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

arXiv: https://arxiv.org/abs/2206.09450 · HTML: https://mlsanity.com/paper/2206.09450/

## 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 (most cited first, 21 of 21)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018)
- [Improving Robustness Without Sacrificing Accuracy with Patch Gaussian Augmentation](https://mlsanity.com/paper/1906.02611/) (2019)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Learning to Compose Domain-Specific Transformations for Data Augmentation](https://mlsanity.com/paper/1709.01643/) (2017)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Data augmentation instead of explicit regularization](https://mlsanity.com/paper/1806.03852/) (2018)
- [Relaxing Equivariance Constraints with Non-stationary Continuous Filters](https://mlsanity.com/paper/2204.07178/) (2022)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spaces](https://mlsanity.com/paper/1910.06552/) (2019)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Further advantages of data augmentation on convolutional neural networks](https://mlsanity.com/paper/1906.11052/) (2019)
- [Does Data Augmentation Lead to Positive Margin?](https://mlsanity.com/paper/1905.03177/) (2019)
- [Do Deep Networks Transfer Invariances Across Classes?](https://mlsanity.com/paper/2203.09739/) (2022)

## Built on by (most cited first, 17 of 17)

- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [Learning Rotation-Equivariant Features for Visual Correspondence](https://mlsanity.com/paper/2303.15472/) (2023)
- [Provably Learning Diverse Features in Multi-View Data with Midpoint Mixup](https://mlsanity.com/paper/2210.13512/) (2022)
- [Machine learning and invariant theory](https://mlsanity.com/paper/2209.14991/) (2022)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Panda: A pretrained forecast model for chaotic dynamics](https://mlsanity.com/paper/2505.13755/) (2025)
- [Almost Equivariance via Lie Algebra Convolutions](https://mlsanity.com/paper/2310.13164/) (2023)
- [Approximately Equivariant Neural Processes](https://mlsanity.com/paper/2406.13488/) (2024)
- [Equivariant geometric convolutions for emulation of dynamical systems](https://mlsanity.com/paper/2305.12585/) (2023)
- [For Better or For Worse? Learning Minimum Variance Features With Label Augmentation](https://mlsanity.com/paper/2402.06855/) (2024)
- [LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures](https://mlsanity.com/paper/2402.01045/) (2024)
- [SIDDA: SInkhorn Dynamic Domain Adaptation for Image Classification with Equivariant Neural Networks](https://mlsanity.com/paper/2501.14048/) (2025)
- [Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural network](https://mlsanity.com/paper/2305.10110/) (2023)
- [Deep deterministic policy gradient with symmetric data augmentation for lateral attitude tracking control of a fixed-wing aircraft](https://mlsanity.com/paper/2407.11077/) (2024)
- [eCP: Equivariant Conformal Prediction with pre-trained models](https://mlsanity.com/paper/2602.03986/) (2026)
- [Smoothness Errors in Dynamics Models and How to Avoid Them](https://mlsanity.com/paper/2602.05352/) (2026)
- [How Do Transformers Learn to Represent Symmetries?](https://mlsanity.com/paper/2610.10305/) (2026)

## 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.