mlsanityData to 14 Oct 2026

Generative Adversarial Symmetry Discovery

arXiv 2302.00236 ↗First posted 1 Feb 2023cs.LGcited by 42

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Abstract (arXiv)

Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group SO(n), restricted Lorentz group SO(1,3)^+ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 29 of its 44 references that are in the map. First posted on arXiv 1 Feb 2023.

Builds on

29 of 44 references.

References · 29

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  3. 2022Generative Adversarial Networkscited by 5,627
  4. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,527
  5. 2014Conditional Generative Adversarial Netscited by 2,162
  6. 2017Deep Setscited by 1,421
  7. 2016Group Equivariant Convolutional Networkscited by 1,165
  8. 2021E(n) Equivariant Graph Neural Networkscited by 965
  9. 2019Hamiltonian Neural Networkscited by 712
  10. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 506
  11. 2018Spherical CNNscited by 456
  12. 2019General E(2)-Equivariant Steerable CNNscited by 446
17 more
  1. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  2. 2017Data Augmentation Generative Adversarial Networkscited by 278
  3. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  4. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  5. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  7. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
  8. 2019Deep Scale-spaces: Equivariance Over Scalecited by 114
  9. 2018A Kernel Theory of Modern Data Augmentationcited by 106
  10. 2019B-Spline CNNs on Lie Groupscited by 97
  11. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  12. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  13. 2020Meta-Learning Symmetries by Reparameterizationcited by 76
  14. 2021Learning Partial Equivariances from Datacited by 45
  15. 2020Detecting Symmetries with Neural Networkscited by 34
  16. 2022LieGG: Studying Learned Lie Group Generatorscited by 31
  17. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 10; 2025: 14; 2026: 12.

42 papers.

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  1. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  2. 2023Latent Space Symmetry Discoverycited by 29
  3. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  4. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 20
  5. 2024Learning Infinitesimal Generators of Continuous Symmetries from Datacited by 17
  6. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 16
  7. 2024Symmetry-Informed Governing Equation Discoverycited by 15
  8. 2024Symmetry Discovery Beyond Affine Transformationscited by 15
  9. 2024Relaxed Equivariance via Multitask Learningcited by 13
  10. 2024A Generative Model of Symmetry Transformationscited by 10
  11. 2024Symmetry Discovery for Different Data Typescited by 8
  12. 2023A Unified Framework for Discovering Discrete Symmetriescited by 7
30 more
  1. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  2. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 7
  3. 2024Neural Isometries: Taming Transformations for Equivariant MLcited by 6
  4. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 6
  5. 2025AtlasD: Automatic Local Symmetry Discoverycited by 5
  6. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  7. 2025Governing Equation Discovery from Data Based on Differential Invariantscited by 4
  8. 2026Data Augmentation: A Fourier Analysis Perspectivecited by 4
  9. 2023Non-parametric Hypothesis Tests for Distributional Group Symmetrycited by 3
  10. 2025Symmetry Understanding of 3D Shapes via Chirality Disentanglementcited by 3
  11. 2025Discovering Symmetry Groups with Flow Matchingcited by 3
  12. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 3
  13. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 3
  14. 2025Geometric Kolmogorov-Arnold Superposition Theoremcited by 2
  15. 2025Learning finite symmetry groups of dynamical systems via equivariance detectioncited by 2
  16. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  17. 2025Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actionscited by 2
  18. 2023Efficient Model-Agnostic Multi-Group Equivariant Networkscited by 1
  19. 2024Data-driven discovery of self-similarity using neural networkscited by 1
  20. 2024SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservationcited by 1
  21. 2025RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalizationcited by 1
  22. 2026Sparse Data Augmentation for Optimization with Provable Guaranteescited by 1
  23. 2025Interpretable Discovery of One-parameter Subgroups: A Modular Framework for Elliptical, Hyperbolic, and Parabolic Symmetriescited by 0
  24. 2026Spectral Discovery of Continuous Symmetries via Generalized Fourier Transformscited by 0
  25. 2026EqOD: Symmetry-Informed Stability Selection for PDE Identificationcited by 0
  26. 2026Blind Recovery of Latent Domains via Unsupervised Symmetry Discoverycited by 0
  27. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0
  28. 2026Discovering Symmetries in Neural Network Parameter Spacescited by 0
  29. 2026Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurementscited by 0
  30. 2026Learning Operators for Symmetry Discovery: From Lie Groups to Local Symmetry Geometrycited by 0