Maria Esteban Casadevall

The project aims to develop new equivariant deep learning frameworks that integrate geometric and topological principles into AI models. It would seek to derive optimal geometry-grounded representations and their theoretical properties. These representations will guarantee that networks satisfy geometric constraints, such as imposed physical laws. In particular, we will develop theory and methods for infering them from observations, evaluate their computational fit for geometric reasoning, and explore practical implications. This will provide AI systems with a built-in structure, enabling more reliable, data-efficient, and interpretable representations of real-world phenomena.