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Q-Ising neural network dynamics: a comparative review of various architectures

D. Bolle·G. Jongen·G. M. Shim
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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.

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D. Bolle, G. Jongen, G. M. Shim. 1999-07-26. Q-Ising neural network dynamics: a comparative review of various architectures. https://arxiv.org/abs/cond-mat/9907390

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