The presence and stability of mixture states in Q-state Potts neural networks are studied for different learning rules within the replica-symmetric mean-field-theory approach. The retrieval properties of the asymmetric mixture states are examined in the case of biased patterns. For the storage of a finite number of such patterns, these properties are compared for the usual Hebb learning rule and some variants obtained by subtracting, for a certain pattern, the average of the Potts neuron state over all the other patterns. The latter are introduced to suppress the symmetric mixture states. Furthermore, the embedding of an additional, infinite number of unbiased patterns stored with the Hebb rule is allowed. The storage capacity and the temperature-capacity phase diagram are discussed in these cases. A detailed analysis is made for the Q=3 model and two classes of representative bias parameters.

• Received 9 April 1993

DOI:https://doi.org/10.1103/PhysRevE.48.2250