Categorical Foundations of Explainable AI: A Unifying Theory

• URL: http://arxiv.org/abs/2304.14094v3
• Date: Sun, 17 Sep 2023 06:16:39 GMT
• Title: Categorical Foundations of Explainable AI: A Unifying Theory
• Authors: Pietro Barbiero, Stefano Fioravanti, Francesco Giannini, Alberto Tonda, Pietro Lio, Elena Di Lavore
• Abstract summary: 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, and (iv) analyze commonly overlooked aspects of explaining methods.
• Score: 8.637435154170916
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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