mlsanityData to 7 Oct 2026

What is an equivariant neural network?

arXiv 2205.07362 ↗First posted 15 May 2022cs.LG math.RT stat.MLcited by 21

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Abstract (arXiv)

We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of equivariance or neural networks. The basic mathematical ideas are simple but are often obscured by engineering complications that come with practical realizations. We extract and focus on the mathematical aspects, and limit ourselves to a cursory treatment of the engineering issues at the end.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 11 of its 25 references that are in the map. First posted on arXiv 15 May 2022.

Builds on

11 of 25 references.

References · 11

  1. 2017Deep Setscited by 1,394
  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  4. 2019Making Convolutional Networks Shift-Invariant Againcited by 390
  5. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  8. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
  9. 2019On the Universality of Invariant Networkscited by 151
  10. 2019Deep neural network solution of the electronic Schr"odinger equationcited by 124
  11. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 7; 2024: 5; 2025: 3; 2026: 2.

21 papers.

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  1. 2025An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networkscited by 19
  2. 2022Brauer's Group Equivariant Neural Networkscited by 17
  3. 2022Connecting Permutation Equivariant Neural Networks and Partition Diagramscited by 9
  4. 2023Any-dimensional equivariant neural networkscited by 8
  5. 2023A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networkscited by 6
  6. 2023How Jellyfish Characterise Alternating Group Equivariant Neural Networkscited by 5
  7. 2023Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groupscited by 5
  8. 2023Graph Automorphism Group Equivariant Neural Networkscited by 4
  9. 2024Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physicscited by 4
  10. 2024Equivariant neural networks and piecewise linear representation theorycited by 3
  11. 2022Split personalities in Bayesian Neural Networks: the case for full marginalisationcited by 1
  12. 2022VC dimensions of group convolutional neural networkscited by 1
9 more
  1. 2024A large language model-type architecture for high-dimensional molecular potential energy surfacescited by 1
  2. 2023Discrete neural nets and polymorphic learningcited by 0
  3. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  4. 2024CNN-based Compressor Mass Flow Estimator in Industrial Aircraft Vapor Cycle Systemcited by 0
  5. 2024Lie-Equivariant Quantum Graph Neural Networkscited by 0
  6. 2025Precoder Learning by Leveraging Unitary Equivariance Propertycited by 0
  7. 2025Feature Shift Localization Networkcited by 0
  8. 2026Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentialscited by 0
  9. 2026REViT: Roto-reflection Equivariant Convolutional Vision Transformercited by 0