Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformers
arxiv(2023)
摘要
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, but has a smaller symmetry group and is not as sample-efficient, while
the projective model is not sufficiently expressive. Both the conformal algebra
and an improved version of the projective algebra define powerful, performant
architectures.
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