Computing Representations for Lie Algebraic NetworksDownload PDF

Published: 07 Nov 2022, Last Modified: 05 May 2023NeurReps 2022 OralReaders: Everyone
Keywords: Lie Groups, Group Representations, Equivariance, Object Tracking
TL;DR: Present a solver for representations of arbitrary Lie groups and use it to build Poincaré-equivariant networks for object tracking.
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 Lie group representations to derive the equivariant kernels and nonlinearities. We present three contributions motivated by frontier applications of equivariance beyond rotations and translations. First, we relax the requirement for explicit Lie group representations with a novel algorithm that finds representations of arbitrary Lie groups given only the structure constants of the associated Lie algebra. Second, we provide a self-contained method and software for building Lie group-equivariant neural networks using these representations. Third, we contribute a novel benchmark dataset for classifying objects from relativistic point clouds, and apply our methods to construct the first object-tracking model equivariant to the Poincaré group.
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