  Convolutional Neural Networks have become the standard for image
classification tasks, however, these architectures are not invariant to
translations of the input image. This lack of invariance is attributed to the
use of stride which ignores the sampling theorem, and fully connected layers
which lack spatial reasoning. We show that stride can greatly benefit
translation invariance given that it is combined with sufficient similarity
between neighbouring pixels, a characteristic which we refer to as local
homogeneity. We also observe that this characteristic is dataset-specific and
dictates the relationship between pooling kernel size and stride required for
translation invariance. Furthermore we find that a trade-off exists between
generalization and translation invariance in the case of pooling kernel size,
as larger kernel sizes lead to better invariance but poorer generalization.
Finally we explore the efficacy of other solutions proposed, namely global
average pooling, anti-aliasing, and data augmentation, both empirically and
through the lens of local homogeneity.
