mlsanityData to 7 Oct 2026

Connecting Permutation Equivariant Neural Networks and Partition Diagrams

arXiv 2212.08648 ↗First posted 16 Dec 2022cs.LG math.CO math.RTcited by 9

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Abstract (arXiv)

Permutation equivariant neural networks are often constructed using tensor powers of ℝn as their layer spaces. We show that all of the weight matrices that appear in these neural networks can be obtained from Schur-Weyl duality between the symmetric group and the partition algebra. In particular, we adapt Schur-Weyl duality to derive a simple, diagrammatic method for calculating the weight matrices themselves.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 6 of its 44 references that are in the map. First posted on arXiv 16 Dec 2022.

Builds on

6 of 44 references.

References · 6

  1. 2017Deep Setscited by 1,394
  2. 2018Invariant and Equivariant Graph Networkscited by 339
  3. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  4. 2018Deep Models of Interactions Across Setscited by 68
  5. 2020The general theory of permutation equivarant neural networks and higher order graph variational encoderscited by 28
  6. 2022What is an equivariant neural network?cited by 21

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Cited by year

Citing papers per year: 2023: 6; 2024: 2; 2025: 1.

9 papers.

  1. 2023Fast computation of permutation equivariant layers with the partition algebracited by 7
  2. 2023How Jellyfish Characterise Alternating Group Equivariant Neural Networkscited by 5
  3. 2023Graph Automorphism Group Equivariant Neural Networkscited by 4
  4. 2023Categorification of Group Equivariant Neural Networkscited by 2
  5. 2024Separation Power of Equivariant Neural Networkscited by 2
  6. 2024Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representationscited by 2
  7. 2023An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layerscited by 1
  8. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  9. 2025Permutation Equivariant Neural Networks for Symmetric Tensorscited by 0