mlsanityData to 7 Oct 2026

Universal Equivariant Multilayer Perceptrons

arXiv 2002.02912 ↗First posted 7 Feb 2020cs.LG cs.NE math.GRcited by 49

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Abstract (arXiv)

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant MLPs with a single hidden layer. In particular, it is shown that having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance). A corollary is unconditional universality of equivariant MLPs for Abelian groups, such as CNNs with a single hidden layer. A second corollary is the universality of equivariant MLPs with a high-order hidden layer, where we give both group-agnostic bounds and means for calculating group-specific bounds on the order of hidden layer that guarantees universal equivariance (invariance).

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 11; 2023: 10; 2024: 6; 2025: 9; 2026: 7.

49 papers.

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  1. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  2. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  3. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  4. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  5. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  6. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  7. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 27
  8. 2023E(2)-Equivariant Vision Transformercited by 27
  9. 2024A Canonicalization Perspective on Invariant and Equivariant Learningcited by 25
  10. 2022A PAC-Bayesian Generalization Bound for Equivariant Networkscited by 17
  11. 2021Equivariant Networks for Pixelized Spherescited by 16
  12. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11
37 more
  1. 2022Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groupscited by 11
  2. 2022Implicit Convolutional Kernels for Steerable CNNscited by 9
  3. 2024A Characterization Theorem for Equivariant Networks with Point-wise Activationscited by 9
  4. 2022Deep Neural Network Approximation of Invariant Functions through Dynamical Systemscited by 8
  5. 2021Universal approximation and model compression for radial neural networkscited by 7
  6. 2026Identifiable Equivariant Networks are Layerwise Equivariantcited by 7
  7. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  8. 2023A Unified Framework for Discovering Discrete Symmetriescited by 6
  9. 2022A Classification of G-invariant Shallow Neural Networkscited by 5
  10. 2023How Jellyfish Characterise Alternating Group Equivariant Neural Networkscited by 5
  11. 2025Rotation Equivariant Arbitrary-scale Image Super-Resolutioncited by 5
  12. 2023Graph Automorphism Group Equivariant Neural Networkscited by 4
  13. 2025Symmetry-Aware Generative Modeling through Learned Canonicalizationcited by 4
  14. 2025On Universality Classes of Equivariant Networkscited by 4
  15. 2025On Universality of Deep Equivariant Networkscited by 3
  16. 2026Vanilla Group Equivariant Vision Transformer: Simple and Effectivecited by 3
  17. 2021Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?cited by 2
  18. 2023Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representationscited by 2
  19. 2023Neural Discovery of Permutation Subgroupscited by 2
  20. 2024Symmetries in Overparametrized Neural Networks: A Mean-Field Viewcited by 2
  21. 2024Separation Power of Equivariant Neural Networkscited by 2
  22. 2025A unified framework for establishing the universal approximation of transformer-type architecturescited by 2
  23. 2022A tradeoff between universality of equivariant models and learnability of symmetriescited by 1
  24. 2024Optimal Symmetries in Binary Classificationcited by 1
  25. 2025TeleLoRA: Teleporting Model-Specific Alignment Across LLMscited by 1
  26. 2026Rotation Equivariant Mamba for Vision Taskscited by 1
  27. 2022Design equivariant neural networks for 3D point cloudcited by 0
  28. 2023Invariant Layers for Graphs with Nodes of Different Typescited by 0
  29. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  30. 2024Decomposition of Equivariant Maps via Invariant Maps: Application to Universal Approximation under Symmetrycited by 0
  31. 2025FS-KAN: Permutation Equivariant Kolmogorov-Arnold Networks via Function Sharingcited by 0
  32. 2025If you can distinguish, you can express: Galois theory, Stone--Weierstrass, machine learning, and linguisticscited by 0
  33. 2025Drawback of Enforcing Equivariance and its Compensation via the Lens of Expressive Powercited by 0
  34. 2026A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of O(2)cited by 0
  35. 2026No Equivariant Architecture Covers All Equivariant Attentioncited by 0
  36. 2026Graded Representation Theory of Equivariant Neural Networkscited by 0
  37. 2026Transversal Pooling Neural Networkscited by 0