Geometric Representation Learning

The field studies how to represent data whose structure is not well described by ordinary flat vectors, including point clouds, graphs, molecules, shapes, and signals. Approaches include rotation- and group-equivariant networks, learning directly on Riemannian, spherical, or hyperbolic spaces, and using geodesic distances, curvature, or spectral structure to guide training. These methods aim to preserve meaningful geometry so models can generalize across changes in viewpoint, sampling, or domain, with applications from 3D perception and robotics to biology and medical imaging. A central challenge is choosing geometry that fits the task: explicit geometric constraints can improve robustness and data efficiency, but may add computational cost or hinder downstream learning when the chosen structure is mismatched.