A New Kind of Hopfield Networks for Finding Global Optimum

TL;DR

This paper introduces a novel Hopfield network with modified difference equations that implement an advanced optimization algorithm, aiming to reliably find global optima instead of getting trapped in local minima.

Contribution

It proposes a new set of difference equations for Hopfield networks that directly encode a powerful optimization algorithm to improve global convergence.

Findings

Enhanced ability to find global optima

Reduced sensitivity to initial conditions

Faster convergence to solutions

Abstract

The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation of a Hopfield network, defined by a set of difference equations, can easily be trapped into one local optimum or another, sensitive to initial conditions, perturbations, and neuron update orders. It doesn't know how long it will take to converge, as well as if the final solution is a global optimum, or not. In this paper, we present a Hopfield network with a new set of difference equations to fix those problems. The difference equations directly implement a new powerful optimization algorithm.