Hierarchical Neural Networks, p-Adic PDEs, and Applications to Image Processing

TL;DR

This paper introduces a new p-adic reaction-diffusion neural network with delay, analyzes its stability, and reviews its applications to image processing, highlighting novel mathematical and computational approaches.

Contribution

It presents a novel p-adic neural network model with delay and offers a stability analysis along with a comprehensive review of p-adic neural networks in image processing.

Findings

Stability conditions for the new neural network model

Numerical simulations demonstrating network responses

Overview of p-adic neural networks in image applications

Abstract

The first goal of this article is to introduce a new type of p-adic reaction-diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of p-adic cellular neural networks and their applications to image processing.