Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: This paper proposes a general class of GNN. The new model class generalizes the aggregation step to multiple levels of neighbors. The new model generalizes existing models. Theoretically, the paper shows the generalized models enjoy better discriminative power. The paper also conducts experiments to demonstrate the effectiveness of the new model class.


Comments:
1. The design of new models is straightforward, and the theoretical analysis is trivial, given Xu et al. 2019. The paper would be improved if the author(s) can provide optimization or generalization analysis.

2. The statement about experiments is misleading. The paper claims SOTA results on several datasets. However, this paper does not report recent SOTA results:
https://arxiv.org/abs/1809.02670
https://arxiv.org/abs/1810.00826
https://arxiv.org/abs/1905.13192

3. The use of the phrase "random walk" is weird. As there is no randomness at all.


review_title: Official Blind Review #1

final_score: rating: 8: Accept
review_content: The paper proposes minor modifications to Graph Convolutional Networks (GCNs) that as proven by the authors enable learning of local features in networks, namely the aggregation over powers of the adjacency matrix (effectively counting random walks within the neighborhood) and aggregating over connections within nodes in the neighborhood.

GCNs are of interest to 
The paper is well written and clear.
The mathemeatical derivations are clearly structured.
The authors provide a large set of experiments on simulated and real data from different domains and relevant supervised tasks (node classifiation, graph classification and graph regression).
Source code is provided.

experimental results:
- For the simulation in Table 2, a 1-layer network seems like it would hield an advantage for the unstructured Erdös Renyi graphs. As I understand, the proposed GCN should by construction count the triangles (target variable) for each node embedding and then predict a linear function of those aggregated. My intuition says that this may even be an advantage over adding more layers. The text states the opposite. Here it would be interesting to see the effect of adding layers, or aggregating over longer random walks.
Here, it would be important to get the prediction of an untrained baseline in addition to the GCN baseline (e.g. the expected number of triangles/4cycles based on number of nodes in the Erdös Renyi model) to understand the scale the Mean Squared Error lives on and what the relative improvement means.
review_title: Official Blind Review #2

final_score: rating: 3: Weak Reject
review_content: The paper proposes a generalized framework for GNN. It proposes a representational hierarchy of GNNs. (D-1, L-1,..D-n, L-n). L-k is the k-hop neighborhood including all edges. And D-k is L-k without edges between the outermost nodes. The discriminative power of a network using L-1 is > WL-1. On various graph classification/regression tasks, the proposed method shows good performance. Show promising result on QM7b QM9 graph regression task  (counting triangles, cycles etc) which are highly relevant to the proposed method.

Some concerns:

1, the theoretical results seem a bit incremental compared with (Xu et al. 2018).

2. it would be nice to comment on how this will affect cases with nontrivial node features and general node classification tasks.

3.  the empirical results are not very convincing. On standard datasets/tasks, the baselines are not state-of-the-arts. The results only show the advantage of the proposed idea over basic GCNs. Synthetic and results on QM7b QM9 are specific for triangles and cycles which is the model designed for. Overall, it is not very clear what the proposed idea brings to GNN in a general setting.

Given these concerns, I am leaning toward weak reject at this moment. 

review_title: Official Blind Review #3

Meta-review: This paper proposes a modification to GCNs that generalizes the aggregation step to multiple levels of neighbors, that in theory, the new class of models have better discriminative power. The main criticism raised is that there is lack of sufficient evidence to distinguish this works theoretical contribution from that of Xu et al. Two reviewers also pointed out the concerns around experiment results and suggested to includes more recent state of the art SOTA results. While authors disagree that the contributions of their work is incremental, reviewers concerns are good samples of the general readers of this paper— general readers may also read this paper as incremental. We highly encourage authors to take another cycle of edits to better distinguish their work from others before future submissions. 

Decision: Reject