Amplitude equations of associative memory patterns in spatially distributed systems

Akke Mats Houben

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arXiv · 2506.13576

Amplitude equations of associative memory patterns in spatially distributed systems

Akke Mats Houben

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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.

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Akke Mats Houben. 2025-06-16. Amplitude equations of associative memory patterns in spatially distributed systems. https://arxiv.org/abs/2506.13576

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