Tropical Dynamic Networks: Tropical Eigenvalues and Eigenvectors for Nonlinear Systems and Dynamic Topology of Virtual Spaces

Introduction

As deep learning continues to shape modern artificial intelligence, the ability to model non-linear systems has become more crucial, particularly in dynamic environments where relationships between data points evolve over time. While Convolutional Neural Networks (CNNs) have excelled in tasks such as image classification, they face limitations when tackling highly non-linear and dynamic systems.

In this blog, we take a deep dive into creating an ensemble model that integrates CNNs with a Tropical Dynamic Network, leveraging the powerful concepts of Tropical Algebra. We will explore:

• Tropical Algebra, including tropical eigenvalues and tropical eigenvectors, and how they differ from their classical counterparts.
• The concept of Dynamic Topology in virtual spaces, where the relationships between elements evolve over time.
• Combining these powerful ideas into an ensemble model that incorporates both CNN’s spatial learning capabilities and the non-linear, dynamic properties modelled by the tropical dynamic network.
• The mathematical theorems that provide the foundation for tropical algebra…