A note on the complex and bicomplex valued neural networks

TL;DR

This paper extends the perceptron convergence proof from complex-valued neural networks to bicomplex-valued neural networks, advancing the theoretical understanding of neural networks based on bicomplex algebra.

Contribution

It formulates and proves the perceptron convergence algorithm for bicomplex multivalued neural networks, filling a gap in the theoretical framework.

Findings

Proof of perceptron convergence for CMVNNs

Formulation of perceptron convergence for BMVNNs

Theoretical results on bicomplex neural networks

Abstract

In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra.