text: The paper presents a Depthwise Separable Graph Convolution network that aims at generalizing Depthwise convolutions, that exhibit a nice performance in image related tasks, to the graph domain.  In particular it targets Graph Convolutional Networks. In the abstract the authors mention that the Depthwise Separable Graph Convolution that they propose is the key to understand the connections between geometric convolution methods and traditional 2D ones.  I am afraid I have to disagree  as the proposed approach is not giving any better understanding of what needs to be done and why.  It is an efficient way to mimic what has worked so far for the planar domain  but I would not consider it as fundamental in "closing the gap". I feel that the text is often redundant and that it could be simplified a lot. For example the authors state in various parts that DSC does not work on non-Euclidean data.  Section 2 should be clearer and used to better explain related approaches to motivate the proposed one. In fact, the entire motivation, at least for me, never went beyond the simple fact that this happens to be a good way to improve performance.  The intuition given is not sufficient to substantiate some of the claims on generality and understanding of graph based DL. In 3.1, at point (2), the authors mention that DSC filters are learned from the data whereas GC uses a constant matrix.  This is not correct,  as also reported in equation 2.  The matrix U is learned from the data as well. Equation (4) shows that the proposed approach would weight Q different GC layers.  In practical terms this is a linear combination of these graph convolutional layers. What is not clear is the \Delta_{ij} definition.  It is first introduced in 2.3 and described as the relative position of pixel i and pixel j on the image, but then used in the context of a graph in (4).  What is the coordinate system used by the authors in this case?  This is a very important point that should be made clearer. Why is the Related Work section at the end?  I would put it at the front. The experiments compare with the recent relevant literature.  I think that having less number of parameters is a good thing in this setting  as the data is scarce, however I would like to see a more in-depth comparison with respect to the number of features produced by the model itself.  For example GCN has a representation space (latent) much smaller than DSCG. No statistics over multiple runs are reported,  and given the high variance of results on these datasets I would like them to be reported. I think the separability of the filters in this case brings the right level of simplification to the learning task,  however as it also holds for the planar case it is not clear whether this is necessarily the best way forward. What are the underlying mathematical insights that lead towards selecting separable convolutions? Overall I found the paper interesting but not ground-breaking.  A nice application of the separable principle to GCN.  Results are also interesting  but should be further verified by multiple runs.