Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper revisits the traditional problem of approximating graph convolutional networks using Chebyshev polynomials. The paper shows that the performance of the network can be greatly improved by using Chebyshev Interpolation to replace the coefficients of ChebNet on both homophilous and heterophilous graphs.
strengths_and_weaknesses: This work is mostly well-written with informative content and new ideas that are worth publishing.

Strengths:

•	The use of Chebyshev Interpolation is both theoretically and practically justified.

•	ChebNetII's performance improvement is significant, particularly for semi-supervised node classification tasks.

•	Following on from the second point, to the best of my knowledge, this paper presents the first empirical study of semi-supervised node classification with polynomial graph filters.

•	ChebNetII scales to the graph Papers100M, which has more than a billion edges.

•	The overall presentation is satisfactory.

Weaknesses:

•	There should be a clearer explanation of the distinction between ChebBase and ChebNet.

•	It would be interesting to showcase some of the filters that ChebNetII has learned. What distinguishes them from the ones learned by BernNet?

Minor points:

•	The best results should also be highlighted in Table 3.

questions: The questions have been discussed in detail as above. To sum up, the main questions are:

•	The difference between ChebBase and ChebNet should be better explained.

•	It would be interesting to showcase some of the filters that ChebNetII has learned. What distinguishes them from the ones learned by BernNet?

•	The best results should also be highlighted in Table 3.

limitations: Yes,  the limitation of this work has been well discussed.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper revisited the Chebyshev approximation and showed that the inferior performance of ChebNet is due to illegal learnt coefficients. On the basis of this insight, a new GNN model called ChebNetII is proposed enhancing the Chebyshev polynomial approximation and reducing the Runge phenomenon. ChebNetII can achieve the state-of- art performance on some open graph datasets.
strengths_and_weaknesses: *Strengths: The authors showed a sharp eye for the subtle inferior performance of ChebNet compared with GCN, GPR-GNN and BernNet and proposed two questions to generalize the problem. By citing related theorems, both the questions are explained clearly. The novel model ChebNet resolves the questions without introducing expensive additional computation complexity.
*Weaknesses: The main theoretical frame is assembled by existing results. It is okay but maybe it makes the paper not very innovative. 

questions: 1.	Do you have some suggestions about the choice of $K$? Does it the same as the original ChebNet?
2.	What does ‘weakly singular’ mean? The vanishing of the derivative of $f$ seems inequivalent to ‘$f$ be locally given by a convergent power series in the interval $(-1,1)$’ at line 132. Could you please give some clear mathematical explanation?
3.	Why one can assert $w_0=w_1$ implies a high-pass filter and $w_0=-w_1$ at line 102 implies a low-pass filter?
limitations: CheNetII seems to have broad applications besides the experiments shown in the paper. One can show more future directions in the paper.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes an extension to ChebNet by introducing Chebyshev Interpolation. The proposed methods is simple, yet provides theoretical support and improved performances for node classification. 
strengths_and_weaknesses: Strengths:
1.) Simple model with theoretical support
2.) Experimental results are favorable.
3.) Paper is well written and easy to read.

Weaknesses:
1.) Theoretical comparisons to adaptive learning of GPRGNN is not clear.
2.) Incremental work though the contribution is useful.

questions: Can ChebNetII be extended with any adaptive learning such as in GPRGNN?

Compared to GPRGNN or MixHop, does ChebNetII learn by convolution using higher-order hops from a node?  


Experiments are descent, however, dataset are a bit old. There is a new homophily measure and new non-homophilic benchmark datasets introduced by [Lim et al., 2021a, Lim et al., 2021b].
Can the authors provide few more experiment with the new new non-hohopnilic datasets?

Can the authors include LINK [Zheleva and Getoor, 2009] as a baseline methods?  LINK only uses from the adjacency matrix and gives good indication to learning without node features and convolutions.

Reference:
   
[Zheleva and Getoor, 2009] Zheleva, E. and Getoor, L. (2009). To join or not to join: The illusion of privacy in  social networks with mixed public and private user profiles. WWW ’09.

[Lim et al., 2021a] Lim, D., Hohne, F. M., Li, X., Huang, S. L., Gupta, V., Bhalerao, O. P., and Lim, S.-N.  (2021a). Large scale learning on non-homophilous graphs: New benchmarks and strong simple methods. In  NeurIPS.
 
[Lim et al., 2021b] Lim, D., Li, X., Hohne, F., and Lim, S.-N. (2021b). New benchmarks for learning on  non-homophilous graphs. Workshop on Graph Learning Benchmarks, WWW 2021.
limitations: Limitations and potential negative societal impact are not well expressed.
review_title: null

Meta-review: metareview: The authors consider the traditional problem of approximating graph convolutional networks using Chebyshev polynomial, which is known as Chebnet. Then, the authors propose a new GNN model called ChebNetII enhancing for reducing the Runge phenomenon; this is an important contribution to GNN. Overall, the reviewers are positive about the paper. Thus, I also vote for acceptance. 
confidence: Certain
Decision: Accept