Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments

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Main Authors: Singh, Jaspreet, Bosilj, Petra, Cielniak, Grzegorz
Format: Preprint
Published: 2026
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author Singh, Jaspreet
Bosilj, Petra
Cielniak, Grzegorz
author_facet Singh, Jaspreet
Bosilj, Petra
Cielniak, Grzegorz
contents The convolutional neural networks (CNNs) are not inherently shift invariant or equivariant. The downsampling operation, used in CNNs, is one of the key reasons which breaks the shift invariant property of a CNN. Conversely, downsampling operation is important to improve computational efficiency and increase the area of the receptive field for more contextual information. In this work, we propose Gaussian-Hermite Sampling (GHS), a novel downsampling strategy designed to achieve accurate shift invariance. GHS leverages Gaussian-Hermite polynomials to perform shift-consistent sampling, enabling CNN layers to maintain invariance to arbitrary spatial shifts prior to training. When integrated into standard CNN architectures, the proposed method embeds shift invariance directly at the layer level without requiring architectural modifications or additional training procedures. We evaluate the proposed approach on CIFAR-10, CIFAR-100, and MNIST-rot datasets. Experimental results demonstrate that GHS significantly improves shift consistency, achieving 100% classification consistency under spatial shifts, while also improving classification accuracy compared to baseline CNN models.
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id arxiv_https___arxiv_org_abs_2603_17098
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments
Singh, Jaspreet
Bosilj, Petra
Cielniak, Grzegorz
Computer Vision and Pattern Recognition
The convolutional neural networks (CNNs) are not inherently shift invariant or equivariant. The downsampling operation, used in CNNs, is one of the key reasons which breaks the shift invariant property of a CNN. Conversely, downsampling operation is important to improve computational efficiency and increase the area of the receptive field for more contextual information. In this work, we propose Gaussian-Hermite Sampling (GHS), a novel downsampling strategy designed to achieve accurate shift invariance. GHS leverages Gaussian-Hermite polynomials to perform shift-consistent sampling, enabling CNN layers to maintain invariance to arbitrary spatial shifts prior to training. When integrated into standard CNN architectures, the proposed method embeds shift invariance directly at the layer level without requiring architectural modifications or additional training procedures. We evaluate the proposed approach on CIFAR-10, CIFAR-100, and MNIST-rot datasets. Experimental results demonstrate that GHS significantly improves shift consistency, achieving 100% classification consistency under spatial shifts, while also improving classification accuracy compared to baseline CNN models.
title Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments
topic Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2603.17098