Topological Sequences Connected With Inverse Graphs of Finite Flexible Weak Inverse Property Quasigroups: An Approach From Polynomials to Machine Learning

Abstract

Research on the confluence of algebra, graph theory, and machine learning has resulted in significant discoveries in mathematics, computer science, and artificial intelligence. Polynomial coefficients can be beneficial in machine learning. They indicate feature significance, nonlinear interactions, and error dynamics. Moreover, they empower models to extrapolate complex real-world data, facilitating tasks like regression, classification, optimized performance, and feature adaptation. The structural characteristics of flexible weak inverse property quasigroups are very close to the conventional group structures, and the class of these nonassociative groups plays an important role in real-time applications. This manuscript studies the relationship between topological sequences Tf and inverse graphs ΓCλ×Z3,⊙ of finite flexible weak inverse property quasigroups, and it presents a new computational framework with applications ranging from polynomials to machine learning. We define and analyze topological sequences based on the structural properties of quasi-inverse graphs. Polynomial representations are provided, allowing for a thorough algebraic approach of the topological properties of these graphs. In particular, the coefficients of these polynomials have been demonstrated to give important information for improving the predictive and explanatory capacity of machine learning models.