Phase Transitions of an Oscillator Neural Network with a Standard Hebb Learning Rule

TL;DR

This paper investigates phase transition phenomena in an oscillator neural network with Hebb learning, revealing its storage capacity, retrieval quality, and effects of asymmetry and coupling modifications.

Contribution

It provides a detailed analysis of phase transitions and storage capacity in oscillator networks using Hebb learning, with new insights into improving capacity through coupling modifications.

Findings

Storage capacity is approximately 0.042, better than previous models.

Retrieval quality is lower despite improved capacity.

Asymmetry in phase dynamics can accelerate network response.

Abstract

Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the network. By self-consistent signal-to-noise analysis (SCSNA), it was found that the storage capacity is given by $\alpha_c = 0.042$, which is better than that of Cook's model. However, the retrieval quality is worse. In addition, an investigation was made into an acceleration effect caused by asymmetry of the phase dynamics. Finally, it was numerically shown that the storage capacity can be improved by modifying the shape of the coupling function.