提出可泛化到任意有限群的抗混叠下采样方法，提升G-CNN性能
Group Downsampling with Equivariant Anti-aliasing
- 基于有限群构造子群，实现通用下采样框架
- 引入带限性概念并设计抗混叠机制，减少信息失真
- 在图像分类中提升精度与等变性，同时压缩模型大小
下采样层是卷积神经网络中的关键组件，有助于扩大感受野、降低内存与计算量。本文研究了在群等变架构（如G-CNN）中对一般有限群上的信号进行下采样的泛化方法，目标是在保持抗混叠的前提下对信号进行下采样。具体包括：(a) 给定有限群和下采样率，提出算法选择合适的子群；(b) 在给定群与子群的基础上，定义带限性并提出抗混叠方案。该方法推广了经典采样理论中的下采样概念。当信号位于循环群（即周期信号）时，该方法退化为理想低通滤波后子采样的标准操作。实验表明，在图像分类任务中，所提下采样操作能提升准确率，更好地保持等变性，并减小模型规模。
原文摘要 · Abstract (English)
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
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