Q-Ising neural network dynamics: a comparative review of various architectures
Abstract
This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise ratio analysis, taking into account all feedback correlations, which are strongly dependent upon these architectures the evolution of the distribution of the local field is found. This leads to a recursive scheme determining the complete time evolution of the order parameters of the network. Arbitrary Q and mainly zero temperature are considered. For the asymmetrically diluted and the layered feedforward network a closed-form solution is obtained while for the symmetrically diluted and fully connected architecture the feedback correlations prevent such a closed-form solution. For these symmetric networks equilibrium fixed-point equations can be derived under certain conditions on the noise in the system. They are the same as those obtained in a thermodynamic replica-symmetric mean-field theory approach.
Cite
@article{arxiv.cond-mat/9907390,
title = {Q-Ising neural network dynamics: a comparative review of various architectures},
author = {D. Bolle and G. Jongen and G. M. Shim},
journal= {arXiv preprint arXiv:cond-mat/9907390},
year = {2007}
}
Comments
To appear in the proceedings of the Int. Conf. on Math. Phys. and Stochastic Analysis (Lisbon, October, 1998), ed. S. Albevero et all (World Scientific)