Geometry-grounded Representation Learning and Generative Modeling

By recognizing that nearly all data is rooted in our physical world, and thus inherently grounded in geometry and physics, it becomes evident that learning systems should preserve this grounding throughout the process of representation learning in order to be meaningful. For example, preserving group transformation laws and symmetries through equivariant layers is crucial in domains such as computational physics, chemistry, robotics, and medical imaging. It leads to effective and generalizable architectures and improved data efficiency. Similarly, in generative models applied to non-Euclidean data spaces, maintaining the manifold structure is essential to obtain meaningful samples. Therefore, this workshop focuses on the principle of grounding in geometry, which we define as follows: A representation, method, or theory is grounded in geometry if it can be amenable to geometric reasoning, that is, it abides by the mathematics of geometry.