标题： 具有等变抗混叠的组下采样 显示英文标题

标题： Group Downsampling with Equivariant Anti-aliasing

摘要： 下采样层是CNN架构中的关键构建模块，有助于增加感受野以学习高级特征，并减少模型的内存/计算量。 在这项工作中，我们研究了均匀下采样层在群等变架构（例如G-CNN）中的泛化能力。 也就是说，我们的目标是在具有抗混叠的情况下对一般有限群上的信号（特征图）进行下采样。 这包括以下内容： (a) 给定一个有限群和下采样率，我们提出了一种算法来选择合适的子群。 (b) 给定一个群和子群，我们研究带限性的概念并提出如何执行抗混叠操作。 值得注意的是，我们的方法推广了基于经典采样理论的下采样概念。 当信号位于循环群（即周期性信号）上时，我们的方法恢复了理想低通滤波器的标准下采样后接子采样操作的结果。 最后，我们在图像分类任务上进行了实验，表明所提出的下采样操作可以提高准确性，更好地保留等变性，并且在集成到G-等变网络中时可以减小模型规模。 显示英文摘要

摘要： Downsampling layers are crucial building blocks in CNN architectures, which help to increase the receptive field for learning high-level features and reduce the amount of memory/computation in the model. In this work, we study the generalization of the uniform downsampling layer for group equivariant architectures, e.g., G-CNNs. That is, we aim to downsample signals (feature maps) on general finite groups with anti-aliasing. This involves the following: (a) Given a finite group and a downsampling rate, we present an algorithm to form a suitable choice of subgroup. (b) Given a group and a subgroup, we study the notion of bandlimited-ness and propose how to perform anti-aliasing. Notably, our method generalizes the notion of downsampling based on classical sampling theory. When the signal is on a cyclic group, i.e., periodic, our method recovers the standard downsampling of an ideal low-pass filter followed by a subsampling operation. Finally, we conducted experiments on image classification tasks demonstrating that the proposed downsampling operation improves accuracy, better preserves equivariance, and reduces model size when incorporated into G-equivariant networks