Mean-field theory for the Q-state Potts-glass neural network with biased patterns

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.

[1]  Albrecht Rau,et al.  Learning multi-class classification problems , 1992 .

[2]  Servet Martínez,et al.  A lower bound for the memory capacity in the Potts-Hopfield model , 1992 .

[3]  Kanter.  Potts-glass models of neural networks. , 1988, Physical review. A, General physics.

[4]  D. Amit,et al.  Statistical mechanics of neural networks near saturation , 1987 .

[5]  Sompolinsky,et al.  Information storage in neural networks with low levels of activity. , 1987, Physical review. A, General physics.

[6]  Désiré Bollé,et al.  On the parallel dynamics of theQ-state Potts andQ-Ising neural networks , 1993 .

[7]  Main overlap dynamics for multistate neural networks , 1991 .

[8]  Jean-Pierre Naef,et al.  Reetrant spin glass behaviour in the replica symmetric solution of the Hopfield neural network model , 1992 .

[9]  Image evolution in Potts-glass neural networks , 1989 .

[10]  A Zippelius,et al.  Invariant recognition in Potts glass neural networks , 1992 .

[11]  Kim,et al.  Statistical-mechanical formulation of the Willshaw model with local inhibition. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[12]  Jean-Pierre Nadal,et al.  Storage capacity of a Potts-perceptron , 1991 .

[13]  Désiré Bollé,et al.  Stability properties of Potts neural networks with biased patterns and low loading , 1991 .

[14]  D. Thouless,et al.  Stability of the Sherrington-Kirkpatrick solution of a spin glass model , 1978 .

[15]  Kim,et al.  Potts-glass model of layered feedforward neural networks. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[16]  Sompolinsky,et al.  Storing infinite numbers of patterns in a spin-glass model of neural networks. , 1985, Physical review letters.

[17]  Huyghebaert,et al.  Thermodynamic properties of the Q-state Potts-glass neural network. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  Véronique Gayrard,et al.  Thermodynamic limit of theq-state Potts-Hopfield model with infinitely many patterns , 1992 .