mlsanityData to 7 Oct 2026

Meta-Learning Symmetries by Reparameterization

arXiv 2007.02933 ↗First posted 6 Jul 2020cs.LG stat.MLcited by 75

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Abstract (arXiv)

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only works when practitioners know the symmetries of the task and can manually construct an architecture with the corresponding equivariances. Our goal is an approach for learning equivariances from data, without needing to design custom task-specific architectures. We present a method for learning and encoding equivariances into networks by learning corresponding parameter sharing patterns from data. Our method can provably represent equivariance-inducing parameter sharing for any finite group of symmetry transformations. Our experiments suggest that it can automatically learn to encode equivariances to common transformations used in image processing tasks. We provide our experiment code at https://github.com/AllanYangZhou/metalearning-symmetries.

Key facts. Cited by 75 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jul 2020.

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Citing papers per year: 2021: 18; 2022: 19; 2023: 18; 2024: 8; 2025: 9; 2026: 3.

75 papers.

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  1. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  2. 2023Generalization on the Unseen, Logic Reasoning and Degree Curriculumcited by 73
  3. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  4. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  5. 2021Learning Partial Equivariances from Datacited by 44
  6. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  7. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  8. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  9. 2023Generative Adversarial Symmetry Discoverycited by 40
  10. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  11. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  12. 2023Latent Space Symmetry Discoverycited by 29
38 more
  1. 2022LieGG: Studying Learned Lie Group Generatorscited by 28
  2. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
  3. 2021Grounding inductive biases in natural images:invariance stems from variations in datacited by 25
  4. 2021Introducing Symmetries to Black Box Meta Reinforcement Learningcited by 25
  5. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  6. 2021Last Layer Marginal Likelihood for Invariance Learningcited by 21
  7. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 19
  8. 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
  9. 2022Equivariance Discovery by Learned Parameter-Sharingcited by 18
  10. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  11. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 18
  12. 2022Automatic Data Augmentation via Invariance-Constrained Learningcited by 17
  13. 2022Learning Invariant Weights in Neural Networkscited by 16
  14. 2022Learning Instance-Specific Augmentations by Capturing Local Invariancescited by 15
  15. 2021Addressing the Topological Defects of Disentanglement via Distributed Operatorscited by 14
  16. 2023Magnitude Invariant Parametrizations Improve Hypernetwork Learningcited by 14
  17. 2024Symmetry Discovery Beyond Affine Transformationscited by 14
  18. 2021Learning Augmentation Distributions using Transformed Risk Minimizationcited by 13
  19. 2023On genuine invariance learning without weight-tyingcited by 13
  20. 2022Do Deep Networks Transfer Invariances Across Classes?cited by 12
  21. 2023Neural Fourier Transform: A General Approach to Equivariant Representation Learningcited by 12
  22. 2024On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theorycited by 10
  23. 2021Machine learning a manifoldcited by 9
  24. 2021Identifying Physical Law of Hamiltonian Systems via Meta-Learningcited by 8
  25. 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environmentscited by 8
  26. 2022Learning from Symmetry: Meta-Reinforcement Learning with Symmetrical Behaviors and Language Instructionscited by 8
  27. 2022Equivariance-aware Architectural Optimization of Neural Networkscited by 8
  28. 2024Tilt your Head: Activating the Hidden Spatial-Invariance of Classifierscited by 7
  29. 2024Symmetry Discovery for Different Data Typescited by 7
  30. 2022Deep invariant networks with differentiable augmentation layerscited by 6
  31. 2023A Unified Framework for Discovering Discrete Symmetriescited by 6
  32. 2024Learning Symmetries via Weight-Sharing with Doubly Stochastic Tensorscited by 5
  33. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 5
  34. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  35. 2022Meta-ticket: Finding optimal subnetworks for few-shot learning within randomly initialized neural networkscited by 4
  36. 2022Learning Continuous Rotation Canonicalization with Radial Beam Samplingcited by 4
  37. 2023Using and Abusing Equivariancecited by 4
  38. 2024Noether's razor: Learning Conserved Quantitiescited by 4

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