mlsanityData to 7 Oct 2026

Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution

arXiv 2310.02299 ↗First posted 3 Oct 2023cs.LG cs.AIcited by 19

Not on the map. Why?

Abstract (arXiv)

Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic structures. Thus, identifying sources of asymmetry is an important tool for understanding physical systems. In this paper, we focus on learning asymmetries of data using relaxed group convolutions. We provide both theoretical and empirical evidence that this flexible convolution technique allows the model to maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in various physical systems. We employ various relaxed group convolution architectures to uncover various symmetry-breaking factors that are interpretable and physically meaningful in different physical systems, including the phase transition of crystal structure, the isotropy and homogeneity breaking in turbulent flow, and the time-reversal symmetry breaking in pendulum systems.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 42 of its 71 references that are in the map. First posted on arXiv 3 Oct 2023.

Builds on

42 of 71 references.

References · 42

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2017Deep Setscited by 1,394
  4. 2016Group Equivariant Convolutional Networkscited by 1,154
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  6. 2021E(n) Equivariant Graph Neural Networkscited by 951
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  9. 2019General E(2)-Equivariant Steerable CNNscited by 441
  10. 2016Steerable CNNscited by 298
  11. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  12. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
30 more
  1. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  2. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  3. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  4. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  5. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  6. 2022e3nn: Euclidean Neural Networkscited by 171
  7. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  8. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 123
  9. 2020Deep Learning for Time Series Forecasting: Tutorial and Literature Surveycited by 117
  10. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  11. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  12. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  13. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  14. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  15. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  16. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  17. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  18. 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 45
  19. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  20. 2023Generative Adversarial Symmetry Discoverycited by 40
  21. 2020Finding Symmetry Breaking Order Parameters with Euclidean Neural Networkscited by 30
  22. 2020Revisiting Spatial Invariance with Low-Rank Local Connectivitycited by 29
  23. 2020Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processescited by 29
  24. 2023Latent Space Symmetry Discoverycited by 29
  25. 2020Trajectory Prediction using Equivariant Continuous Convolutioncited by 26
  26. 2019Scale Steerable Filters for Locally Scale-Invariant Convolutional Neural Networkscited by 22
  27. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  28. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 18
  29. 2018Stochastic Learning under Random Reshuffling with Constant Step-sizescited by 14
  30. 2018Rotation Equivariance and Invariance in Convolutional Neural Networkscited by 12

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 9; 2026: 4.

19 papers.

Sort:

  1. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  2. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 15
  3. 2025Learning (Approximately) Equivariant Networks via Constrained Optimizationcited by 10
  4. 2024Approximate Equivariance in Reinforcement Learningcited by 9
  5. 2025A Tale of Two Symmetries: Exploring the Loss Landscape of Equivariant Modelscited by 8
  6. 2024Relaxed Equivariant Graph Neural Networkscited by 7
  7. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 6
  8. 2024Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensorscited by 5
  9. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  10. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  11. 2025MaNGO - Adaptable Graph Network Simulators via Meta-Learningcited by 3
  12. 2024Segment as You Wish -- Free-Form Language-Based Segmentation for Medical Imagescited by 2
7 more
  1. 2026Approximate Equivariance via Projection-based Regularisationcited by 2
  2. 2025PEnGUiN: Partially Equivariant Graph NeUral Networks for Sample Efficient MARLcited by 1
  3. 2024Learning Ordering in Crystalline Materials with Symmetry-Aware Graph Neural Networkscited by 0
  4. 2025Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolutioncited by 0
  5. 2026An Exploratory Study into using Machine-Learning for Fast Step-by-step Emulation of Numerical Mechanical Thrombectomy Simulations for Ischemic Strokecited by 0
  6. 2026Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Constructioncited by 0
  7. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0