Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

TL;DR

This paper investigates a neural network model of associative memory using phase oscillators with distributed natural frequencies, demonstrating how successful retrieval occurs via synchronization and analyzing the effects of noise and frequency distribution on memory performance.

Contribution

The study introduces an effective transfer function for analyzing extensive pattern storage in oscillator networks and derives macroscopic equations describing synchronization-based retrieval.

Findings

Synchronization phenomena depend on the natural frequency distribution.

Two retrieval states are identified based on synchronization degree.

Theoretical results agree with numerical simulations.

Abstract

We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on $[0,2\pi)$ so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce the effective transfer function by assuming the fixed-point equation of the form of the TAP equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.