Part of International Conference on Representation Learning 2025 (ICLR 2025) Conference
Md Ashiqur Rahman, Raymond A. Yeh
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