Novel Complex-Valued Hopfield Neural Networks with Phase and Magnitude Quantization

TL;DR

This paper presents two innovative complex-valued Hopfield neural networks that utilize phase and magnitude quantization, significantly increasing the number of states and potential applications compared to existing models.

Contribution

Introduction of two novel CvHNN architectures with phase and magnitude quantization using ceiling-type activation functions in different coordinate systems.

Findings

Increased number of states in the proposed CvHNNs.

Enhanced potential applications for complex-valued neural networks.

Novel activation functions based on coordinate representations.

Abstract

This research paper introduces two novel complex-valued Hopfield neural networks (CvHNNs) that incorporate phase and magnitude quantization. The first CvHNN employs a ceiling-type activation function that operates on the rectangular coordinate representation of the complex net contribution. The second CvHNN similarly incorporates phase and magnitude quantization but utilizes a ceiling-type activation function based on the polar coordinate representation of the complex net contribution. The proposed CvHNNs, with their phase and magnitude quantization, significantly increase the number of states compared to existing models in the literature, thereby expanding the range of potential applications for CvHNNs.