  Group equivariant convolutional neural networks 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 afforded by these architectures, group equivariant networks
have seen limited application in the context of perceptual quantities such as
hue and saturation, even though their variation can lead to significant
reductions in classification performance. In this paper, we introduce
convolutional neural networks equivariant to variations in hue and saturation
by design. To achieve this, we leverage the observation that hue and saturation
transformations can be identified with the 2D rotation and 1D translation
groups respectively. Our hue-, saturation-, and fully color-equivariant
networks achieve equivariance to these perceptual transformations without an
increase in network parameters. We demonstrate the utility of our networks on
synthetic and real world datasets where color and lighting variations are
commonplace.
