Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 6: Weak Accept
review_content: The authors proposed a message passing neural network-based graph matching methods. The overall framework can be viewed as a graph siamese network, where two set of points are passing through the same graph neural network, and then two new embeddings are generated. Using the two embedding the similarity between points can be computed and then the final matching can be generated. 

The overall structure of this paper is similar to [1] and [2], the authors should discuss the difference of the proposed with these two papers, if it is possible, the authors may try to compare with these two methods in experiments. Currently, I think the main contribution of the paper should be the new message-passing scheme (in Sec. 3.2). However, from the current experiment, I can not see if the performance improvement is from the new message-passing scheme.

In fact, the message passing scheme is also related to the dual decomposition framework, which is previously used in the graph matching area. For example, in [3], a message-passing algorithm derived from dual decomposition is used to solve the graph matching problem. The authors may also consider add some discussion the difference between message-passing derived from dual decomposition and the message passing in the graph neural network.

==================================== After Revision ==============================================
In the new experiment, the authors proved that the new message-passing scheme (i.e. the consensus stage) in Sec 3.2 can successfully improve the performance by refining original assignment. Thus I modify the score to weak accept.


[1] Wang, Yue, and Justin M. Solomon. "Deep Closest Point: Learning Representations for Point Cloud Registration.", ICCV 2019,
[2] Zhen Zhang, and Wee Sun Lee. "Deep Graphical Feature Learning for the Feature Matching Problem.", ICCV 2019
[3] Paul Swoboda et. al. "A study of Lagrangean decompositions and dual ascent solvers for graph matching.", CVPR 2017
review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: This paper proposes a two-stage GNN-based architecture to establish correspondences between two graphs. The first step is to learn node embeddings using a GNN to obtain soft node correspondences between two graphs. The second step is to iteratively refine them using the constraints of matching consensus in local neighborhoods between graphs. The overall refining process resembles the classic graph matching algorithm of graduated assignment (Gold & Rangarajan, 1996), but generalizes it using deep neural representation. Experiments show that the proposed algorithm performs well on real-world tasks of image matching and knowledge graph entity alignment.

The paper is interesting and has some good potential but lacks some important evaluations and analyses. My main concerns are as follows. 

1) The consensus in the second stage is crucial? 
As the title shows, the main technical contribution lies in the second stage of consensus inducing. But, for the real tasks, in the experiments, the gain by the second stage is not significant or often negligible (L=0 vs. L=10 or 20  in Table 1,2,3). The results of the first stage (L=0) already give better results than all the baselines in many cases, so that most gains appear to come from the usage of GNNs for representation. This makes the major contribution of this work less significant.  I hope the authors justify this. And, I guess that's maybe because the consensus information may also be induced in the first stage by matching nodes with relational presentations learned using a GNN. To see this, the authors may run the second stage only without the first stage. 

2) Comparison to the graduated assignment (GA) process
As discussed in 3.3, the proposed neighborhood consensus can be viewed as a generalization of GA of Eq.6 with trainable neural modules. But, it's not actually shown what is the gain by this generalization. This needs to be shown experimentally by substituting the second stage by GA process.  

3) Robustness to node addition or removal. 
All the experiments look assuming only edges are varied. Is this algorithm robust to node addition or removal, occurring in many practical graph matching problems? This needs to be also discussed.   

======================================

The rebuttal succeeds in addressing most of my concerns so that I upgrade my initial rating to weak accept. I hope all the points in the rebuttal are included in the final manuscript. 
review_title: Official Blind Review #1

final_score: rating: 6: Weak Accept
review_content: This paper suggests a framework for answering graph matching questions consisting of local node embeddings with a message passing refinement step.

The paper has well written text, offers what appear to be nice experiments validating the method and discusses its own limitations.

I am giving a weak accept.  

I the weak accept is my reflection of my inability to provide useful feedback.  This is also out of domain for me and I am not a useful reviewer for this paper.

As a general comment, I will say that the paper adopts a highly mathematical style that will be off putting to many readers.  Many of the expressions are 'high entropy'  For instance, the embedding network is given as $\mathbf{\Psi}_{\theta_1}$ throughout.  This is seven levels of typographical distinction for the main character of the story.  This is a (1) bold (2) capital (3) Greek letter with a (4) subscript that is (5) greek with a (6) subscript that is (7) numeric.  I understand that each of these levels of distinction has a purpose and a meaning, but it is also arguably a much richer designation that is necessary.  Generally the paper feels like this, as if its being too unnecessarily specific.  Personally I found the paper rather difficult to read and decompose, which I believe does count against the paper.  The overly specific nature of paper will cut into its potential readership strongly.
review_title: Official Blind Review #3

Meta-review: The paper proposed an end-to-end network architecture for graph matching problems, where first a GNN is applied to compute the initial soft correspondence, and then a message passing network is applied to attempt to resolve structural mismatch. The reviewers agree that the second component (message passing) is novel, and after the rebuttal period, additional experiments were provided by the authors to demonstrate the effectiveness of this. Overall this is an interesting network solution for graph-matching, and would be a worthwhile addition to the literature.
Decision: Accept (Poster)