title: Group Downsampling with Equivariant Anti-aliasing
summary: 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
paper_authors._id: 680edc612488a3b6b9feb9d0
paper_authors.name: Md Ashiqur Rahman
paper_authors.status: extracted_confirmed
paper_authors.statusLastChangedAt: 2025-04-28T03:56:25.436Z
paper_authors._id: 661e07e02a8496916011c08a
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/6vIkL4LJ0bLeJL99E20F_.jpeg
paper_authors.fullname: Md Ashiqur Rahman
paper_authors.type: user
paper_authors.user: ashiq24
paper_authors._id: 680edc612488a3b6b9feb9d1
paper_authors.name: Raymond A. Yeh
paper_title: Group Downsampling with Equivariant Anti-aliasing
paper_summary: 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
paper_ai_summary: The proposed method enhances downsampling in group equivariant architectures by incorporating anti-aliasing and subgroup selection, improving classification accuracy and model efficiency.
paper_ai_keywords: downsampling layers CNN architectures group equivariant architectures G-CNNs finite groups subgroup bandlimited-ness anti-aliasing sampling theory image classification tasks equivariance