Unfortunately reviewer_2 did not engage in the discussion even though it was needed, my recommendation is thus mainly based on the 3 other reviews. This paper investigates the expressive power of Graph neural networks by studying to which extent they can compute graph moments. This is an interesting and original approach and the theoretical findings are sound and relevant to the community. In preparing the camera-ready version of the paper, the authors should take the following points in consideration. The reviewers mentioned that the exposition of some of the contributions are somehow overstated and should be tuned down. Experimental evaluations on real data and comparisons with existing GCNs (even though the purpose of the paper is not to beat SOTA, this would make an informative addition) would improve the paper. Lastly, the paper could be polished with a thorough proof reading to improve its clarity.