Amplitude equations of associative memory patterns in spatially distributed systems

TL;DR

This paper derives amplitude equations for associative memory patterns in distributed systems, revealing universal dynamics of pattern formation and memory recall, including pattern completion and propagating fronts.

Contribution

It introduces coupled amplitude equations for associative memories in spatially distributed systems, linking memory dynamics to classical pattern-forming instabilities.

Findings

Short-range connections support spatio-temporal memory patterns.

Amplitude equations describe pattern completion and selection.

Memory recall dynamics are universal and akin to pattern formation.

Abstract

Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the spatio-temporal dynamics of memory recall. They capture pattern completion and selection, and show that short-range connections can sustain spatio-temporal memory pattern dynamics in the form of propagating patterning fronts. The derived amplitude equations are of the same form as those describing classical pattern-forming instabilities, indicating a universality of the dynamics of memory recall and pattern formation in non-equilibrium systems.