A Hypertoroidal Covering for Perfect Color Equivariance

• URL: http://arxiv.org/abs/2603.04256v1
• Date: Wed, 04 Mar 2026 16:43:02 GMT
• Title: A Hypertoroidal Covering for Perfect Color Equivariance
• Authors: Yulong Yang, Zhikun Xu, Yaojun Li, Christine Allen-Blanchette,
• Abstract summary: We introduce a color equivariant architecture that is truly equivariant.<n>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.<n>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.
• Score: 3.793458006209272
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

Related papers

• Learning Color Equivariant Representations [1.9594704501292781]
  We introduce group convolutional neural networks (GCNNs) equivariant to color variation.<n>GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.
  arXiv  Detail & Related papers  (2024-06-13T21:02:03Z)
• Color Equivariant Convolutional Networks [50.655443383582124]
  CNNs struggle if there is data imbalance between color variations introduced by accidental recording conditions. We propose Color Equivariant Convolutions ( CEConvs), a novel deep learning building block that enables shape feature sharing across the color spectrum. We demonstrate the benefits of CEConvs in terms of downstream performance to various tasks and improved robustness to color changes, including train-test distribution shifts.
  arXiv  Detail & Related papers  (2023-10-30T09:18:49Z)
• Explicit Correspondence Matching for Generalizable Neural Radiance Fields [66.99907718824782]
  We present a new NeRF method that is able to generalize to new unseen scenarios and perform novel view synthesis with as few as two source views.<n>The explicit correspondence matching is quantified with the cosine similarity between image features sampled at the 2D projections of a 3D point on different views.<n>Our method achieves state-of-the-art results on different evaluation settings, with the experiments showing a strong correlation between our learned cosine feature similarity and volume density.
  arXiv  Detail & Related papers  (2023-04-24T17:46:01Z)
• The Lie Derivative for Measuring Learned Equivariance [84.29366874540217]
  We study the equivariance properties of hundreds of pretrained models, spanning CNNs, transformers, and Mixer architectures. We find that many violations of equivariance can be linked to spatial aliasing in ubiquitous network layers, such as pointwise non-linearities. For example, transformers can be more equivariant than convolutional neural networks after training.
  arXiv  Detail & Related papers  (2022-10-06T15:20:55Z)
• Imaging with Equivariant Deep Learning [9.333799633608345]
  We review the emerging field of equivariant imaging and show how it can provide improved generalization and new imaging opportunities. We show the interplay between the acquisition physics and group actions and links to iterative reconstruction, blind compressed sensing and self-supervised learning.
  arXiv  Detail & Related papers  (2022-09-05T02:13:57Z)
• Neural Color Operators for Sequential Image Retouching [62.99812889713773]
  We propose a novel image retouching method by modeling the retouching process as performing a sequence of newly introduced trainable neural color operators. The neural color operator mimics the behavior of traditional color operators and learns pixelwise color transformation while its strength is controlled by a scalar. Our method consistently achieves the best results compared with SOTA methods in both quantitative measures and visual qualities.
  arXiv  Detail & Related papers  (2022-07-17T05:33:19Z)
• Revisiting Transformation Invariant Geometric Deep Learning: An Initial Representation Perspective [38.314914702299056]
  We propose Transformation In Neural Networks (TinvNN), a straightforward and general plug-in for geometric data.<n>Specifically, we realize transformation invariant and distance-preserving initial point representations by modifying multi-dimensional scaling.<n>We prove that TinvNN can strictly guarantee transformation invariant, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Frame Averaging for Equivariant Shape Space Learning [85.42901997467754]
  A natural way to incorporate symmetries in shape space learning is to ask that the mapping to the shape space (encoder) and mapping from the shape space (decoder) are equivariant to the relevant symmetries. We present a framework for incorporating equivariance in encoders and decoders by introducing two contributions.
  arXiv  Detail & Related papers  (2021-12-03T06:41:19Z)
• Quantised Transforming Auto-Encoders: Achieving Equivariance to Arbitrary Transformations in Deep Networks [23.673155102696338]
  Convolutional Neural Networks (CNNs) are equivariant to image translation. We propose an auto-encoder architecture whose embedding obeys an arbitrary set of equivariance relations simultaneously. We demonstrate results of successful re-rendering of transformed versions of input images on several datasets.
  arXiv  Detail & Related papers  (2021-11-25T02:26:38Z)
• Geometric Correspondence Fields: Learned Differentiable Rendering for 3D Pose Refinement in the Wild [96.09941542587865]
  We present a novel 3D pose refinement approach based on differentiable rendering for objects of arbitrary categories in the wild. In this way, we precisely align 3D models to objects in RGB images which results in significantly improved 3D pose estimates. We evaluate our approach on the challenging Pix3D dataset and achieve up to 55% relative improvement compared to state-of-the-art refinement methods in multiple metrics.
  arXiv  Detail & Related papers  (2020-07-17T12:34:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.