# Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2310.08429 · HTML: https://mlsanity.com/paper/2310.08429/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 12 Oct 2023.

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

- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Rotation-invariant convolutional neural networks for galaxy morphology prediction](https://mlsanity.com/paper/1503.07077/) (2015)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networks](https://mlsanity.com/paper/1604.06318/) (2016)
- [Learning rotation invariant convolutional filters for texture classification](https://mlsanity.com/paper/1604.06720/) (2016)
- [Flip-Rotate-Pooling Convolution and Split Dropout on Convolution Neural Networks for Image Classification](https://mlsanity.com/paper/1507.08754/) (2015)

## Built on by (most cited first, 16 of 16)

- [The dark side of the forces: assessing non-conservative force models for atomistic machine learning](https://mlsanity.com/paper/2412.11569/) (2024)
- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)
- [Attribute-Based Robotic Grasping with Data-Efficient Adaptation](https://mlsanity.com/paper/2501.02149/) (2025)
- [Efficient Rotation Invariance in Deep Neural Networks through Artificial Mental Rotation](https://mlsanity.com/paper/2311.08525/) (2023)
- [SRE-Conv: Symmetric Rotation Equivariant Convolution for Biomedical Image Classification](https://mlsanity.com/paper/2501.09753/) (2025)
- [Do we need equivariant models for molecule generation?](https://mlsanity.com/paper/2507.09753/) (2025)
- [Invariance Measures for Neural Networks](https://mlsanity.com/paper/2310.17404/) (2023)
- [SEAL - A Symmetry EncourAging Loss for High Energy Physics](https://mlsanity.com/paper/2511.01982/) (2025)
- [Quantitative Approximation Rates for Group Equivariant Learning](https://mlsanity.com/paper/2602.20370/) (2026)
- [Image-to-Image Translation Framework Embedded with Rotation Symmetry Priors](https://mlsanity.com/paper/2604.12805/) (2026)
- [Accelerating Material Property Prediction using Generically Complete Isometry Invariants](https://mlsanity.com/paper/2401.15089/) (2024)
- [On the effectiveness of Rotation-Equivariance in U-Net: A Benchmark for Image Segmentation](https://mlsanity.com/paper/2412.09182/) (2024)
- [Tight Constraint Prediction of Six-Degree-of-Freedom Transformer-based Powered Descent Guidance](https://mlsanity.com/paper/2501.00930/) (2025)
- [Deep learning of geometrical cell division rules](https://mlsanity.com/paper/2507.22587/) (2025)
- [Feature Dynamics as Implicit Data Augmentation: A Depth-Decomposed View on Deep Neural Network Generalization](https://mlsanity.com/paper/2509.20334/) (2025)
- [Computing a Characteristic Orientation for Rotation-Independent Image Analysis](https://mlsanity.com/paper/2602.20930/) (2026)

## Abstract (arXiv)

Convolutional Neural Networks (CNN) offer state of the art performance in various computer vision tasks. Many of those tasks require different subtypes of affine invariances (scale, rotational, translational) to image transformations. Convolutional layers are translation equivariant by design, but in their basic form lack invariances. In this work we investigate how best to include rotational invariance in a CNN for image classification. Our experiments show that networks trained with data augmentation alone can classify rotated images nearly as well as in the normal unrotated case; this increase in representational power comes only at the cost of training time. We also compare data augmentation versus two modified CNN models for achieving rotational invariance or equivariance, Spatial Transformer Networks and Group Equivariant CNNs, finding no significant accuracy increase with these specialized methods. In the case of data augmented networks, we also analyze which layers help the network to encode the rotational invariance, which is important for understanding its limitations and how to best retrain a network with data augmentation to achieve invariance to rotation.