MaGyQ · Machine learning models via differential Geometry and Quantum theory

New machine learning advancements call for new mathematical modelling of algorithms towards interpretability and explainability. In this project we develop foundational mathematical techniques in geometric deep learning and information geometry synergically combining methods of symplectic geometry, deformation quantization and noncommutative geometry. We provide new effective geometric models for the parameter space of deep learning algorithms. We also focus on the discrete realizations of such modelling tackling Laplacians on graphs extending our investigation to graph neural networks and geometric deep learning, towards the key EU priorities of Horizon Europe.