Dynamics of fully connected attractor neural networks near saturation

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Abstract
We present an exact dynamical theory, valid on finite time scales, to describe the fully connected Hopfield model near saturation in terms of deterministic flow equations for order parameters. Two transparent assumptions allow us to perform a replica calculation of the distribution of intrinsic noise components of the alignment fields. Numerical simulations indicate that our equations describe the dynamics correctly in the region where replica symmetry is stable. In equilibrium our theory reproduces the saddle-point equations obtained in the thermodynamic analysis by Amit et al.

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