Title: Designing Affine-Invariant Neural Networks for Photometric Corruption Robustness and Generalization
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Computer Vision, Robust neural network, invariance, equivariance, biological imaging, microscopy, classification, object localization

Abstract: 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 scale equivariance and shift invariance by design, enabling full invariance to global 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 prior provides certified robustness to affine transformations and enhances generalization across non-affine corruptions and domain shifts in challenging real-world applications like biological image analysis. This work establishes \textit{SEqSI} as a practical and principled approach for building photometrically robust models without major trade-offs.

TL;DR: Scale-Equivariant & Shift-Invariant NN rendered Affine invariant for application to image classification and object localization