Enhanced Error-free Retrieval in Kuramoto-type Associative-memory Networks via Two-memory Configuration

TL;DR

This paper enhances error-free pattern retrieval in Kuramoto-type associative-memory networks by introducing a two-memory configuration and stability analysis, significantly improving retrieval accuracy and robustness for various pattern sets.

Contribution

It proposes a novel two-memory configuration and stability analysis method that guarantees error-free retrieval in Kuramoto-type associative-memory networks.

Findings

The two-memory setup reduces stable patterns and enlarges basins.

Stability analysis determines critical parameters for pattern distinction.

Numerical simulations confirm improved retrieval accuracy.

Abstract

We study the associative-memory network of Kuramoto-type oscillators that stores a set of memorized patterns (memories). In [Phys. Rev. Lett., 92 (2004), 108101], Nishikawa, Lai and Hoppensteadt showed that the capacity of this system for pattern retrieval with small errors can be made as high as that of the Hopfield network. Some stability analysis efforts focus on mutually orthogonal memories; however, the theoretical results do not ensure error-free retrieval in general situations. In this paper, we present a route for using the model in pattern retrieval problems with small or large errors. We employ the eigenspectrum analysis of Jacobians and potential analysis of the gradient flow to derive the stability/instability of binary patterns. For two memories, the eigenspectrum of Jacobian at each pattern can be specified, which enables us to give the critical value of the parameter to distinguish the memories from all other patterns in stability. This setting of two memories substantially reduces the number of stable patterns and enlarges their basins, allowing us to recover defective patterns. We extend this approach to general cases and present a deterministic method for ensuring error-free retrieval across a general set of standard patterns. Numerical simulations and comparative analyses illustrate the approach.