HyperXAI

The HyperXAI project investigates the mathematical foundations of explainable artificial intelligence (XAI) for hypercomplex neural networks (HvNN). While the rapid expansion of artificial neural networks (ANNs), particularly deep learning, has produced major advances in fields such as image recognition and natural language processing, the reasoning behind their decisions often remains opaque. This challenge becomes even more critical when models deal with complex data structures such as colour information, multidimensional signals, or higher-order spatial relations. Hypercomplex neural networks—based on algebras such as complex numbers, quaternions, and Cayley–Dickson extensions—offer promising solutions, yet systematic approaches to their explainability are still at an early stage. HyperXAI addresses this gap by integrating advanced mathematics with physics-inspired methodologies to develop rigorous frameworks for explainability and trustworthiness in HvNN. The project will design novel XAI methods tailored to hypercomplex architectures, validate them on synthetic and publicly available benchmark datasets across multiple data modalities, and propose a unified framework for HvNN interpretability. By embedding explainability directly into HvNN models, HyperXAI will enhance transparency, reproducibility, and reliability. Beyond methodological advances, the project will build a sustainable international network of researchers from Poland, Spain, Czechia, Latvia, Azerbaijan, Türkiye, Iraq, South Korea, and Brazil, representing diverse traditions in mathematics, physics, and computer science. Through staff exchanges, joint research, training schools, and open science practices, HyperXAI will strengthen interdisciplinary expertise and foster the development of a new generation of researchers. By consolidating the theoretical and computational basis of explainability for HvNN, the project will stimulate the adoption of hypercomplex XAI within the global scientific comm