Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformers

arXiv:2311.04744v2 Announce Type: replace
Abstract: The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer architecture given any geometric (or Clifford) algebra. We study versions of this architecture for Euclidean, projective, and conformal algebras, all of which are suited to represent 3D data, and evaluate them in theory and practice. The simplest Euclidean architecture is computationally cheap, …

abstract algebra architecture arxiv construct cs.ai cs.lg deep learning scalable study transformer transformer architecture transformers type versions