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.

介绍了一种使用可控滤波器建立尺度等变卷积网络的通用理论，并将其他常见块推广为尺度等变块，此方法具有计算效率和数值稳定性，同时在 MNIST-scale 数据集和 STL-10 数据集中实现了领先水平的分类结果。