Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising
For practitioners of image-to-image prediction, this work provides a simple, zero-cost method to enforce NE on any backbone, improving robustness to distribution shifts without architectural constraints.
The paper characterizes the full Normalization Equivariance (NE) function class, showing that a function is NE iff it admits a normalize-process-denormalize factorization. This leads to a parameter-free wrapper (WNE) that enforces NE around any backbone, improving robustness in blind denoising with no GPU overhead, while architectural NE baselines incur up to 1.6x slowdown.
Normalization Equivariance (NE), equivariance to global contrast and brightness transforms, improves robustness to distribution shift in image-to-image prediction. Existing methods enforce this prior by constraining internal layers to NE-compatible families, limiting compatibility with standard components such as attention and LayerNorm, and adding runtime cost. We characterize the full NE function class: a function is NE if and only if it admits a normalize-process-denormalize factorization. This turns exact NE enforcement, for the ideal wrapper, from an internal architectural constraint into an input-output parameterization problem, allowing a parameter-free wrapper (WNE) to enforce NE around any backbone, including transformers. In a single-noise mismatch diagnostic for blind denoising, the wrapper improves CNN and transformer robustness with no measurable GPU overhead; architectural NE baselines incur up to a 1.6x slowdown.