Scale-Equivariant Neural Networks with Decomposed Convolutional Filters
Encoding the input scale information explicitly into the representation learned by a convolutional neural network is beneficial for many vision tasks especially when dealing with multiscale input signals.We study, in this paper, a scale-equivariant CNN architecture with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve scale-equivariant representations.To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components.A further benefit of the truncated filter expansion is the improved deformation robustness of the equivariant representation.Numerical experiments demonstrate that the proposed scale-equivariant neural network with decomposed convolutional filters achieves significantly improved performance in multiscale image classification and better interpretability than regular CNNs at a reduced model size.
We construct scale-equivariant convolutional neural networks in the most general form with both computational efficiency and proved deformation robustness.The authors propose a CNN architecture that is theoretically equivariant to isotropic scalings and translations by adding an extra scale-dimension to activation tensors.