Population Level Activity in Large Random Neural Networks

Author:

James MacLaurin, Moshe Silverstein, Pedro Vilanova

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Probability (math.PR)

journal:

date:

2024-01-27 00:00:00

Abstract

We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how the structure of the limiting equations depends on the energy landscape of the random connectivity. The method is to determine the convergence of the double empirical measure (this yields population density equations for the joint distribution of the spins and fields). An additional advantage to utilizing the double empirical measure is that it yields a means of obtaining accurate finite-dimensional approximations to the dynamics.

PDF: Population Level Activity in Large Random Neural Networks.pdf