This WP will address key challenges in modern machine learning, with a focus on topological data analysis (TDA), graph neural networks (GNN) and the integration of sheaf neural networks (SNN) with a physically informed neural network (PINN) architecture. This WP will also study generative models such as Riemannian flow-matching focussing on symmetric spaces (link with WP1), leveraging the theoretical insights and mathematical structures developed in WP1. Input from the WP2 themes on information geometry will be critical. The proposed methodologies will be validated on questions and real-world datasets coming from concrete applications from the non-academic partners.