mlsanityData to 14 Oct 2026

Latent Space Symmetry Discovery

arXiv 2310.00105 ↗First posted 29 Sep 2023cs.LGcited by 29

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Abstract (arXiv)

Equivariant neural networks require explicit knowledge of the symmetry group. Automatic symmetry discovery methods aim to relax this constraint and learn invariance and equivariance from data. However, existing symmetry discovery methods are limited to simple linear symmetries and cannot handle the complexity of real-world data. We propose a novel generative model, Latent LieGAN (LaLiGAN), which can discover symmetries of nonlinear group actions. It learns a mapping from the data space to a latent space where the symmetries become linear and simultaneously discovers symmetries in the latent space. Theoretically, we show that our model can express nonlinear symmetries under some conditions about the group action. Experimentally, we demonstrate that our method can accurately discover the intrinsic symmetry in high-dimensional dynamical systems. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 31 of its 51 references that are in the map. First posted on arXiv 29 Sep 2023.

Builds on

31 of 51 references.

References · 31

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2017Deep Setscited by 1,421
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  4. 2018Spherical CNNscited by 456
  5. 2019General E(2)-Equivariant Steerable CNNscited by 446
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  7. 2018Towards a Definition of Disentangled Representationscited by 296
  8. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  9. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  10. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  11. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  12. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
19 more
  1. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
  2. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  3. 2019B-Spline CNNs on Lie Groupscited by 97
  4. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 83
  5. 2020Meta-Learning Symmetries by Reparameterizationcited by 76
  6. 2021Equivariant Contrastive Learningcited by 66
  7. 2018Explorations in Homeomorphic Variational Auto-Encodingcited by 65
  8. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  9. 2021Learning Partial Equivariances from Datacited by 45
  10. 2023Self-supervised learning of Split Invariant Equivariant representationscited by 44
  11. 2023Generative Adversarial Symmetry Discoverycited by 42
  12. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 39
  13. 2019Symmetry-Based Disentangled Representation Learning requires Interaction with Environmentscited by 35
  14. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 33
  15. 2022LieGG: Studying Learned Lie Group Generatorscited by 31
  16. 2022Rotationally Equivariant 3D Object Detectioncited by 21
  17. 2022Equivariant Representation Learning via Class-Pose Decompositioncited by 17
  18. 2021Learning Augmentation Distributions using Transformed Risk Minimizationcited by 13
  19. 2023A Unified Framework for Discovering Discrete Symmetriescited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 13; 2026: 10.

29 papers.

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  1. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 20
  2. 2024Learning Infinitesimal Generators of Continuous Symmetries from Datacited by 17
  3. 2024Symmetry-Informed Governing Equation Discoverycited by 15
  4. 2025Interpretable Machine Learning in Physics: A Reviewcited by 14
  5. 2026Flow Equivariant World Models: Memory for Partially Observed Dynamic Environmentscited by 8
  6. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 7
  7. 2024Neural Isometries: Taming Transformations for Equivariant MLcited by 6
  8. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 6
  9. 2025AtlasD: Automatic Local Symmetry Discoverycited by 5
  10. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  11. 2024Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structurescited by 4
  12. 2025Governing Equation Discovery from Data Based on Differential Invariantscited by 4
17 more
  1. 2026Data Augmentation: A Fourier Analysis Perspectivecited by 4
  2. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 3
  3. 2026Efficient Learning and Symmetry Discovery under Exact Invariancescited by 3
  4. 2025MatrixNet: Learning over symmetry groups using learned group representationscited by 2
  5. 2024SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservationcited by 1
  6. 2025SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equationscited by 1
  7. 2025Learning symmetries in datasetscited by 1
  8. 2025RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalizationcited by 1
  9. 2025Modeling Time Series Dynamics with Fourier Ordinary Differential Equationscited by 0
  10. 2025LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetriescited by 0
  11. 2025Learning Group Actions In Disentangled Latent Image Representationscited by 0
  12. 2026LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecturecited by 0
  13. 2026Spectral Discovery of Continuous Symmetries via Generalized Fourier Transformscited by 0
  14. 2026Blind Recovery of Latent Domains via Unsupervised Symmetry Discoverycited by 0
  15. 2026On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancementcited by 0
  16. 2026LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systemscited by 0
  17. 2026Discovering Symmetries in Neural Network Parameter Spacescited by 0