Invariance to spatial transformations such as translations and rotations is a desirable property and a basic design principle for classification neural networks. However, the commonly used convolutional neural networks (CNNs) are actually very sensitive to even small translations. There exist vast works to achieve exact or approximate transformation invariance by designing transformation-invariant models or assessing the transformations. These works usually make changes to the standard CNNs and harm the performance on standard datasets. In this paper, rather than modifying the classifier, we propose a pre-classifier restorer to recover translated (or even rotated) inputs to the original ones which will be fed into any classifier for the same dataset. The restorer is based on a theoretical result which gives a sufficient and necessary condition for an affine operator to be translational equivariant on a tensor space.

翻译：对平移、旋转等空间变换具有不变性是分类神经网络期望的特性及基本设计原则。然而，常用的卷积神经网络（CNN）实际上对即使微小的平移也非常敏感。已有大量工作通过设计变换不变性模型或评估变换来实现精确或近似的变换不变性。这些工作通常会对标准CNN进行修改，从而降低其在标准数据集上的性能。本文提出了一种分类器前的恢复器，将发生平移（甚至旋转）的输入恢复至原始状态，而非修改分类器本身；恢复后的输入可被任何适用于同一数据集的分类器处理。该恢复器基于一个理论结果，该结果给出了仿射算子在张量空间上满足平移等变性的充分必要条件。