mlsanityData to 7 Oct 2026

Symmetry Discovery Beyond Affine Transformations

arXiv 2406.03619 ↗First posted 5 Jun 2024cs.LG stat.MLcited by 14

Not on the map. Why?

Abstract (arXiv)

Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline a framework for discovering continuous symmetry in data beyond the affine transformation group. We also provide a similar framework for discovering discrete symmetry. We experimentally compare our method to an existing method known as LieGAN and show that our method is competitive at detecting affine symmetries for large sample sizes and superior than LieGAN for small sample sizes. We also show our method is able to detect continuous symmetries beyond the affine group and is generally more computationally efficient than LieGAN.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 12 of its 26 references that are in the map. First posted on arXiv 5 Jun 2024.

Builds on

12 of 26 references.

References · 12

  1. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 93
  2. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  3. 2020On the Benefits of Invariance in Neural Networkscited by 78
  4. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  5. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
  6. 2020Learning Invariances in Neural Networkscited by 52
  7. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
  8. 2023Generative Adversarial Symmetry Discoverycited by 40
  9. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 27
  10. 2018McTorch, a manifold optimization library for deep learningcited by 16
  11. 2021Machine learning a manifoldcited by 9
  12. 2018Symmetry constrained machine learningcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 7; 2026: 7.

14 papers.

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  1. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 6
  2. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 5
  3. 2025Governing Equation Discovery from Data Based on Differential Invariantscited by 4
  4. 2025Discovering Symmetry Groups with Flow Matchingcited by 3
  5. 2026Data Augmentation: A Fourier Analysis Perspectivecited by 3
  6. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  7. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 2
  8. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 2
  9. 2025RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalizationcited by 1
  10. 2025Interpretable Discovery of One-parameter Subgroups: A Modular Framework for Elliptical, Hyperbolic, and Parabolic Symmetriescited by 0
  11. 2026Spectral Discovery of Continuous Symmetries via Generalized Fourier Transformscited by 0
  12. 2026Blind Recovery of Latent Domains via Unsupervised Symmetry Discoverycited by 0
2 more
  1. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0
  2. 2026Discovering Symmetries in Neural Network Parameter Spacescited by 0