheless it is shown that it can be done with networks that use neurons which have only a discrete set of possible activities. This is demonstrated for the pseudo-inverse rule for the synaptic couplings, where only the stability of the patterns shrinks with increasing number Q of grey tones one wants to store. If the patterns are uncorrelated one can use the Hebb rule and in this case the mean field theory is presented. Applying this rule the storage capacity decreases as Q -2 with the number of grey tones.