Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1999-07-26
Physics
Condensed Matter
Disordered Systems and Neural Networks
To appear in the proceedings of the Int. Conf. on Math. Phys. and Stochastic Analysis (Lisbon, October, 1998), ed. S. Albevero
Scientific paper
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.
Bolle D.
Jongen G.
Shim G. M.
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