# Learning Color Equivariant Representations

arXiv: https://arxiv.org/abs/2406.09588 · HTML: https://mlsanity.com/paper/2406.09588/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Equivariant Multi-View Networks](https://mlsanity.com/paper/1904.00993/) (2019)
- [Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning](https://mlsanity.com/paper/2306.13924/) (2023)
- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [CIRCLe: Color Invariant Representation Learning for Unbiased Classification of Skin Lesions](https://mlsanity.com/paper/2208.13528/) (2022)
- [Color Equivariant Convolutional Networks](https://mlsanity.com/paper/2310.19368/) (2023)
- [Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolution](https://mlsanity.com/paper/2303.00326/) (2023)

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

- [DaD: Distilled Reinforcement Learning for Diverse Keypoint Detection](https://mlsanity.com/paper/2503.07347/) (2025)
- [Discovering Phase Space Structure in Learned Hamiltonian Systems](https://mlsanity.com/paper/2509.23003/) (2025)
- [A Hypertoroidal Covering for Perfect Color Equivariance](https://mlsanity.com/paper/2603.04256/) (2026)
- [Local-Canonicalization Equivariant Graph Neural Networks for Sample-Efficient and Generalizable Swarm Robot Control](https://mlsanity.com/paper/2509.14431/) (2025)
- [Transformation Laws in Neural Representations: Structure, Realisability, and Construction](https://mlsanity.com/paper/2609.18190/) (2026)

## Abstract (arXiv)

In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale. Despite the improved interpretability, accuracy and generalizability of these architectures, GCNNs have seen limited application in the context of perceptual quantities. Notably, the recent CEConv network uses a GCNN to achieve equivariance to hue transformations by convolving input images with a hue rotated RGB filter. However, this approach leads to invalid RGB values which break equivariance and degrade performance. We resolve these issues with a lifting layer that transforms the input image directly, thereby circumventing the issue of invalid RGB values and improving equivariance error by over three orders of magnitude. Moreover, we extend the notion of color equivariance to include equivariance to saturation and luminance shift. Our hue-, saturation-, luminance- and color-equivariant networks achieve strong generalization to out-of-distribution perceptual variations and improved sample efficiency over conventional architectures. We demonstrate the utility of our approach on synthetic and real world datasets where we consistently outperform competitive baselines.