Approximate Synchronization of Memristive Hopfield Neural Networks

TL;DR

This paper introduces a new concept of approximate synchronization for memristive Hopfield neural networks, demonstrating robust convergence properties and extending the results to networks with Hebbian learning rules for unsupervised training.

Contribution

It proposes and rigorously analyzes the concept of approximate synchronization in memristive Hopfield neural networks, including explicit conditions for convergence and extensions to learning rules.

Findings

Global solution dynamics are robustly dissipative.

Approximate synchronization occurs under explicit threshold conditions.

Results extend to networks with Hebbian learning rules.

Abstract

Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this paper a new concept of approximate synchronization is proposed and investigated for Hopfield neural networks coupled with nonlinear memristors. It is proved that global solution dynamics are robustly dissipative and a sharp ultimate bound is acquired. Through \emph{a priori} uniform estimates on the interneuron differencing equations, it is rigorously shown that approximate synchronization to any prescribed small gap at an exponential convergence rate of the memristive Hopfield neural networks occurs if an explicitly computable threshold condition is satisfied by the interneuron coupling strength coefficient. The main result is further extended to memristive Hopfield neural networks with Hebbian learning rules for a broad range of applications in unsupervised train learning.