Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments

TL;DR

This paper introduces Gaussian-Hermite Sampling (GHS), a novel downsampling method that enhances shift invariance in CNNs, leading to perfect shift consistency and improved accuracy without architectural changes.

Contribution

The paper presents GHS, a new shift-consistent sampling technique that maintains shift invariance in CNNs at the layer level without extra training or modifications.

Findings

GHS achieves 100% classification consistency under spatial shifts.

GHS improves classification accuracy on CIFAR-10, CIFAR-100, and MNIST-rot datasets.

GHS enhances shift invariance without architectural modifications.

Abstract

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.