# Exploiting Learned Symmetries in Group Equivariant Convolutions

arXiv: https://arxiv.org/abs/2106.04914 · HTML: https://mlsanity.com/paper/2106.04914/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Scale-Equivariant Steerable Networks](https://mlsanity.com/paper/1910.11093/) (2019)
- [Roto-Translation Covariant Convolutional Networks for Medical Image Analysis](https://mlsanity.com/paper/1804.03393/) (2018)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [CubeNet: Equivariance to 3D Rotation and Translation](https://mlsanity.com/paper/1804.04458/) (2018)
- [Rethinking Depthwise Separable Convolutions: How Intra-Kernel Correlations Lead to Improved MobileNets](https://mlsanity.com/paper/2003.13549/) (2020)
- [Deep Rotation Equivariant Network](https://mlsanity.com/paper/1705.08623/) (2017)
- [Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey](https://mlsanity.com/paper/2006.16867/) (2020)
- [Co-Attentive Equivariant Neural Networks: Focusing Equivariance On Transformations Co-Occurring In Data](https://mlsanity.com/paper/1911.07849/) (2019)
- [A Data and Compute Efficient Design for Limited-Resources Deep Learning](https://mlsanity.com/paper/2004.09691/) (2020)

## Built on by (most cited first, 5 of 5)

- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groups](https://mlsanity.com/paper/2110.13059/) (2021)
- [What Affects Learned Equivariance in Deep Image Recognition Models?](https://mlsanity.com/paper/2304.02628/) (2023)
- [Flopping for FLOPs: Leveraging equivariance for computational efficiency](https://mlsanity.com/paper/2502.05169/) (2025)
- [Color Equivariant Convolutional Networks](https://mlsanity.com/paper/2310.19368/) (2023)

## Abstract (arXiv)

Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and find certain conditions under which they become highly redundant. We show that GConvs can be efficiently decomposed into depthwise separable convolutions while preserving equivariance properties and demonstrate improved performance and data efficiency on two datasets. All code is publicly available at github.com/Attila94/SepGrouPy.