Learning-rate dependent clustering and self-development in a network of coupled phase oscillators

TL;DR

This paper studies how the learning rate influences the formation of synchronized clusters in a Kuramoto model with Hebbian learning, revealing conditions for self-organization and memory-like pattern retention.

Contribution

It introduces a dynamic coupling model with a learning rate parameter, analyzing its impact on cluster formation and self-development in coupled oscillators.

Findings

Fast learning leads to multiple synchronized clusters and all-to-all connectivity.

Slow learning prevents the formation of multiple clusters and self-development.

The network can generate and recall stable patterns similar to memory processes.

Abstract

We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously co-active. Two stable synchronized clusters in anti-phase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that self-development of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.