Global Convergence of Analytic Neural Networks with Event-triggered Synaptic Feedbacks

TL;DR

This paper proves the stability of a general class of analytic neural networks with event-triggered synaptic feedback, reducing communication frequency while maintaining convergence, and verifies the results through numerical examples.

Contribution

It introduces a novel event-triggered rule for neural networks that ensures stability and reduces communication, including a proof of convergence using the Łojasiewicz inequality.

Findings

Neural networks remain stable under the event-triggered rule.

The event-triggered rule reduces information transmission frequency.

Numerical examples demonstrate the network's optimization capabilities.

Abstract

In this paper, we investigate convergence of a class of analytic neural networks with event-triggered rule. This model is general and include Hopfield neural network as a special case. The event-trigger rule efficiently reduces the frequency of information transmission between synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of its neighbours at its latest triggering time but changes until the next triggering time of this neuron that is determined by certain criterion via its neighborhood information. It is proved that the analytic neural network is completely stable under this event-triggered rule. The main technique of proof is the ${\L}$ojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the optimisation capability of the network dynamics.