On the macroscopic description of recurrent neural network dynamics

Abstract

It is expected that the dynamics of recurrent neural networks can be described by a set of macroscopic order parameters. For such descriptions to exist, macroscopic specification of microscopic states of neural networks during the dynamics has to be possible. We study this problem for the case of Coolen-Sherrington (CS) theory, which successfully describes qualitative aspects of the dynamics of the Hopfield-type recurrent neural network. We show that the macroscopic specification is incomplete in CS theory by providing direct evidence that the equipartitioning assumption employed by CS theory prevents the theory from describing the dynamics quantitatively.