Continuous-Valued Octonionic Hopfield Neural Network

Abstract

In this paper, we generalize the famous Hopfield neural network to unit octonions. In the proposed model, referred to as the continuous-valued octonionic Hopfield neural network (CV-OHNN), the next state of a neuron is obtained by setting its octonionic activation potential to length one. We show that, like the traditional Hopfield network, a CV-OHNN operating in an asynchronous update mode always settles down to an equilibrium state under mild conditions on the octonionic synaptic weights.