Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: This paper proposed an auxiliary loss based on mutual information for graph neural network. Such loss is to maximize the mutual information between edge representation and corresponding edge feature in GNN ‘message passing’ function. By assuming a gaussian distribution of edge feature given edge representation, the training can be done efficiently with tractable density. Experiments on molecule regression and knowledge graph completion show better performance than MPNN. 

Overall the paper is written in a clear way which is easy to follow. The idea of using mutual information as some kind of regularization is also interesting. However, there are some concerns I have with the paper:

Regarding formulation

1. The derivation up to Eq(8) looks fine to me, where the assumptions are reasonable. However from Eq(8) one can see this is reduced to an ‘auto-encoder’ type of regularization, where one can have a trivial solution for reconstruction -- the identity network, when the hidden dimension is larger than input dimension. And in this paper, dimension of W should always be larger than the dimension of e (for example, in molecules e should be low dimension vector with the bond type, distance, etc., while W should have dimension that matches the node embeddings).

I think the original loss (i.e., the supervised MSE, cross entropy etc) would help a bit with such degenerated case, but it is possible that the learned f(e) contains both identity mapping (or equivalent) and the representation that contributes to original loss.  

2. Actually I’m also not sure if I get the motivation here. If one needs to do this regularization for edges, why don’t we consider this auxiliary loss for node embeddings as well? As in molecules, atoms have more interesting features than bonds, which should account more if the mutual information loss is needed. 

Regarding experiment

1. In Figure 1, the training loss of EIGNN is better than MPNN. This is a bit counterintuitive to me, as I think the auxiliary is a kind of regularization -- which might help with generalization but not necessarily the training loss. 

2. The original paper of MPNN reports the relative MAE. Is it possible to report the results using the same metric as previous paper? It would make the comparison more consistent -- though showing the improvement in current way is not too bad. 

3. I think one simple ablation study would to concat the edge feature directly inside the ‘message passing’ procedure, or have some ‘residual’ type of connection for edge features. 

review_title: Official Blind Review #4

final_score: rating: 3: Weak Reject
review_content: This paper introduces a mutual information term into the training objective of message passing graph neural networks.  The additional term favors the preservation on information in a mapping from an input edge feature vector e_{i,j} to a weight matrix f(e_{i,j}) used in computing messages across the edge from node i to node j.  A variational lower bound on the mutual information is used in training.  Impressive empirical results are given for chemical property prediction and relation prediction in knowledge graphs.  I have no real complaints other than I might recommend citing the original work on infomax:

"Self Organization in a Perceptual Network", Ralph Linsker, 1988.

Postscript:  I have been swayed by the complaints of reviewer 1 and reduced my score to weak reject.
review_title: Official Blind Review #1

final_score: rating: 8: Accept
review_content: In this paper, the authors proposed a new kind of graph neural network that can use continuous edge features. Specifically, a variational lower bound is proposed for mutual information and integrated into the GNN model so that MI between edge features and the message passing channel is maximized. Experiments on molecule graph datasets and knowledge graph datasets show the effectiveness of the proposed method compared to the state-of-the-art GNN models.

Utilizing continuous edge features in GNN is an important and difficult task. The authors proposed an elegant solution. The paper is well written and extensive experiments on large scale datasets are compared with 9 competitors that are all outperformed by EIGNN on nearly all the cases.

To conclude, I think the paper will be a good addition to the conference.
review_title: Official Blind Review #3

final_score: rating: 6: Weak Accept
review_content: This paper proposed a new graph neural network to utilize the edge features. In particular, it proposes the Edge Information maximized Graph Neural Network (EIGNN) that maximizes the Mutual Information (MI) between edge features and message passing channels. The MI is reformulated as a differentiable objective via a variational approach. The experimental results have some improvement over existing methods.  Overall, the idea is novel and well presented. 

Pros:
1. The idea of utilizing edge features looks novel.
2. The writing is clear.
3. Extensive experiments are done to verify the performance of the proposed method.

Cons:
1. The theoretical analysis is just a regular routine. 
2. How does the hyper-parameter affect the performance? In other words, how does the component of the edge features affect the model performance?
review_title: Official Blind Review #2

Meta-review: This paper proposed an auxiliary loss based on mutual information for graph neural network. Such loss is to maximize the mutual information between edge representation and corresponding edge feature in GNN ‘message passing’ function. GNN with edge features have already been proposed in the literature. Furthermore,  the reviewers think the paper needs to improve further in terms of explain more clearly the motivation and rationale behind the method. 
Decision: Reject