Truly Scale-Equivariant Deep Nets with Fourier Layers
Md Ashiqur Rahman Raymond A. Yeh
In computer vision, models must be able to adapt to changes in image
resolution to effectively carry out tasks such as image segmentation; This is
known as scale-equivariance. Recent works have made progress in developing
scale-equivariant convolutional neural networks, e.g., through weight-sharing
and kernel resizing. However, these networks are not truly scale-equivariant in
practice. Specifically, they do not consider anti-aliasing as they formulate
the down-scaling operation in the continuous domain. To address this
shortcoming, we directly formulate down-scaling in the discrete domain with
consideration of anti-aliasing. We then propose a novel architecture based on
Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute
zero equivariance-error. Following prior works, we test this model on
MNIST-scale and STL-10 datasets. Our proposed model achieves competitive
classification performance while maintaining zero equivariance-error.