Dilated convolution with learnable spacings

Dilated convolution is basically a convolution with a wider kernel created by regularly inserting spaces between the kernel elements. In this article, we present a new version of the dilated convolution in which the spacings are made learnable via backpropagation through an interpolation technique. We call this method "Dilated Convolution with Learnable Spacings" (DCLS) and we generalize its approach to the n-dimensional convolution case. However, our main focus here will be the 2D case for which we developed two implementations: a naive one that constructs the dilated kernel, suitable for small dilation rates, and a more time/memory efficient one that uses a modified version of the "im2col" algorithm. We then illustrate how this technique improves the accuracy of existing architectures on semantic segmentation task on Pascal Voc 2012 dataset via a simple drop-in replacement of the classical dilated convolutional layers by DCLS ones. Furthermore, we show that DCLS allows to reduce the number of learnable parameters of the depthwise convolutions used in the recent ConvMixer architecture by a factor 3 with no or very low reduction in accuracy and that by replacing large dense kernels with sparse DCLS ones. The code of the method is based on Pytorch and available at: https://github.com/K-H-Ismail/Dilated-Convolution-with-Learnable-Spacings-PyTorch.