Active oscillatory associative memory

TL;DR

This paper investigates how active noise and nonlinear interactions in oscillator models influence associative memory, revealing that active noise enhances pattern retrieval robustness and nonlinear couplings improve memory in nonequilibrium conditions.

Contribution

It introduces a model of associative memory driven by active noise, analytically derives an effective energy correction, and demonstrates improved memory robustness due to nonlinearity and active noise.

Findings

Active noise enhances pattern retrieval robustness.

Nonlinear interactions deepen energy wells and strengthen couplings.

Theoretical predictions align with simulation results.

Abstract

Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.