# Variational Partial Group Convolutions for Input-Aware Partial Equivariance of Rotations and Color-Shifts

arXiv: https://arxiv.org/abs/2407.04271 · HTML: https://mlsanity.com/paper/2407.04271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Population Based Augmentation: Efficient Learning of Augmentation Policy Schedules](https://mlsanity.com/paper/1905.05393/) (2019)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Relaxing Equivariance Constraints with Non-stationary Continuous Filters](https://mlsanity.com/paper/2204.07178/) (2022)
- [MetaAugment: Sample-Aware Data Augmentation Policy Learning](https://mlsanity.com/paper/2012.12076/) (2020)
- [Regularizing Towards Soft Equivariance Under Mixed Symmetries](https://mlsanity.com/paper/2306.00356/) (2023)
- [Learning Instance-Specific Augmentations by Capturing Local Invariances](https://mlsanity.com/paper/2206.00051/) (2022)
- [Learning to Transform for Generalizable Instance-wise Invariance](https://mlsanity.com/paper/2309.16672/) (2023)

## Built on by (most cited first, 1 of 1)

- [RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization](https://mlsanity.com/paper/2505.13289/) (2025)

## Abstract (arXiv)

Group Equivariant CNNs (G-CNNs) have shown promising efficacy in various tasks, owing to their ability to capture hierarchical features in an equivariant manner. However, their equivariance is fixed to the symmetry of the whole group, limiting adaptability to diverse partial symmetries in real-world datasets, such as limited rotation symmetry of handwritten digit images and limited color-shift symmetry of flower images. Recent efforts address this limitation, one example being Partial G-CNN which restricts the output group space of convolution layers to break full equivariance. However, such an approach still fails to adjust equivariance levels across data. In this paper, we propose a novel approach, Variational Partial G-CNN (VP G-CNN), to capture varying levels of partial equivariance specific to each data instance. VP G-CNN redesigns the distribution of the output group elements to be conditioned on input data, leveraging variational inference to avoid overfitting. This enables the model to adjust its equivariance levels according to the needs of individual data points. Additionally, we address training instability inherent in discrete group equivariance models by redesigning the reparametrizable distribution. We demonstrate the effectiveness of VP G-CNN on both toy and real-world datasets, including MNIST67-180, CIFAR10, ColorMNIST, and Flowers102. Our results show robust performance, even in uncertainty metrics.