mlsanityData to 7 Oct 2026

Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebras

arXiv 2303.07157 ↗First posted 13 Mar 2023math.RT cs.AIcited by 1

Not on the map. Why?

Abstract (arXiv)

We develop an elementary method to compute spaces of equivariant maps from a homogeneous space G/H of a Lie group G to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant sections in homogeneous vector bundles, and take a special interest in the case where the fibres are algebras. These latter cases have a natural global algebra structure. We classify these automorphic algebras for the case where the homogeneous space has compact stabilisers. This work has applications in the theoretical development of geometric deep learning and also in the theory of automorphic Lie algebras.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 12 of its 38 references that are in the map. First posted on arXiv 13 Mar 2023.

Builds on

12 of 38 references.

References · 12

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2019General E(2)-Equivariant Steerable CNNscited by 441
  3. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  4. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  5. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  7. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  8. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  9. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  10. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  11. 2021Homogeneous vector bundles and G-equivariant convolutional neural networkscited by 21
  12. 2019Covariance in Physics and Convolutional Neural Networkscited by 12

Built on by

Cited by year

Citing papers per year: 2024: 1.

1 paper.

  1. 2024Equivariant Manifold Neural ODEs and Differential Invariantscited by 2