提出新型下采样方法，让CNN对空间平移保持不变性
Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments
- 用高斯-埃尔米特多项式实现平移一致采样
- 在多个数据集上实现100%平移一致性分类
- 无需修改网络结构或额外训练，适合图像分类任务
卷积神经网络（CNN）本身不具备平移不变性或等变性。其中，下采样操作是破坏平移不变性的关键原因。然而，下采样对于提升计算效率和扩大感受野以获取更多上下文信息至关重要。本文提出高斯-埃尔米特采样（GHS），一种新型下采样策略，旨在实现精确的平移不变性。GHS利用高斯-埃尔米特多项式进行平移一致采样，使CNN层在训练前即具备对任意空间平移的不变性。将该方法集成到标准CNN架构中后，可在不改变网络结构或增加训练步骤的前提下，在层级别直接嵌入平移不变性。我们在CIFAR-10、CIFAR-100和MNIST-rot数据集上进行了评估，实验结果表明，GHS显著提升了平移一致性，在空间平移下实现了100%的分类一致性，同时相比基线CNN模型提升了分类准确率。
原文摘要 · Abstract (English)
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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