אירועים והרצאות בפקולטה למדעי המחשב ע"ש הנרי ומרילין טאוב

Classical approaches to geometric differential invariants begin by specifying a transformation group, analytically deriving the corresponding invariant differential quantities, and constructing numerical schemes to approximate them. This work takes a data-driven perspective and introduces a self-supervised deep learning framework for learning group-equivariant semi-local geometric operators directly from point samples of planar curves. Specifically, we train a neural network to act as a discrete differentiation operator. Remarkably, the learned operator behaves as a discrete approximation to differentiation with respect to the corresponding group-invariant arc length. The framework requires no fixed parameterization and remains robust under non-uniform sampling and noise. Experiments demonstrate that the learned operators generalize across a wide range of curve geometries and successfully handle line-preserving transformation groups, including the Euclidean, similarity and equi-affine groups. The learned differential operators transfer directly to downstream shape-analysis tasks without retraining. The resulting framework is a data-driven foundation for approximating geometric invariants from discrete observations.