通过镜像对称性分解，让神经网络更省算力。
Flopping for FLOPs: Leveraging equivariance for computational efficiency
- 用镜像对称与反对称特征分解特征空间，实现块对角线结构。
- 相比普通网络，每参数计算量减少一半，总算力降低约50%。
- 适合需要高效对称感知的视觉任务，如图像分类、目标检测。
将几何不变性融入神经网络能提升参数效率，但通常会增加计算成本。本文提出新型等变神经网络，在保持对称性的同时，每参数浮点运算量（FLOPs）与标准非等变网络相当。聚焦于计算机视觉中常见的水平镜像（翻转）不变性，核心思想是将特征空间参数化为镜像对称和镜像反对称成分，即翻转群的不可约表示。这使得线性层可分解为块对角形式，所需浮点运算量减半。该方法同时降低总算力和实际运行时间，为高效、可扩展的对称感知架构提供了实用解决方案。
原文摘要 · Abstract (English)
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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