Amplitude equations of associative memory patterns in spatially distributed systems
Neurons and Cognition
2025-10-20 v3 Disordered Systems and Neural Networks
Pattern Formation and Solitons
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.
Cite
@article{arxiv.2506.13576,
title = {Amplitude equations of associative memory patterns in spatially distributed systems},
author = {Akke Mats Houben},
journal= {arXiv preprint arXiv:2506.13576},
year = {2025}
}
Comments
4 pages, 2 figures. Replacement: clarification of arguments