DYNAMICS OF FULLY CONNECTED ATTRACTOR NEURAL NETWORKS NEAR SATURATION

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