A hierarchy of macrodynamical equations for associative memory

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The present paper proposes a hierarchy of macrodynamical equations for the recalling process of the autocorrelation associative memory model with synchronous dynamics. The present theory takes account of direct correlations between the cross talk noise terms at different time steps. The storage capacity and the basin of attraction obtained by the present theory are in good agreement with results by computer simulations. The first-order equation corresponds to the Amari and Maginu theory. The higher-order equation coincides with the storage capacity obtained by the replica theory.

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