While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to deep graph similarity learning. Recent work has considered either global-level graph-graph interactions or low-level node-node interactions, ignoring the rich cross-level interactions between parts of a graph and a whole graph. In this paper, we propose a Hierarchical Graph Matching Network (HGMN) for computing the graph similarity between any pair of graph-structured objects. Our model jointly learns graph representations and a graph matching metric function for computing graph similarity in an end-to-end fashion. The proposed HGMN model consists of a multi-perspective node-graph matching network for effectively learning crosslevel interactions between parts of a graph and a whole graph, and a siamese graph neural network for learning global-level interactions between two graphs. Our comprehensive experiments demonstrate that our proposed HGMN consistently outperforms state-of-the-art graph matching network baselines for both classification and regression tasks.
In this paper, a hierarchical graph matching network, which considers both graph-graph interaction and node-graph interaction, is proposed. Specifically, the graph-graph interaction is modeled through graph level embeddings learned by GCN with pooling layers. While node-graph interaction is modeled using node embedding learned by GCN and attentive graph embedding aggregated from node embedding. 
Some concerns about the paper are as follows:
1)	The novelty of the paper is incremental. The major contribution of the paper lies in the propose of multi-perspective matching function $f_m()$, which is somewhat similar to the Neural Tensor Networks proposed in [1] and utilized in [2] Although, in [2], the Neural Tensor Network is used to measure the similarity between graph-level embeddings.
2)	Some of the technical details of the paper is not clearly presented or well explained. 
a.	In Eq. (7), attentive graph-level embeddings are calculated using weighted average of its node embeddings. However, it is not clear which node $i$ from the other graph should be used to calculate the weights (\alpha_{I,j}, \beta_{i,j}). Furthermore, it is also not clear why the attention score should solely base on a single node from the other graph rather than the information of the entire graph. 
b.	In Eq. (10), it would be better if the authors could provide more motivations about using Bi-LSTM aggregator. Especially, the embeddings to be aggregated are unordered. What are the two directions in Bi-LSTM in this case? What is the benefit of using Bi-LSTM as aggregator compared with LSTM aggregator or other aggregators? 
Some other questions to be clarified:
1)	Why different similarity score functions are adopted for the classification task and the regression task? 
2)	For the classification task, the mean squared error loss is adopted. Why not using other more commonly used loss for classification task? 
Suggestions:
It would be better if the authors could empirically show the effectiveness of the Bi-LSTM aggregator.
It would be helpful if the authors could conduct some investigation on how the number of perspectives affect the performance of the model.
[1] Reasoning With Neural Tensor Networks for Knowledge Base Completion
[2] SimGNN: A Neural Network Approach to Fast Graph Similarity Computation