Synaptic plasticity alters the nature of chaos transition in neural networks

TL;DR

This paper introduces a new method to analyze how synaptic plasticity, especially Hebbian learning, changes the nature of chaos transitions in neural networks, revealing that learning can shift chaos onset from continuous to discontinuous.

Contribution

The study develops a neuron-synapse coupled quasi-potential method to demonstrate how different learning rules alter chaos transition types in neural networks.

Findings

Hebbian learning can change chaos transition from continuous to discontinuous.

Large Hebbian strength reduces the synaptic gain needed for chaos onset.

Feedback and homeostatic learning preserve chaos transition location and type.

Abstract

In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic properties of the coupled dynamics. Here, we develop the neuron-synapse coupled quasi-potential method to demonstrate how learning induces the qualitative change in macroscopic behaviors of recurrent neural networks. We find that under the Hebbian learning, a large Hebbian strength will alter the nature of the chaos transition, from a continuous type to a discontinuous type, where the onset of chaos requires a smaller synaptic gain compared to the non-plastic counterpart network. In addition, our theory predicts that under feedback and homeostatic learning, the location and type of chaos transition are retained, and only the chaotic fluctuation is adjusted. Our theoretical calculations are supported by numerical simulations.