Mean-field theory for the Q-state Potts-glass neural network with biased patterns
D. Bollé, Ronald Cools, Patrick J. Dupont, Jozef Huyghebaert · Journal of Physics A Mathematical and General · 1993
A systematic study of the Q-state Potts model of neural networks, extended to include biased patterns, is made for extensive loading alpha . Mean-field equations are written down within the replica symmetric approximation, for general Q and arbitrary temperature T. For the Q=3 model and two classes of representative bias parameters, the storage capacity and retrieval quality at zero temperature are discussed as functions of the bias, taking into account the Mattis retrieval state and the lowest symmetric states. The T- alpha diagram is obtained and the stability properties of the retrieval state are analysed at finite temperatures. A comparison is made with the biased Hopfield model.