  The translational equivariant nature of Convolutional Neural Networks (CNNs)
is a reason for its great success in computer vision. However, networks do not
enjoy more general equivariance properties such as rotation or scaling,
ultimately limiting their generalization performance. To address this
limitation, we devise a method that endows CNNs with simultaneous equivariance
with respect to translation, rotation, and scaling. Our approach defines a
convolution-like operation and ensures equivariance based on our proposed
scalable Fourier-Argand representation. The method maintains similar efficiency
as a traditional network and hardly introduces any additional learnable
parameters, since it does not face the computational issue that often occurs in
group-convolution operators. We validate the efficacy of our approach in the
image classification task, demonstrating its robustness and the generalization
ability to both scaled and rotated inputs.
