We propose a novel antialiasing method to increase shift invariance in convolutional neural networks (CNNs). More precisely, we replace the conventional combination "real-valued convolutions + max pooling" ($\mathbb R$Max) by "complex-valued convolutions + modulus" ($\mathbb C$Mod), which produce stable feature representations for band-pass filters with well-defined orientations. In a recent work, we proved that, for such filters, the two operators yield similar outputs. Therefore, $\mathbb C$Mod can be viewed as a stable alternative to $\mathbb R$Max. To separate band-pass filters from other freely-trained kernels, in this paper, we designed a "twin" architecture based on the dual-tree complex wavelet packet transform, which generates similar outputs as standard CNNs with fewer trainable parameters. In addition to improving stability to small shifts, our experiments on AlexNet and ResNet showed increased prediction accuracy on natural image datasets such as ImageNet and CIFAR10. Furthermore, our approach outperformed recent antialiasing methods based on low-pass filtering by preserving high-frequency information, while reducing memory usage.

本文提出了一种新的抗锯齿方法，通过使用复数卷积和模运算代替实数卷积和最大池化，以提高卷积神经网络的平移不变性，同时基于双树复小波分组变换设计了一个“双生”结构，实现了与标准卷积神经网络类似的输出效果，提高了图像分类的预测准确性，并且保留了高频信息同时减少内存使用。

从CNN到平移不变双小波模型