  The effectiveness of Convolutional Neural Networks (CNNs) has been
substantially attributed to their built-in property of translation
equivariance. However, CNNs do not have embedded mechanisms to handle other
types of transformations. In this work, we pay attention to scale changes,
which regularly appear in various tasks due to the changing distances between
the objects and the camera. First, we introduce the general theory for building
scale-equivariant convolutional networks with steerable filters. We develop
scale-convolution and generalize other common blocks to be scale-equivariant.
We demonstrate the computational efficiency and numerical stability of the
proposed method. We compare the proposed models to the previously developed
methods for scale equivariance and local scale invariance. We demonstrate
state-of-the-art results on MNIST-scale dataset and on STL-10 dataset in the
supervised learning setting.
