Venue: ICLR 2022 Track Blog

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: This blog post covers Graph Coarsening based on the paper "Graph Coarsening With Neural Networks". Overall, the blog post is interesting and does an adequate job of developing intuitions for the main paper of interest. The biggest confusion I had reading the blog post is that there is very little description of the vertex map $\pi$. Is $\pi$ always given to us? The blog should do a better job of either pointing to papers that propose different choices of $\pi$ or explicitly mention that this is not something they cover in detail. Here are other minor suggestions that would improve the exposition of the blog post:

- The gif of the GOREN framework really should just be a static image. The last frame in the gif is the most important but it only stays for a fraction of a second.
- When describing the Rayleigh Quotient, the blog reads: "This is because the eigenvectors and eigenvalues of the linear operator A are more directly related to its Rayleigh Quotient." Can you please expand on this a bit more, at the moment it's a bit vague. Perhaps adding an equation would be good here.
- The similarity function uses \mathcal{L}, but this in fact not the loss used in GOREN. This was a bit confusing, I would recommend changing the notation so the similarity function is different.
- The figure containing empirical results using GOREN has text that is too small. Please make this bigger so it is more legible.


review_title: Graph Coarsening Blog Review

final_score: rating: 7: Good paper, accept
review_content: The blog mainly focuses on the paper “Graph Coarsening With Neural Networks” https://openreview.net/forum?id=uxpzitPEooJ . It states the motivation and problem clearly, covers the key design of the framework, and points out some future directions. Overall, I think it is a good blog post and recommend acceptance. There are a few places I think the author can improve the writing upon.

- “Traditional coarsening approaches aim to retain the spectral properties between original and coarse graphs. This involves…” 
- I won’t say these two papers are traditional methods. There are early works but published only one or two years before the paper, with different formulations on what spectral property a coarsening method should preserve. 
- I find the definition of “graph partitioning” is a bit confusing
- somehow the location of \hat is off on my machine. 
- For a n vector \hat{f}: why not just say for a vector of length n
- Establishing a link between original and coarsened graphs requires a brief visit into their operations. 
- do you mean operator instead? I suggest you expand this a bit and say to compare two graphs the paper defines the operators on both original graph and coarse graph. 
- when you introduce loss(L, \hat{L}), you didn’t define what k is.
- why call weight assignment and adjustment? In the original paper, they used the term weight assignment map.
- Node assignment in supernodes can be learned using a separate GNN following GOREN. 
- I think what you mean is that there is a separate GNN doing learning to “group” (instead of the fixed coarsening algorithm) *followed* by a GOREN. Somehow I find node assignment is a bit confusing 
- GOREN utilizes differentiable loss functions including mappings. These mapping use trivial spectral structures. 

	I cannot really follow the connection here. What do you mean by trivial spectral structure?

review_title: blog review

Decision: Accept