Categorical Foundations of Explainable AI

  • Barbiero P
  • Fioravanti S
  • Giannini F
  • et al.
ArXiv: 2304.14094
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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 ``\textit{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.




Barbiero, P., Fioravanti, S., Giannini, F., Tonda, A., Lio, P., & Di Lavore, E. (2023). Categorical Foundations of Explainable AI. Retrieved from

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