# Data Augmentation and Regularization for Learning Group Equivariance

arXiv: https://arxiv.org/abs/2502.06547 · HTML: https://mlsanity.com/paper/2502.06547/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Provably Strict Generalisation Benefit for Equivariant Models](https://mlsanity.com/paper/2102.10333/) (2021)
- [On the Benefits of Invariance in Neural Networks](https://mlsanity.com/paper/2005.00178/) (2020)
- [Implicit Bias of Linear Equivariant Networks](https://mlsanity.com/paper/2110.06084/) (2021)
- [Optimization Dynamics of Equivariant and Augmented Neural Networks](https://mlsanity.com/paper/2303.13458/) (2023)
- [Emergent Equivariance in Deep Ensembles](https://mlsanity.com/paper/2403.03103/) (2024)
- [Ensembles provably learn equivariance through data augmentation](https://mlsanity.com/paper/2410.01452/) (2024)
- [On the Implicit Bias of Linear Equivariant Steerable Networks](https://mlsanity.com/paper/2303.04198/) (2023)
- [Symmetries in Overparametrized Neural Networks: A Mean-Field View](https://mlsanity.com/paper/2405.19995/) (2024)

## Built on by (most cited first, 3 of 3)

- [An analytic theory of convolutional neural network inverse problems solvers](https://mlsanity.com/paper/2601.10334/) (2026)
- [Conservation Laws from Data Symmetry in Neural Networks](https://mlsanity.com/paper/2606.10913/) (2026)
- [Equivariance and Augmentation for Bayesian Neural Networks](https://mlsanity.com/paper/2606.26273/) (2026)

## Abstract (arXiv)

In many machine learning tasks, known symmetries can be used as an inductive bias to improve model performance. In this paper, we consider learning group equivariance through training with data augmentation. We summarize results from a previous paper of our own, and extend the results to show that equivariance of the trained model can be achieved through training on augmented data in tandem with regularization.