The advance of node pooling operations in Graph Neural Networks (GNNs) has lagged behind the feverish design of new message-passing techniques, and pooling remains an important and challenging endeavor for the design of deep architectures. In this paper, we propose a pooling operation for GNNs that leverages a differentiable unsupervised loss based on the minCUT optimization objective. For each node, our method learns a soft cluster assignment vector that depends on the node features, the target inference task (e.g., a graph classification loss), and, thanks to the minCUT objective, also on the connectivity structure of the graph. Graph pooling is obtained by applying the matrix of assignment vectors to the adjacency matrix and the node features. The proposed method can also be used as a stand-alone module to cluster vertexes in annotated graphs and solve unsupervised problems. We validate the effectiveness of the proposed pooling method on downstream tasks, including supervised graph classification and a set of unsupervised tasks, which reveal the limitations of existing GNN pooling approaches.
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
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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.