mlsanityData to 14 Oct 2026

AtlasD: Automatic Local Symmetry Discovery

arXiv 2504.10777 ↗First posted 15 Apr 2025cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a misrepresentation of the true symmetry. In this paper, we formalize the notion of local symmetry as atlas equivariance. Our proposed pipeline, automatic local symmetry discovery (AtlasD), recovers the local symmetries of a function by training local predictor networks and then learning a Lie group basis to which the predictors are equivariant. We demonstrate AtlasD is capable of discovering local symmetry groups with multiple connected components in top-quark tagging and partial differential equation experiments. The discovered local symmetry is shown to be a useful inductive bias that improves the performance of downstream tasks in climate segmentation and vision tasks.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 32 of its 43 references that are in the map. First posted on arXiv 15 Apr 2025.

Builds on

32 of 43 references.

References · 32

  1. 2017Deep Setscited by 1,421
  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2018Spherical CNNscited by 456
  5. 2019General E(2)-Equivariant Steerable CNNscited by 446
  6. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  7. 2019Deep Scale-spaces: Equivariance Over Scalecited by 114
  8. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  9. 2018CGNet: A Light-weight Context Guided Network for Semantic Segmentationcited by 94
  10. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 92
  11. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  12. 2020Meta-Learning Symmetries by Reparameterizationcited by 76
20 more
  1. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 75
  2. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 73
  3. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 65
  4. 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 46
  5. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  6. 2021Learning Partial Equivariances from Datacited by 45
  7. 2023Generative Adversarial Symmetry Discoverycited by 42
  8. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  9. 20183D G-CNNs for Pulmonary Nodule Detectioncited by 36
  10. 2023Latent Space Symmetry Discoverycited by 29
  11. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  12. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  13. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 19
  14. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  15. 2023Neural Fourier Transform: A General Approach to Equivariant Representation Learningcited by 12
  16. 2024A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNscited by 8
  17. 2023Learning Lie Group Symmetry Transformations with Neural Networkscited by 6
  18. 2019Learning a Local Symmetry with Neural-Networkscited by 5
  19. 2024Noether's razor: Learning Conserved Quantitiescited by 4
  20. 2022Direction of Arrival Estimation of Sound Sources Using Icosahedral CNNscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 3
  2. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 3
  3. 2026Blind Recovery of Latent Domains via Unsupervised Symmetry Discoverycited by 0
  4. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0
  5. 2026Learning Operators for Symmetry Discovery: From Lie Groups to Local Symmetry Geometrycited by 0