A Hypertoroidal Covering for Perfect Color Equivariance

TL;DR

This paper introduces a novel color equivariant neural network architecture using hypertoroidal covering, which improves robustness and performance by accurately modeling color and geometric transformations without artifacts.

Contribution

The authors propose a truly equivariant architecture that lifts interval-valued color features to a circular domain, overcoming artifacts of previous methods and extending to geometric transformations.

Findings

Achieves better accuracy on fine-grained classification tasks.

Improves robustness in medical imaging applications.

Outperforms conventional and existing equivariant models.

Abstract

When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modeled hue variation with 2D rotations, and saturation and luminance transformations as 1D translations. While this approach improves neural network robustness to color variations in a number of contexts, we find that approximating saturation and luminance (interval valued quantities) as 1D translations introduces appreciable artifacts. In this paper, we introduce a color equivariant architecture that is truly equivariant. Instead of approximating the interval with the real line, we lift values on the interval to values on the circle (a double-cover) and build equivariant representations there. Our approach resolves the approximation artifacts of previous methods, improves interpretability and generalizability, and achieves better predictive performance than conventional and equivariant baselines on tasks such as fine-grained classification and medical imaging tasks. Going beyond the context of color, we show that our proposed lifting can also extend to geometric transformations such as scale.