Innovative Models Based on Geometric Calculus for Explainable Artificial Intelligence

Traditional data-driven machine learning approaches show very high performance even if their internal mechanisms are very cryptic (“black-box” models). However, in some critical contexts, model interpretability is mandatory to explain the learned functionality, becoming even a legal requirement. The emerging field of eXplainable Artificial Intelligence (XAI) aims at developing new methods to make AI technologies more transparent. This work explores the relevant role that geometric calculus, based on Clifford geometric algebra, can play in obtaining more interpretable AI systems. We outline state-of-the-art innovative approaches that exploit geometric calculus to reformulate neural network models. Leveraging the simplicity and intuitiveness of the underlying mathematical framework, these sys-tems allow for clear geometric interpretations of their decision-making processes, while preserving prediction accuracy. Our investigations suggest that empowering deep learning models with geometric calculus capabilities paves the way for both intrinsically interpretable and high-performance AI systems.