Our work runs from the mathematics of symmetry in neural networks to applications in the physical sciences and in medicine.
We work out how to build symmetry into neural networks: which group to use, how to share weights over it, and how to do so without giving up the speed and flexibility of a standard architecture. Encoding the symmetries of a problem is what buys data efficiency and lets a model generalize from far less.
We represent data as continuous fields rather than grids of samples, so a model no longer depends on resolution or sampling pattern. Our equivariant neural fields attach a pose to each latent, so the field transforms with the data and can be edited locally.
We build generative models for data that lives on manifolds and other structured spaces, mostly through flow matching. Riemannian variational flow matching, developed in our group, takes this onto curved spaces for material and protein design.
A graph is the natural encoding for relational data, but it records only pairwise connections. We lift message passing onto simplicial and cellular complexes so a network can act on higher-order interactions, and we study what such representations can and cannot tell apart.
We apply geometric deep learning across the sciences: molecular properties, peptide and protein structure, PDE forecasting, and wave travel times. Symmetry is the common thread, since the physics does not change when you rotate the coordinate frame.
An ECG and a cardiac MRI are two windows on the same underlying state, each showing a different part of it. We build representations of a subject's anatomy and function that stay faithful to that state, across cardiac MRI, ECG, histopathology slides, and retinal OCT.