Stability properties of Potts neural networks with biased patterns and low loading

Abstract

The q-state Potts glass model of neural networks is extended to include biased patterns. For a finite number of such patterns, the existence and stability properties of the Mattis states and symmetric states are discussed in detail as a function of the bias. Analytic results are presented for all q at zero temperature. For finite temperatures numerical results are obtained for q=3 and two classes of representative bias parameters. A comparison is made with the Hopfield model.