A spherical Hopfield model

Abstract

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings.

9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the manuscript

References in corpus (2)

• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Exactly solvable model of a quantum spin glass

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