Flopping for FLOPs: Leveraging equivariance for computational efficiency

• URL: http://arxiv.org/abs/2502.05169v2
• Date: Tue, 24 Jun 2025 07:03:53 GMT
• Title: Flopping for FLOPs: Leveraging equivariance for computational efficiency
• Abstract summary: This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable number of floating-point operations (FLOPs) per parameter to standard non-equivariant networks.<n>Our approach reduces both FLOPs and wall-clock time, providing a practical solution for efficient, scalable symmetry-aware architectures.
• Score: 13.909111585519652
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable number of floating-point operations (FLOPs) per parameter to standard non-equivariant networks. We focus on horizontal mirroring (flopping) invariance, common in many computer vision tasks. The main idea is to parametrize the feature spaces in terms of mirror-symmetric and mirror-antisymmetric features, i.e., irreps of the flopping group. This decomposes the linear layers to be block-diagonal, requiring half the number of FLOPs. Our approach reduces both FLOPs and wall-clock time, providing a practical solution for efficient, scalable symmetry-aware architectures.

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