We study the effect of injecting local scale equivariance into Convolutional
Neural Networks. This is done by applying each convolutional filter at multiple
scales. The output is a vector field encoding for the maximally activating
scale and the scale itself, which is further processed by the following
convolutional layers. This allows all the intermediate representations to be
locally scale equivariant. We show that this improves the performance of the
model by over $20\%$ in the scale equivariant task of regressing the scaling
factor applied to randomly scaled MNIST digits. Furthermore, we find it also
useful for scale invariant tasks, such as the actual classification of randomly
scaled digits. This highlights the usefulness of allowing for a compact
representation that can also learn relationships between different local scales
by keeping internal scale equivariance.

研究注入本地规模等变性对卷积神经网络的影响，通过在多个尺度上应用每个卷积滤波器来实现。输出是一个向量场编码，用于表示最大激活尺度和尺度本身，这进一步由以下卷积层进行处理。这可使所有中间表示在本地上成为规模等变的。研究发现，这种方法在 MNIST 数字的随机缩放因素回归等已知规模等变任务中会显着提高模型性能超过 20％。此外，还发现该方法对于实际随机缩放数字的分类等尺度不变任务也有用。