Unifying Renormalization with Markov Categories

Abstract

This paper explores a novel approach for modeling renormalization processes using Markov categories, a formalism rooted in category theory. By leveraging the abstraction provided by Markov categories, we aim to provide a coherent framework that bridges stochastic processes with renormalization theory, potentially enhancing the interpretability and application of these crucial transformations. Our study elucidates theoretical insights, outlines computational benefits, and suggests interdisciplinary applications, espe cially in conjunction with machine learning methodologies. Key comparisons with existing models highlight the advantages in terms of flexibility and abstraction.