Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: This paper proposes a graph pooling method by utilizing the Mincut regularization loss. It is an interesting idea and performs well in a number of tasks. However, due to the limitation of novelty and poor organizations, this paper cannot meet the standard of ICLR. The detailed reasons why I give a weak reject are listed as follows:

1. Even though the proposed minCUT pool is interesting, the contribution is not enough to get published in the ICLR. If I understand correctly, the only difference is the unsupervised loss, compared with the previous work, Diffpool [1].
 
2. The paper needs to be reorganized to demonstrate its contribution. The proposed method section only has around 1.5 pages, making it difficult to understand the proposed method clearly. Therefore, more details and analyses about the proposed method should be included to support and clarify the idea.
 
3. The paper needs to be improved for its theoretical derivations and proof. For example, it is not clear why Equation (6) is correct, which is the main contribution of this paper. The authors provide intuitive thoughts but there are not theoretical derivations and proof. The term $L_c$ comes from Equation (2) but why is it correct to only compute the trace?
 
4. Some experiments cannot support the claim very well.  For example, the graph clustering experiments are not convincing. The goal of graph pooling is to learn high-level graph embeddings but not perform graph clustering. It is not proper to evaluate the graph pooling method using graph clustering tasks. Or, the author should clarify the motivation to do this experiment. If the model is trained for graph classification or node classification, then why should the node clusters lead to high NMI or CS scores?

[1]. Ying et al., Hierarchical Graph Representation Learning with Differentiable Pooling, NIPS 2018


==========Update===========

I have read authors response and other reviews. While the authors address some of my concerns, I still believe the contribution/novelty is limited. I am sticking to my score.
review_title: Official Blind Review #4

final_score: rating: 3: Weak Reject
review_content: The authors propose a differentiable pooling method for graph data, known as minCUTpool. It learns a clustering assignment matrix using MLPs and then add regularization terms to encourage the clustering results close to the minCUT. The experimental results show that the regularization terms can help improve the performance.

Cons:
1. The novelty is limited. Compared with existing work DiffPool, the proposed method is improving the Diffpool by adding two regularization terms. In addition, the main regularization $L_c$ is already proposed in previous studies. 
2. The motivation is not clear. Why should we apply minCut for graph pooling? Intuitively, how is the minCUT related to graph representation learning? The minCut can identify dense graph components but why these dense components should be different clusters in graph pooling? In addition, the author claim “cluster together nodes which have similar features”. How could minCut terms lead to such conclusion? 
3.  Important baselines are missing, such as Sortpool (Zhang et al, An end-to-end deep learning architecture for graph classification, AAAI 2018), Self-attention pool (Lee et al, Self-Attention Graph Pooling, ICML 2019). 
4. The graph classification results are not convincing enough. In the original Top-K paper (Gao et al , Graph U-Net, ICML2019), the reported results for Proteins and DD datasets are 77.68%, 82.43%, which are significantly better than the results reported in this paper. 
review_title: Official Blind Review #1

final_score: rating: 8: Accept
review_content: This paper proposes a solution to the important problem of pooling in graph neural networks. The method relies on minimizing a surrogate function inside the standard SGD loop and in conjunction with the optimization of the model parameters - such loss function aiming at optimizing the minCut on the graph. By that it aims to effective achieve a soft clustering of nodes that are both well connected and that have similar embeddings. This in an elegant choice, somewhat resembling the DiffPool method since it's also end-to-end trainable. However it adds the local graph connectivity information due to the minCut loss (and related orthogonality penalty to achieve non trivial solutions on the relaxed minCut continuous problem). Such local graph connectivity is indeed important information to consider when carrying out pooling.
Results show good performance improvement on different tasks of graph clustering, node and whole graph classification. The paper is well written and clear to read. The math is solid and the concept is well substantiated by results.
I found no mention about code release and I would solicit the authors to release the code to reproduce the experiments.
review_title: Official Blind Review #2

Meta-review: Two reviewers are negative on this paper while the other reviewer is positive. Overall, the paper does not make the bar of ICLR. A reject is recommended.
Decision: Reject