# Color Equivariant Convolutional Networks

arXiv: https://arxiv.org/abs/2310.19368 · HTML: https://mlsanity.com/paper/2310.19368/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [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)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Zero-Shot Day-Night Domain Adaptation with a Physics Prior](https://mlsanity.com/paper/2108.05137/) (2021)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [LieGG: Studying Learned Lie Group Generators](https://mlsanity.com/paper/2210.04345/) (2022)
- [Enabling equivariance for arbitrary Lie groups](https://mlsanity.com/paper/2111.08251/) (2021)
- [What Affects Learned Equivariance in Deep Image Recognition Models?](https://mlsanity.com/paper/2304.02628/) (2023)
- [Understanding trained CNNs by indexing neuron selectivity](https://mlsanity.com/paper/1702.00382/) (2017)
- [Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey](https://mlsanity.com/paper/2006.16867/) (2020)
- [Image Colorization By Capsule Networks](https://mlsanity.com/paper/1908.08307/) (2019)
- [Offset equivariant networks and their applications](https://mlsanity.com/paper/2207.00292/) (2022)
- [Exploiting Learned Symmetries in Group Equivariant Convolutions](https://mlsanity.com/paper/2106.04914/) (2021)

## Built on by (most cited first, 7 of 7)

- [DaD: Distilled Reinforcement Learning for Diverse Keypoint Detection](https://mlsanity.com/paper/2503.07347/) (2025)
- [Towards a Unified Representation Evaluation Framework Beyond Downstream Tasks](https://mlsanity.com/paper/2505.06224/) (2025)
- [Explicit Discovery of Nonlinear Symmetries from Dynamic Data](https://mlsanity.com/paper/2510.01855/) (2025)
- [Learning Color Equivariant Representations](https://mlsanity.com/paper/2406.09588/) (2024)
- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [A Hypertoroidal Covering for Perfect Color Equivariance](https://mlsanity.com/paper/2603.04256/) (2026)
- [Transformation Laws in Neural Representations: Structure, Realisability, and Construction](https://mlsanity.com/paper/2609.18190/) (2026)

## Abstract (arXiv)

Color is a crucial visual cue readily exploited by Convolutional Neural Networks (CNNs) for object recognition. However, CNNs struggle if there is data imbalance between color variations introduced by accidental recording conditions. Color invariance addresses this issue but does so at the cost of removing all color information, which sacrifices discriminative power. In this paper, we propose Color Equivariant Convolutions (CEConvs), a novel deep learning building block that enables shape feature sharing across the color spectrum while retaining important color information. We extend the notion of equivariance from geometric to photometric transformations by incorporating parameter sharing over hue-shifts in a neural network. We demonstrate the benefits of CEConvs in terms of downstream performance to various tasks and improved robustness to color changes, including train-test distribution shifts. Our approach can be seamlessly integrated into existing architectures, such as ResNets, and offers a promising solution for addressing color-based domain shifts in CNNs.