The signal-to-noise analysis of the Little–Hopfield model revisited

Abstract

Using the generating functional analysis an exact recursion relation is\nderived for the time evolution of the effective local field of the fully\nconnected Little-Hopfield model. It is shown that, by leaving out the feedback\ncorrelations arising from earlier times in this effective dynamics, one\nprecisely finds the recursion relations usually employed in the signal-to-noise\napproach. The consequences of this approximation as well as the physics behind\nit are discussed. In particular, it is pointed out why it is hard to notice the\neffects, especially for model parameters corresponding to retrieval. Numerical\nsimulations confirm these findings. The signal-to-noise analysis is then\nextended to include all correlations, making it a full theory for dynamics at\nthe level of the generating functional analysis. The results are applied to the\nfrequently employed extremely diluted (a)symmetric architectures and to\nsequence processing networks.\n