Optimal capacity of the Blume-Emery-Griffiths perceptron

Abstract

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the imbedding stability parameter. The stability of the replica-symmetric approximation is studied via the analogue of the Almeida-Thouless line. A comparison is made with other three-state perceptrons.

Gardner optimal capacity of the diluted Blume–Emery–Griffiths neural network

“…However, an underlying reason why there is such an enlargement of the basin of attraction and hence of the retrieval properties of the network seems still to be absent. This enhancement of retrieval has also been found [6] for the BEG-perceptron…”

“…and one recovers the optimal capacity found in the fully connected case [6]. When the pattern activity a goes to 1 the system is forced into two possible states, as in the Gardner model with dilution [15].…”

“…It was also shown that this enhancement of the retrieval properties is not restricted to the use of the Hebbian learning rule but that it is inherent to the model. Indeed, by studying the Gardner optimal capacity [5] in replica symmetric (RS) mean-field theory it was found recently [6] that for the corresponding BEG perceptron with, e.g., zero embedding stability parameter and uniform patterns this capacity is 2.24. Comparing with other three-state neuron perceptron models, we recall that for the Q = 3 Ising perceptron the Gardner optimal capacity can maximally reach 1.5 [7,8], whereas for the Q = 3 clock and Potts model both reach an optimal capacity of 2.40 [9,10].…”

The sparse Blume-Emery-Griffiths model of associative memories

“…In this way, for two state neurons the Hopfield model is retrieved while for the three state problem described above one obtains the BEG model, that was originally introduced as a spin glass model to study phase separation of liquid He 3 -He 4 mixtures. In [4] the non-rigorous replica method is used to study the storage capacity of such networks.…”

Blume–Emery–Griffiths dynamics in social networks

“…In the present work, we investigate the implication of a social network in a stochastic opinion formation model. We first introduce the Blume-Emery-Griffiths (BEG) model [12,13,14] to describe the dynamics of opinion formation, and the model of complex networks we used is social network which is more reality. Our simulation focuses on the average opinion for different situation.…”