Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper introduces adaptive graph diffusion convolution (ADC), a new module that adaptively and automatically determines the neighborhood size for the better feature aggregation of existing GNN frameworks. It extends the graph diffusion convolution (GDC) one step further to make the selection of neighborhood radius learnable. Generally speaking, it is an interesting idea to directly learn different neighborhood radius in different layers. This paper is well-written and easy to follow, and related works are covered comprehensively. Authors further conduct (limited) experiments comparing with selected baselines in node classification tasks, various analysis, and ablation studies demonstrate the strength of this proposed module.  
main_review: My main concerns of this work lie in two aspects. First, the technical novelty is rather limited since the backbone of the model basically follows its predecessor – GDC, including the design graph diffusion, the concept of neighborhood radius, and the heat kernel. It seems like the contribution of this work is merely the proposal of an adaptive version of choosing the neighborhood radius. Second, the authors claim that ADC can be utilized as a plug-in for all GNN layers. However, based on the design of ADC, it leverages the weighted self-multiplication of the Laplacian matrix to achieve the idea of graph diffusion, which makes it hard to apply in non-Laplacian matrix-based GNNs (e.g., GAT and GTN) (as also mentioned by authors in Section 4.1).

There are some additional comments:
1.	Eq. (6) confuses me. It is not obvious how t equals the neighborhood radius for the heat kernel-based GDC. I double-checked the GDC paper and found no evidence of such a claim. Either a detailed explanation or a reference can be provided here.
2.	Since one of the claims in this work is the development of a novel GNN plug-in, it is not adequate of using only one task to demonstrate its ability. Other than node classification, experiments on different tasks (node clustering, link prediction) are expected.
3.	As mentioned in Related Work, the graph diffusion convolution shares lots of commonalities with the conventional graph diffusion method on label propagation. Authors should also consider them [4], [8], [9] or demonstrate how they cannot be compared in this task.
4.	Legends in Fig. 5 are not consistent with the context.

limitations_and_societal_impact: There is no obvious negative societal impact found.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper extends from graph diffusion convolution (GDC) that used hand-tuned neighborhood size for feature aggregation to adaptively learning the size. ADC can automatically learn the neighborhood radius for each GNN layer and
each feature dimension and acts as a plugin to any GNN model. Experimental results and ablation studies show
that learning a unique neighborhood radius for each feature channel in each GNN layer consistently
and improves the performance of downstream graph mining tasks.
main_review: Pros:
1. Improve from GDC that is manually tuned size for each graph by conducting grid search over the validation set, the paper proposes the adaptive diffusion convolution (ADC) to automatically learn the optimal neighborhood size from the data.
2. ADC chooses different neighborhood sizes for each GNN layer and feature channel.

Cons:
1. GDC applies diffusion on the original adjacent matrix to get a dense graph, and then sparsify the dense graph to get a sparse graph (Only one pass graph diffusion); while ADC extends such idea to each GNN layer over adjacent matrix. Therefore, the proposed method also has high computation complexity comparing to GDC. This is not mentioned in the paper.
2. The experimental setup does not follow standard splitting for semi-supervised node classification. Therefore it is difficult to compare the results in the paper to other recent STOA on the semi-supervised node classification (for example, "Direct Multi-hop Attention based Graph Neural Network", https://arxiv.org/pdf/2009.14332.pdf)
3. From the experimental results, the improvement seems not convincing and the reported accuracy improvement is GNN- and data-dependent: the original ARMA and JKNet are generally better than GCN on Cora, Citeseer. However, Fig. 3 did not show the benefit of JKNet (ARMA) vs GCN on Cora, Citeseer.  In fig. 3, the proposed method + ARMA (JKNet) is worse than (proposed method + GCN).  In comparison, GDC + ARMA (JKNet) is usually still better than GDC + GCN. Meanwhile, the proposed method + ARMA is also worse than the performance on COAUTHOR CS and AMZ COMP --- there are no explanations for these inconsistent results.
4. The performance numbers for ADC/GADC are not consistent, on some datasets, ADC is better, some GADC is better. Any explanation?
5. On page 5, feature transformation and propagation are swapped because "Empirically, we find that propagating on the input channels generates better results than propagating on the output channels". This conclusion might be data-dependent or GNN model-dependent: In figure 6,  the experiments were conducted using GCN. Is the same conclusion achieved on JKNet and ARMA models?

** I have read the responses from the authors and adjusted the score based on their answers to my questions. 
limitations_and_societal_impact: Yes.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper proposes an adaptive diffusion convolution strategy that can automatically learn the optimal radius of message passing in graph neural networks and addresses the issue of selecting the optimal radius by hand-tuning. Additionally, this mechanism can serve as a plugin for graph neural networks and improve the model capacity and performance. Eventually, the paper validates this claim on the task of semi-supervised node classification.
main_review: 1.	A novel mechanism to optimally select the neighborhood radius when performing graph diffusion convolution. The paper formulates choosing the radius as a bi-level optimization problem, and the optimization of the radius is performed on the validation set.
2.	It breaks the convention that graph convolution should be based on neighborhood and extends to freely learn an optimal radius for each layer and each feature channel.
3.	Thorough experiments are done to compare with the baseline GDC and explore the relationship between different radius updating mechanisms. 

limitations_and_societal_impact: 1.	There are two methods proposed in the paper, which are ADC and GDC. In the experimental session, comparisons are performed between them. Even though ADC is better than GDC in many cases, there are still some cases where GDC can excel. It would be great if the authors can offer some recommendations for these two methods.
review_title: null

final_score: rating: 8: Top 50% of accepted NeurIPS papers, clear accept
review_content: summary: This paper proposes a strategy for adaptive diffusion convolution (ADC and GADC) that automatically learns the optimal neighborhood aggregation size, and it allows for learning a dedication propagate neighborhood for each GNN layer and each feature channel. They perform ablation studies and compares their method to related work on well-known benchmarks. 
main_review: Originality: The ability to flexibly learn the neighborhood size is original and significant. This is an important contribution and plays very well into previous work as a natural and helpful extension. 

Quality: The paper shows high quality through-out, it’s well done and the experiments are useful and convincing. I would appreciate some kind of visualization of the learned diffusion, that would be interesting. Also, it would be nice to see this on other benchmarks dealing with graph classification and edge classification. 

Clarity: Clear writing and structure. The flow is nice and the material easy to digest.

Significance: I like this work and think it’s a significant contribution. There is however a lot of related work that is dealing with similar problems and I don’t know if there is something that they’ve missed citing and that’s very similar. 
limitations_and_societal_impact: They address it adequately.
review_title: null

Meta-review: This paper proposes a method called adaptive graph diffusion convolution (ADC), which can adaptively decide the neighborhood size for each layer and feature channel. The proposed method can be plugged in to any GNN frameworks. The experimental studies have demonstrated the superiority of the proposed module. The reviewers were split in the beginning, with concerns about novelty etc. After receiving a strong rebuttal from authors, including additional experiments, two reviewers have raised their scores to reflect their satisfaction to the rebuttal. In the end, the reviewers have reached consensus to accept this paper.
Decision: Accept (Poster)