In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on network performance. We show that a change in the input dimension of a network as small as a single pixel can be enough for commonly used architectures to become approximately equivariant, rather than exactly. We investigate the impact of networks not being exactly equivariant and find that approximately equivariant networks generalise significantly worse to unseen symmetries compared to their exactly equivariant counterparts. However, when the symmetries in the training data are not identical to the symmetries of the network, we find that approximately equivariant networks are able to relax their own equivariant constraints, causing them to match or outperform exactly equivariant networks on common benchmark datasets.

翻译：本文展示了群等变卷积神经网络如何利用子采样学习破坏其对称性的等变性。我们聚焦于二维旋转与反射，探究等变性破坏对网络性能的影响。研究表明，即使输入尺寸发生仅一个像素的微小变化，也足以使常见架构从严格等变退化为近似等变。我们通过分析非严格等变网络的影响发现：与严格等变网络相比，近似等变网络在泛化未见过对称性时表现显著较差。然而，当训练数据中的对称性与网络本身对称性不完全一致时，近似等变网络能够松驰自身等变约束，进而在常见基准数据集上达到或超越严格等变网络的性能表现。