Saved in:
Bibliographic Details
Main Authors: Saied, Youssef, Fleuret, François
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.08193
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917550079606784
author Saied, Youssef
Fleuret, François
author_facet Saied, Youssef
Fleuret, François
contents Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and LayerNorm. We introduce Wrapped Normalization Equivariance (WNE), a parameter-free wrapper that normalizes the input, applies any backbone, and denormalizes the output. We prove every NE function admits this factorization, so the wrapper exactly parameterizes the class of NE functions. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable GPU overhead, while architectural NE baselines are up to $1.6\times$ slower.
format Preprint
id arxiv_https___arxiv_org_abs_2605_08193
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising
Saied, Youssef
Fleuret, François
Computer Vision and Pattern Recognition
Artificial Intelligence
Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and LayerNorm. We introduce Wrapped Normalization Equivariance (WNE), a parameter-free wrapper that normalizes the input, applies any backbone, and denormalizes the output. We prove every NE function admits this factorization, so the wrapper exactly parameterizes the class of NE functions. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable GPU overhead, while architectural NE baselines are up to $1.6\times$ slower.
title Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising
topic Computer Vision and Pattern Recognition
Artificial Intelligence
url https://arxiv.org/abs/2605.08193