Title: JCGEL: Joint Color and Geometric Group Equivariant Convolutional Layer
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Group equivariant networks, Disentanglement learnng, Imbalanced dataset, Classification

Abstract: Translation equivariance is one of the key factors for the widespread effectiveness of convolutional neural networks (CNNs) in computer vision.
Building on this principle, group equivariant architectures have been extended beyond translations to encompass both color and geometric symmetries, which commonly arise in vision datasets.
However, despite the commuting nature of their respective group actions, color and geometry have typically been addressed in isolation by theoretical and approximately equivariant approaches.
In this paper, we introduce a \emph{joint color and geometric group equivariant convolution layer (JCGEL)} via weight sharing across the commuting group actions.
Our approach 1) improves robustness in imbalanced regimes, 2) yields factorized representations that separate color and geometric group-related factors, and 3) scales effectively to real-world datasets.
To validate these effects, we instantiate the layer within standard CNNs and evaluate across long-tailed and biased datasets, disentanglement learning benchmarks, and real-world classification tasks, where our model consistently outperforms baselines.
As a drop-in replacement for standard convolutional layers, JCGEL demonstrates generalization across a variety of vision tasks.