# Rotation Equivariance and Invariance in Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1805.12301 · HTML: https://mlsanity.com/paper/1805.12301/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2018.

## Built on by (most cited first, 12 of 12)

- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)
- [Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution](https://mlsanity.com/paper/2310.02299/) (2023)
- [Mesh-based graph convolutional neural networks for modeling materials with microstructure](https://mlsanity.com/paper/2107.00090/) (2021)
- [Universal approximation and model compression for radial neural networks](https://mlsanity.com/paper/2107.02550/) (2021)
- [Swinv2-Imagen: Hierarchical Vision Transformer Diffusion Models for Text-to-Image Generation](https://mlsanity.com/paper/2210.09549/) (2022)
- [A simple equivariant machine learning method for dynamics based on scalars](https://mlsanity.com/paper/2110.03761/) (2021)
- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)
- [Symmetry Structured Convolutional Neural Networks](https://mlsanity.com/paper/2203.02056/) (2022)
- [Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response](https://mlsanity.com/paper/2404.17584/) (2024)
- [Learning Geometric Invariance for Gait Recognition](https://mlsanity.com/paper/2601.05604/) (2026)

## Abstract (arXiv)

Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel scheme using the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode rotational invariance in neural networks, along with a new, efficient convolutional scheme for encoding rotational equivariance throughout convolutional layers. We implemented this scheme for several image classification tasks and demonstrated improved performance, in terms of classification accuracy, time required to train the model, and robustness to hyperparameter selection, over a standard CNN and another state-of-the-art method.