Geometric Deep Learning Extends AI Beyond Flat Grids to Graphs and 3D Structures

Deep learning has long relied on flat grids, such as image pixels and text sequences, which fit CNNs and Transformers well. Many real-world systems, including molecules, social networks, protein structures, and 3D point clouds, are irregular and non-Euclidean, so forcing them into grids can discard important spatial and topological information. Geometric Deep Learning addresses this by building neural operations around mathematical symmetries and geometric transformations, using Graph Neural Networks for relational data and manifold or equivariant networks for curved and 3D spatial domains. Applications highlighted include autonomous driving perception from LiDAR point clouds and detecting multi-account money laundering in financial transaction graphs. Proponents argue the approach offers the mathematical foundation needed for AI in physical sciences and spatial computing.