Learning Irreducible Representations of Noncommutative Lie Groups
Authors: Noah Shutty, Casimir Wierzynski
Keywords: equivariance, object tracking, equivariant neural networks, deep learning, point cloud, lie group, lie algebra, lorentz group, poincaré group
Abstract: Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit group representations to derive the equivariant kernels and nonlinearities. We present two contributions motivated by frontier applications of equivariance beyond rotations and translations. First, we relax the requirement for explicit Lie group representations, presenting a novel algorithm that finds irreducible representations of noncommutative Lie groups given only the structure constants of the associated Lie algebra. Second, we demonstrate that Lorentz-equivariance is a useful prior for object-tracking tasks and construct the first object-tracking model equivariant to the Poincaré group.