mlsanityData to 14 Oct 2026

Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecasting

arXiv 2206.09450 ↗First posted 19 Jun 2022cs.LGcited by 17

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Abstract (arXiv)

Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant networks are two major approaches to injecting symmetry into learning. However, their exact role in improving generalization is not well understood. In this work, we derive the generalization bounds for data augmentation and equivariant networks, characterizing their effect on learning in a unified framework. Unlike most prior theories for the i.i.d. setting, we focus on non-stationary dynamics forecasting with complex temporal dependencies.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 21 of its 29 references that are in the map. First posted on arXiv 19 Jun 2022.

Builds on

21 of 29 references.

References · 21

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2019General E(2)-Equivariant Steerable CNNscited by 446
  4. 2017The Effectiveness of Data Augmentation in Image Classification using Deep Learningcited by 370
  5. 2020Time Series Data Augmentation for Deep Learning: A Surveycited by 226
  6. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 163
  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. 2019Improving Robustness Without Sacrificing Accuracy with Patch Gaussian Augmentationcited by 105
  11. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  12. 2017Learning to Compose Domain-Specific Transformations for Data Augmentationcited by 91
9 more
  1. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 75
  2. 2018Data augmentation instead of explicit regularizationcited by 63
  3. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  4. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  5. 2019Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spacescited by 34
  6. 2020Bridging Physics-based and Data-driven modeling for Learning Dynamical Systemscited by 25
  7. 2019Further advantages of data augmentation on convolutional neural networkscited by 19
  8. 2019Does Data Augmentation Lead to Positive Margin?cited by 18
  9. 2022Do Deep Networks Transfer Invariances Across Classes?cited by 12

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Citing papers per year: 2022: 2; 2023: 4; 2024: 6; 2025: 2; 2026: 3.

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  1. 2024Can AI weather models predict out-of-distribution gray swan tropical cyclones?cited by 26
  2. 2023Learning Rotation-Equivariant Features for Visual Correspondencecited by 23
  3. 2022Provably Learning Diverse Features in Multi-View Data with Midpoint Mixupcited by 14
  4. 2022Machine learning and invariant theorycited by 13
  5. 2024Translation Equivariant Transformer Neural Processescited by 13
  6. 2025Panda: A pretrained forecast model for chaotic dynamicscited by 13
  7. 2023Almost Equivariance via Lie Algebra Convolutionscited by 10
  8. 2024Approximately Equivariant Neural Processescited by 8
  9. 2023Equivariant geometric convolutions for emulation of dynamical systemscited by 3
  10. 2024For Better or For Worse? Learning Minimum Variance Features With Label Augmentationcited by 3
  11. 2024LatticeGraphNet: A two-scale graph neural operator for simulating lattice structurescited by 2
  12. 2025SIDDA: SInkhorn Dynamic Domain Adaptation for Image Classification with Equivariant Neural Networkscited by 2
5 more
  1. 2023Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural networkcited by 1
  2. 2024Deep deterministic policy gradient with symmetric data augmentation for lateral attitude tracking control of a fixed-wing aircraftcited by 1
  3. 2026eCP: Equivariant Conformal Prediction with pre-trained modelscited by 0
  4. 2026Smoothness Errors in Dynamics Models and How to Avoid Themcited by 0
  5. 2026How Do Transformers Learn to Represent Symmetries?cited by 0