mlsanityData to 7 Oct 2026

Learning the Irreducible Representations of Commutative Lie Groups

arXiv 1402.4437 ↗First posted 18 Feb 2014cs.LGcited by 41

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Abstract (arXiv)

We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that is used to derive the elementary particles of a system from its symmetries. Our model employs a newfound Bayesian conjugacy relation that enables fully tractable probabilistic inference over compact commutative Lie groups -- a class that includes the groups that describe the rotation and cyclic translation of images. We train the model on pairs of transformed image patches, and show that the learned invariant representation is highly effective for classification.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Feb 2014.

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Citing papers per year: 2021: 8; 2022: 8; 2023: 13; 2024: 6; 2025: 5; 2026: 1.

41 papers.

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  1. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  2. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  3. 2021Self-Supervised Learning Disentangled Group Representation as Featurecited by 47
  4. 2021Commutative Lie Group VAE for Disentanglement Learningcited by 27
  5. 2022Symmetry-Based Representations for Artificial and Biological General Intelligencecited by 26
  6. 2021Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representationscited by 24
  7. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  8. 2023Steerers: A framework for rotation equivariant keypoint descriptorscited by 21
  9. 2022Bispectral Neural Networkscited by 17
  10. 2025Block-Recurrent Dynamics in Vision Transformerscited by 16
  11. 2022Unsupervised Learning of Equivariant Structure from Sequencescited by 15
  12. 2021Addressing the Topological Defects of Disentanglement via Distributed Operatorscited by 14
29 more
  1. 2024Symmetry Discovery Beyond Affine Transformationscited by 14
  2. 2023Neural Fourier Transform: A General Approach to Equivariant Representation Learningcited by 12
  3. 2024A Characterization Theorem for Equivariant Networks with Point-wise Activationscited by 9
  4. 2024How Deep Networks Learn Sparse and Hierarchical Data: the Sparse Random Hierarchy Modelcited by 7
  5. 2023A polar prediction model for learning to represent visual transformationscited by 6
  6. 2023Learning Lie Group Symmetry Transformations with Neural Networkscited by 6
  7. 2023A Unified Framework for Discovering Discrete Symmetriescited by 6
  8. 2021Hamiltonian latent operators for content and motion disentanglement in image sequencescited by 5
  9. 2022How deep convolutional neural networks lose spatial information with trainingcited by 5
  10. 2021Learning Identity-Preserving Transformations on Data Manifoldscited by 4
  11. 2023CRIN: Rotation-Invariant Point Cloud Analysis and Rotation Estimation via Centrifugal Reference Framecited by 4
  12. 2023Disentanglement Learning via Topologycited by 4
  13. 2022On Non-Linear operators for Geometric Deep Learningcited by 3
  14. 2023A Category-theoretical Meta-analysis of Definitions of Disentanglementcited by 3
  15. 2025A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEscited by 3
  16. 2025Discovering Symmetry Groups with Flow Matchingcited by 3
  17. 2023Learning Internal Representations of 3D Transformations from 2D Projected Inputscited by 2
  18. 2023Enriching Disentanglement: From Logical Definitions to Quantitative Metricscited by 2
  19. 2024Separation Power of Equivariant Neural Networkscited by 2
  20. 2025A group-theoretic framework for machine learning in hyperbolic spacescited by 2
  21. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  22. 2021FILTRA: Rethinking Steerable CNN by Filter Transformcited by 1
  23. 2024Kuramoto Oscillators and Swarms on Manifolds for Geometry Informed Machine Learningcited by 1
  24. 2022Invariance-adapted decomposition and Lasso-type contrastive learningcited by 0
  25. 2022Commutativity and Disentanglement from the Manifold Perspectivecited by 0
  26. 2023Equivariant Representation Learning in the Presence of Stabilizerscited by 0
  27. 2023Learning Linear Groups in Neural Networkscited by 0
  28. 2024Rethinking Disentanglement under Dependent Factors of Variationcited by 0
  29. 2026Spectral Discovery of Continuous Symmetries via Generalized Fourier Transformscited by 0