Restore Translation Using Equivariant Neural Networks
Yihan Wang Lijia Yu Xiao-Shan Gao
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.