Designing Affine-Invariant Neural Networks for Photometric Corruption Robustness and Generalization

Standard Convolutional Neural Networks are notoriously sensitive to photometric variations, a critical flaw that data augmentation only partially mitigates without offering formal guarantees. We introduce the Scale-Equivariant Shift-Invariant (SEqSI) model, a novel architecture that achieves intensity scale equivariance and intensity shift invariance by design, enabling full invariance to global intensity affine transformations with appropriate post-processing. By strategically prepending a single shift-invariant layer to a scale-equivariant backbone, SEqSI provides these formal guarantees while remaining fully compatible with common components like ReLU. We benchmark SEqSI against Standard, Scale-Equivariant (SEq), and Affine-Equivariant (AffEq) models on 2D and 3D image-classification and object-localization tasks. Our experiments demonstrate that SEqSI architectural properties provide certified robustness to affine intensity transformations and enhances generalization across non-affine corruptions and domain shifts in challenging real-world applications like biological image analysis. This work establishes SEqSI as a practical and principled approach for building photometrically robust models without major trade-offs.