The Blume–Emery–Griffiths neural network: dynamics for arbitrary temperature

Abstract

The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution of the distribution of the local fields and, hence, the evolution of the order parameters. A comparison of this approach is made with the generating functional method, allowing to calculate any physical relevant quantity as a function of time. Explicit analytic formula are given in both methods for the first few time steps of the dynamics. Up to the third time step the results are identical. Some arguments are presented why beyond the third time step the results differ for certain values of the model parameters. Furthermore, fixedpoint equations are derived in the stationary limit. Numerical simulations confirm our theoretical findings.

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

“…In this case the crosstalk noise has a Gaussian distribution and the statistical neurodynamics gives exact results. For models that present symmetry in the synapses, we found feedback correlations and it can be shown [21,22] that, when some relevant feedback correlations are ignored, the results of the SNA method are only an approximation to the exact equations of the GFA method. Finding the relevant feedback correlations, for example in the fully connected Little-Hopfield model, is not a trivial task and the GFA method has served as a guide in this search.…”