Speaker: David Ruhe (University of Amsterdam)

Session Chair: Erik Bekkers (University of Amsterdam)

Abstract: In this talk, I will present Clifford Group Equivariant Neural Networks, an innovative method for building E(n)-equivariant networks based on Clifford (geometric) algebras. First, I will give an introduction to the Clifford algebra and its geometric applications. Then, I will introduce the Clifford group and how it always acts through the orthogonal group. As such, a parameterization that is equivariant to the Clifford group will automatically be equivariant to the orthogonal group of, e.g., rotations and reflections. We show that any polynomial (under the algebra’s geometric product) is such a parameterization.  We propose several layers from these insights and conduct experiments in three-, four-, and five-dimensional spaces. One of these experiments even includes equivariance to the nondefinite O(1,3) Lorentz group from the same code implementation. Finally, I will provide guidance on how to utilize our codebase for implementing these algorithms.