Title: Achieving Perfect Color Equivariance via a Hypertoroidal Covering

Abstract

The robustness of standard neural network architectures suffers significantly when the color distribution of input images shifts during inference. In response to this challenge, some researchers have started integrating prior knowledge of color geometry into network design. Existing color-equivariant models typically represent hue changes using 2D rotations, while treating saturation and luminance as 1D translations. Although this methodology enhances resilience to color fluctuations in various scenarios, we demonstrate that modeling saturation and luminance—quantities defined over an interval—as simple 1D translations generates noticeable artifacts.

To address this, we present a color-equivariant architecture that maintains true equivariance. Rather than approximating the interval with the real line, we map values from the interval to the circle via a double-cover. Equivariant representations are then constructed within this lifted space. This strategy eliminates the approximation errors inherent in earlier approaches, thereby boosting interpretability and generalizability. Furthermore, our method outperforms both conventional and existing equivariant baselines in predictive accuracy on tasks including fine-grained classification and medical imaging. Extending our findings beyond color, we also illustrate that this lifting technique can be applied to geometric transformations, such as scaling.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC