Group Downsampling with Equivariant Anti-aliasing
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
680edc612488a3b6b9feb9d0
Md Ashiqur Rahman
extracted_confirmed
2025-04-28T03:56:25.436Z
661e07e02a8496916011c08a
https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/6vIkL4LJ0bLeJL99E20F_.jpeg
Md Ashiqur Rahman
user
ashiq24
680edc612488a3b6b9feb9d1
Raymond A. Yeh
extracted_confirmed
2025-07-16T05:09:55.279Z
62dac2dff014388f90897039
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Raymond Yeh
user
raymondyeh
Group Downsampling with Equivariant Anti-aliasing
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
The proposed method enhances downsampling in group equivariant architectures by incorporating anti-aliasing and subgroup selection, improving classification accuracy and model efficiency.
downsampling layers CNN architectures group equivariant architectures G-CNNs finite groups subgroup bandlimited-ness anti-aliasing sampling theory image classification tasks equivariance