MIXTURE STATES AND STORAGE OF BIASED PATTERNS IN POTTS-GLASS NEURAL NETWORKS

The presence and stability of mixture states in Q-state Potts neural n etworks are studied for different learning rules within the replica-sy mmetric mean-field-theory approach. The retrieval properties of the as ymmetric mixture states are examined in the case of biased patterns. F or the storage of a finite number of such patterns, these properties a re compared for the usual Hebb learning rule and some variants obtaine d by subtracting, for a certain pattern, the average of the Potts neur on state over all the other patterns. The latter are introduced to sup press the symmetric mixture states. Furthermore, the embedding of an a dditional, infinite number of unbiased patterns stored with the Hebb r ule is allowed. The storage capacity and the temperature-capacity phas e diagram are discussed in these cases. A detailed analysis is made fo r the Q = 3 model and two classes of representative bias parameters.