mlsanityData to 7 Oct 2026

Compact Matrix Quantum Group Equivariant Neural Networks

arXiv 2311.06358 ↗First posted 10 Nov 2023cs.LG math.CO math.CTcited by 0

Not on the map. Why?

Abstract (arXiv)

Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning from data that lives in a non-commutative geometry, described formally by non-commutative C*-algebras, since the C*-algebra of continuous functions on a compact matrix group is commutative. To address this limitation, we derive the existence of a new type of equivariant neural network, called compact matrix quantum group equivariant neural networks, which encode symmetries that are described by compact matrix quantum groups. We characterise the weight matrices that appear in these neural networks for the easy compact matrix quantum groups, which are defined by set partitions. As a result, we obtain new characterisations of equivariant weight matrices for some compact matrix groups that have not appeared previously in the machine learning literature.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 24 of its 80 references that are in the map. First posted on arXiv 10 Nov 2023.

Builds on

24 of 80 references.

References · 24

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2017Deep Setscited by 1,394
  3. 2016Group Equivariant Convolutional Networkscited by 1,154
  4. 2021E(n) Equivariant Graph Neural Networkscited by 951
  5. 2018Invariant and Equivariant Graph Networkscited by 339
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  7. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
  8. 2019On the Universality of Invariant Networkscited by 151
  9. 2017Equivariance Through Parameter-Sharingcited by 139
  10. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  11. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  12. 2020On Learning Sets of Symmetric Elementscited by 97
12 more
  1. 2023Clifford Group Equivariant Neural Networkscited by 54
  2. 2020Universal Equivariant Multilayer Perceptronscited by 49
  3. 2023Geometric Clifford Algebra Networkscited by 37
  4. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 26
  5. 2022What is an equivariant neural network?cited by 21
  6. 2022Brauer's Group Equivariant Neural Networkscited by 17
  7. 2022C^*-algebra Net: A New Approach Generalizing Neural Network Parameters to C^*-algebracited by 9
  8. 2022Connecting Permutation Equivariant Neural Networks and Partition Diagramscited by 9
  9. 2023Fast computation of permutation equivariant layers with the partition algebracited by 7
  10. 2023How Jellyfish Characterise Alternating Group Equivariant Neural Networkscited by 5
  11. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  12. 2023Categorification of Group Equivariant Neural Networkscited by 2

Built on by

Not cited yet.