Asymmetrically extremely dilute neural networks with non-trivial dynamics

TL;DR

This paper analyzes asymmetrically extremely dilute neural networks with Langevin dynamics, revealing complex non-trivial behavior and phase transitions, supported by theoretical calculations and simulations.

Contribution

It introduces a solvable model for dilute neural networks with asymmetric interactions, highlighting non-trivial dynamics and persistent order parameters.

Findings

Non-persistent order parameters in the thermodynamic limit

Macroscopic dynamics driven by joint neuron-field distribution

Phase transition lines identified and supported by simulations

Abstract

We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the binary neurons case) that even in statics one cannot eliminate the non-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 present simulation results in support of our theory.