mlsanityData to 7 Oct 2026

The general theory of permutation equivarant neural networks and higher order graph variational encoders

arXiv 2004.03990 ↗First posted 8 Apr 2020cs.LG stat.MLcited by 28

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Abstract (arXiv)

Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Apr 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 7; 2023: 6; 2024: 6; 2025: 3; 2026: 2.

28 papers.

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  1. 2023Permutation Equivariant Neural Functionalscited by 69
  2. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  3. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  4. 2023Neural Functional Transformerscited by 50
  5. 2021Autobahn: Automorphism-based Graph Neural Netscited by 39
  6. 2021Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atzecited by 29
  7. 2024Universal Neural Functionalscited by 25
  8. 2021Multiresolution Equivariant Graph Variational Autoencodercited by 20
  9. 2022Temporal Multiresolution Graph Neural Networks For Epidemic Predictioncited by 11
  10. 2022Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solverscited by 10
  11. 2022Connecting Permutation Equivariant Neural Networks and Partition Diagramscited by 9
  12. 2024Steerable Transformers for Volumetric Datacited by 8
16 more
  1. 2023Fast computation of permutation equivariant layers with the partition algebracited by 7
  2. 2023A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networkscited by 6
  3. 2022Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalismcited by 3
  4. 2025Graph Counterfactual Explainable AI via Latent Space Traversalcited by 3
  5. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  6. 2023P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networkscited by 2
  7. 2024Interpreting Equivariant Representationscited by 2
  8. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  9. 2024Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representationscited by 2
  10. 2022Equivariant neural networks for recovery of Hadamard matricescited by 1
  11. 2026EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusioncited by 1
  12. 2021Symmetry-aware Neural Architecture for Embodied Visual Navigationcited by 0
  13. 2023Target-aware Variational Auto-encoders for Ligand Generation with Multimodal Protein Representation Learningcited by 0
  14. 2024Range-aware Positional Encoding via High-order Pretraining: Theory and Practicecited by 0
  15. 2025Permutation Equivariant Neural Networks for Symmetric Tensorscited by 0
  16. 2026Eigenvalues of the Hessian in Deep Learning: The Origin of Symmetry and Its Breakingcited by 0