mlsanityData to 14 Oct 2026

How Jellyfish Characterise Alternating Group Equivariant Neural Networks

arXiv 2301.10152 ↗First posted 24 Jan 2023cs.LG math.CO math.RTcited by 5

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Abstract (arXiv)

We provide a full characterisation of all of the possible alternating group (An) equivariant neural networks whose layers are some tensor power of ℝn. In particular, we find a basis of matrices for the learnable, linear, An-equivariant layer functions between such tensor power spaces in the standard basis of ℝn. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 12 of its 30 references that are in the map. First posted on arXiv 24 Jan 2023.

Builds on

12 of 30 references.

References · 12

  1. 2017Deep Setscited by 1,421
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2018Invariant and Equivariant Graph Networkscited by 346
  4. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  5. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  6. 2019On the Universality of Invariant Networkscited by 152
  7. 2020On Learning Sets of Symmetric Elementscited by 98
  8. 2019Orientation-aware Semantic Segmentation on Icosahedron Spherescited by 53
  9. 2020Universal Equivariant Multilayer Perceptronscited by 49
  10. 2022What is an equivariant neural network?cited by 21
  11. 2022Brauer's Group Equivariant Neural Networkscited by 17
  12. 2022Connecting Permutation Equivariant Neural Networks and Partition Diagramscited by 9

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Cited by year

Citing papers per year: 2023: 4; 2024: 1.

5 papers.

  1. 2023Graph Automorphism Group Equivariant Neural Networkscited by 4
  2. 2023Categorification of Group Equivariant Neural Networkscited by 2
  3. 2024Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representationscited by 2
  4. 2023An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layerscited by 1
  5. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0