mlsanityData to 7 Oct 2026

Neural Fourier Transform: A General Approach to Equivariant Representation Learning

arXiv 2305.18484 ↗First posted 29 May 2023stat.ML cs.LGcited by 12

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Abstract (arXiv)

Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We propose Neural Fourier Transform (NFT), a general framework of learning the latent linear action of the group without assuming explicit knowledge of how the group acts on data. We present the theoretical foundations of NFT and show that the existence of a linear equivariant feature, which has been assumed ubiquitously in equivariance learning, is equivalent to the existence of a group invariant kernel on the dataspace. We also provide experimental results to demonstrate the application of NFT in typical scenarios with varying levels of knowledge about the acting group.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 29 of its 51 references that are in the map. First posted on arXiv 29 May 2023.

Builds on

29 of 51 references.

References · 29

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  8. 2019General E(2)-Equivariant Steerable CNNscited by 441
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17 more
  1. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  2. 2018Towards a Definition of Disentangled Representationscited by 294
  3. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  4. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  5. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  7. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  8. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  9. 2018Explorations in Homeomorphic Variational Auto-Encodingcited by 65
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  11. 2020Equivariant Neural Renderingcited by 47
  12. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
  13. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  14. 2019Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spherescited by 37
  15. 2018Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks)cited by 16
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  17. 2020Learning Structured Latent Factors from Dependent Data:A Generative Model Framework from Information-Theoretic Perspectivecited by 5

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Cited by year (2026 to 7 Oct)

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

12 papers.

  1. 2023GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformerscited by 75
  2. 2023Steerers: A framework for rotation equivariant keypoint descriptorscited by 21
  3. 2024Neural Isometries: Taming Transformations for Equivariant MLcited by 6
  4. 2024Affine steerers for structured keypoint descriptioncited by 6
  5. 2026DiLA: Disentangled Latent Action World Modelscited by 6
  6. 2025AtlasD: Automatic Local Symmetry Discoverycited by 4
  7. 2025Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actionscited by 2
  8. 2025Inter-environmental world modeling for continuous and compositional dynamicscited by 1
  9. 2023KEEC: Koopman Embedded Equivariant Controlcited by 0
  10. 2025Algebraic Priors for Approximately Equivariant Networkscited by 0
  11. 2026Equivariant Latent Alignment via Flow Matching under Group Symmetriescited by 0
  12. 2026Blind Recovery of Latent Domains via Unsupervised Symmetry Discoverycited by 0