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.

Published as a conference paper at ICLR 2026 show that while this is straightforward for argmax-based tasks (e.g., classification), standard pipelines for threshold-based tasks (e.g., object localization) are incompatible with such architectures. We resolve this by introducing a coherent framework pairing output standardization at inference with a novel Z-scored Mean Squared Error (ZMSE) loss.

• We benchmark SEqSI against Standard, Scale-Equivariant (SEq) (Mohan et al., 2019), and the more restrictive Affine-Equivariant (AffEq) (Herbreteau et al., 2023) models. We show that SEqSI architectural design provides certified robustness to affine transformations and enhances generalization to non-affine corruptions.

• We demonstrate that, unlike normalization pre-processing which only handles global transformations, the architectural properties of SEqSI makes it inherently robust to a range of spatially-varying affine intensity transformations.

• We demonstrate the advantages of SEqSI on challenging biological imaging tasks, including macromolecule classification in Cryo-Electron Tomography (Cryo-ET) and object localization in fluorescence microscopy. In these two application fields, where severe and naturally-occurring photometric shifts cause Standard models to fail, SEqSI architectural guarantees provide robust out-of-distribution generalization, while maintaining high accuracy where baselines collapse (see Fig. 1). Wbp (In-Distribution) Ctfdeconvolved (Out-of-Distribution) Denoised (Out-of-Distribution) Isonetcorrected (Out-of-Distribution) Standard 87.17% ± 1.50% 48.91% ± 11.04% 22.36% ± 6.59% 15.95% ± 1.44% SEqSI 85.15% ± 3.59% 66.51% ± 9.75% 74.53% ± 4.25% 73.21% ± 4.18%