Amplitude equations of associative memory patterns in spatially distributed systems

2025/06/16 by Akke Mats Houben, Houben, Akke Mats
Mathematics · #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2506.13576

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.

Citations

• Beyond catastrophic forgetting in associative networks with self-interactions
• Storing overlapping associative memories on latent manifolds in low-rank spiking networks
• Large Associative Memory Problem in Neurobiology and Machine Learning
• On a Model of Associative Memory with Huge Storage Capacity
• Pattern formation outside of equilibrium
• The chemical basis of morphogenesis

Related

• Transient dynamics of associative memory models
• Active oscillatory associative memory
• Dynamical Properties of Dense Associative Memory
• Dynamical mean field approach to associative memory model with non-monotonic transfer functions
• Memory as activity: pattern formation in a conserved scalar field