Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper tackles the problem of irrelevant propagation to one node and in multi-channels in GNNs via modeling relevances between propagations. The proposed method is called OPEN for Orthogonal Propagation with Ego-Network modeling. The basic idea relies on dimension reduction through principal component analysis to infer the propagation weights. Theoretical and empirical evidence suggests the effectiveness of the proposed method. 
strengths_and_weaknesses: - The paper studies one of the main issues in GNNs; irrelevant propagation and proposes a simple yet effective method to tackle this issue.
- Extensive empirical evaluations are carried out and show the effectiveness of the proposed method.
questions: The proposed method relies mainly on principal component analysis, while many other dimension reduction techniques exist in the literature (e.g., kernel PCA). The authors should elaborate more on this aspect by comparing different dimension reduction strategies and comparing them to the proposed scheme.
limitations: The theoretical analysis (section 3.4) is not consistent. Indeed, the intuitions behind Theorem 1 are not clear and should be clarified more precisely by the authors. It would be more interesting to provide a theoretical quantitative evaluation of the proposed method to prove its effectiveness in theory.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: 
This submission studies local refinement in GNNs via orthogonal propagation with ego-net modeling. The proposed methods are designed to address the problem of irrelevant propagation.  Specifically, the relevance between propagations to one node is modeled by whole ego-network modeling and eigenvector decomposition. Meanwhile, the propagations in multi-channels are implemented by employing all principal components, each of which corresponds to one channel. Experimental results on multiple real-world datasets were provided.
strengths_and_weaknesses: Strength:
1. the design motivation of viewing propagation as dimensionality reduction is new and very interesting. 
2. experiments on real datasets show the effectiveness of the algorithms compared with multiple existing works

Weakness:
1. the clarify and organization of the paper can be improved
2. there are typos and grammar mistakes in the paper.
3. the discussion of novelty compared with previous works is not clear
questions: 1. it is claimed that the algorithm has high efficiency because evd with respect to the neighborhood is less expensive than evd of the entire network. However, the original propagation in GNN does not require any evd, and such evd needs to be computed for egonets of each node for OPEN. Hence, the efficiency claim is not justified. More explanation or experiments in terms of run time need to be provided

2. the algorithm flow is hard to follow. An algorithm table would be helpful to improve clarify

3. The difference between this work and Ortho-GConv [26] is not clear. In the discussion it is mentioned that "Ortho-GConv tends to alleviate oversmoothing issue, while OPEN aims at overfitting issue." but the entire paper as well as the theoretical analysis shows OPEN sovles overfitting issue. This needs to be clarified.

4. why orthogonal propagation is more challenging than orthorgonizing features as claimed? It seems to the reviewer they are similar.


limitations: societal impact not discussed
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: In this paper, the authors propose a new GNN model (OPEN) to tackle the irrelevant propagations issues.
The authors first made observations on two limitations of traditional GNNS: 
 * The propagation weights to each node are computed in a pairwise fashion, which ignores certain global information for that node's neighborhood.
* There are no constraint on the channel specific propagation weights, which could potentially lead to overfitting.

In OPEN, the propagation weights to a node is computed by eigenvalue decomposition (EVD) of the covariance matrix of node representations in ego-network. It is claimed that this would encode global information from ego-network and prevent overfitting is supervised learning.

Since most of the ego-networks are much smaller in size, the EVD can be computed efficiently (with special treatments for Hub nodes).

Also, by design, the propagation weights from different channels are orthogonal in OPEN, therefore it encourages diversity and reduces overfitting risk.

Empirical results show that the proposed architecture outperforms other GNNs on several node classification tasks.
strengths_and_weaknesses: This paper is well presented and easy to follow. The authors first unifies the expression for different GNNs and formulate the problem as finding the right propagation weights. Then they introduce their proposed method via the dimension reduction point of view.

The empirical results shows the proposed model outperforms other baseline GNNs on various node classification tasks. Ablation study also shows that it can indeed prevent over-smoothing issue. 

Even though the method itself is not complicated, I think this could give us a good insight on the limitations of existing GNN architectures.

questions: 
* Can the authors provide more context on how the propagation weights are incorporated in back-propagation? 
* Why the inference process and the back propagation process can't "be seamlessly combined" for layer specific propagation weights?
* I'd suggest to re-phrase the narrates in Theorem 1 to be more specific. Even over-smoothed representations are "relevant to node attributes", just not related to the node itself.
limitations: The authors discussed about connections and differences between OPEN and other GNNs with orthogonal constraint. Limitations such as inability to use layer specific propagation weights are discussed.

To my knowledge the work poses no potential negative societal impact.
review_title: null

Meta-review: metareview: Reviewers recommended borderline accept, borderline reject, and accept. Reviewers found the article studies one of the main issues of GNNs and proposes a simple but effective solution method supported by extensive experimental evaluation. There were some reservations about the comparison with other methods and the theoretical analysis. While some of these items could be addressed during the discussion period, leading to updated more favorable ratings, some reservations about the theoretical part persisted. There were also persisting disagreements about the novelty and about the issues that are solved by the proposed method compared with previous methods. All together I found that the merits outweighed the shortcomings and hence am recommending accept. However, I strongly encourage the authors to carefully consider the reviewers comments when preparing the final manuscript, particularly that they work on the discussion and clarification of the novelty of the method, particularly the issues between over smoothing and overfitting and the corresponding presentation in the work, and the reservations on the theoretical part. 
confidence: Less certain
Decision: Accept