Geometric Deep Learning for Many-Particle and non Euclidean Systems

Across many areas of science, one is required to process data defined on irregular and non-Euclidean domains. For example, in particle physics, measurements in the LHC are highly variable particle collisions with cylindrical calorimeters, whereas the IceCube detector looks for neutrinos using an irregular 3d array of sensors. Despite such non-Euclidean structure, many of these tasks satisfy essential geometric priors, such as stability to deformations. In this talk, I will describe a broad family of neural architectures that leverage such geometric priors to learn efficient models with provable stability. I will also describe recent and current progress on several applications including particle physics and inverse problems.