Asymmetrically extremely dilute neural networks with non-trivial dynamics

摘要

We study graded response attractor neural networks with asymmetricallyextremely dilute interactions and Langevin dynamics. We solve our model in thethermodynamic limit using generating functional analysis, and find (in contrastto the binary neurons case) that even in statics one cannot eliminate thenon-persistent order parameters. The macroscopic dynamics is driven by the(non-trivial) joint distribution of neurons and fields, rather than just the(Gaussian) field distribution. We calculate phase transition lines and presentsimulation results in support of our theory.