Categorical Foundations of Explainable AI: A Unifying Theory

TL;DR

This paper introduces a rigorous mathematical framework for explainable AI using Category theory, providing formal definitions, modeling capabilities, and a foundation for ethical and reliable AI explanations.

Contribution

It offers the first formal, category-theoretic definitions of key XAI concepts, unifying and advancing the theoretical understanding of explainability.

Findings

Formal categorical definitions of explanation and XAI processes

Modeling of existing learning architectures within the framework

Enhanced theoretical basis for XAI taxonomies

Abstract

Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation" which still lacks a precise definition. To bridge this gap, this paper presents the first mathematically rigorous definitions of key XAI notions and processes, using the well-funded formalism of Category theory. We show that our categorical framework allows to: (i) model existing learning schemes and architectures, (ii) formally define the term "explanation", (iii) establish a theoretical basis for XAI taxonomies, and (iv) analyze commonly overlooked aspects of explaining methods. As a consequence, our categorical framework promotes the ethical and secure deployment of AI technologies as it represents a significant step towards a sound theoretical foundation of explainable AI.