Neural networks that use three-state neurons
Jonathan S. Yedidia · Journal of Physics A Mathematical and General · 1989
The dynamics of a neural network which uses three-state neurons (1, 0 and -1) is solved exactly in the limit of non-symmetric and highly dilute synapses. Recursion relations for the 'activity' (the fraction of non-zero neurons) and overlap of the network with a given pattern are derived which have three generic kinds of fixed points: a retrieval fixed point, a chaotic fixed point which corresponds to non-zero activity but no overlap, and a 'zero' fixed point where all the neurons go to the 0 state. As the non-retrieval fixed points both have activities different from the retrieval fixed point, one can easily tell whether a pattern has been recovered. An analysis of which fixed points occur as a function of the thresholds and the storage ratio of the system yields remarkably rich phase diagrams. Optimising the threshold level can be very important, especially when low-activity patterns are stored. A similar analysis can be applied to 'biased' networks using two-state (1,0) neurons. Finally, one finds that mixture states which have an overlap with two patterns can be stabilised by a threshold in the networks using three-state neurons. This property allows 'larger' (higher activity) memories to be naturally constructed out of smaller ones.