Venue: ICLR 2018 conference

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: The paper proposes a new neural network model for learning graphs with arbitrary length, by extending previous models such as graph LSTM (Liang 2016), and graph ConvNets. There are several recent studies dealing with similar topics, using recurrent and/or convolutional architecture. The Related work part of this paper makes a good description of both topics. 

I would expect the paper elaborate more (at least in a more explicit way) about the relationship between the two models (the proposed graph LSTM and the proposed Gated Graph ConvNets). The authors claim that the innovative of the graph Residual ConvNets architecture, but experiments and the model section do not clearly explain the merits of Gated Graph ConvNets over Graph LSTM. The presentation may raise some misunderstanding. A thorough analysis or explanation of the reasons why the ConvNet-like architecture is better than the RNN-like architecture would be interesting. 

In the section of experiments, they compare 5 different methods on two graph mining tasks. These two proposed neural network models seem performing well empirically. 

In my opinion, the two different graph neural network models are both suitable for learning graphs with arbitrary length, 
and both models worth future stuies for speicific problems. 
review_title: the relation between the two proposed models is not very clear

final_score: rating: 3: Clear rejection
review_content: The paper proposes an adaptation of existing Graph ConvNets and evaluates this formulation on a several existing benchmarks of the graph neural network community. In particular, a tree structured LSTM is taken and modified. The authors describe this as adapting it to general graphs, stacking, followed by adding edge gates and residuality.

My biggest concern is novelty, as the modifications are minor. In particular, the formulation can be seen in a different way. As I see it, instead of adapting Tree LSTMs to arbitary graphs, it can be seen as taking the original formulation by Scarselli and replacing the RNN by a gated version, i.e. adding the known LSTM gates (input, output, forget gate). This is a minor modification. Adding stacking and residuality are now standard operations in deep learning, and edge-gates have also already been introduced in the literature, as described in the paper.

A second concern is the presentation of the paper, which can be confusing at some points. A major example is the mathematical description of the methods. When reading the description as given, one should actually infer that Graph ConvNets and Graph RNNs are the same thing, which can be seen by the fact that equations (1) and (6) are equivalent.

Another example, after (2), the important point to raise is the difference to classical (sequential) RNNs, namely the fact that the dependence graph of the model is not a DAG anymore, which introduces cyclic dependencies. 

Generally, a clear introduction of the problem is also missing. What are the inputs, what are the outputs, what kind of problems should be solved? The update equations for the hidden states are given for all models, but how is the output calculated given the hidden states from variable numbers of nodes of an irregular graph?

The model has been evaluated on standard datasets with a performance, which seems to be on par, or a slight edge, which could probably be due to the newly introduced residuality.

A couple of details :

- the length of a graph is not defined. The size of the set of nodes might be meant.

- at the beginning of section 2.1 I do not understand the reference to word prediction and natural language processing. RNNs are not restricted to NLP and I think there is no need to introduce an application at this point.

- It is unclear what does the following sentence means: "ConvNets are more pruned to deep networks than RNNs"?

- What are "heterogeneous graph domains"?

review_title: Residual Gated Graph ConvNets

final_score: rating: 7: Good paper, accept
review_content: The authors revised the paper according to all reviewers suggestions, I am satisfied with the current version.

Summary: this works proposes to employ recurrent gated convnets to solve graph node labeling problems on arbitrary graphs. It build upon several previous works, successively introducing convolutional networks, gated edges convnets on graphs, and LSTMs on trees. The authors extend the tree LSTMs formulation to perform graph labeling on arbitrary graphs, merge convnets with residual connections and edge gating mechanisms. They apply the 2 proposed models to 3 baselines also based on graph neural networks on two problems: sub-graph matching (expressing the problem of sub-graph matching as a node classification problem), and semi supervised clustering.  

Main comments:
It would strengthen the paper to also compare all these network learning based approaches to variational ones. For instance, to a spectral clustering method for the semi supervised clustering, or
solving the combinatorial Dirichlet problem as in Grady: random walks for image segmentation, 2006.

The abstract and the conclusion should be revised, they are very vague.
- The abstract should be self contained and should not contain citations.
- The authors should clarify which problem they are dealing with.
- instead of the "numerical result show the performance of the new model", give some numerical results here, otherwise, this sentence is useless.
- we propose ... as propose -> unclear: what do you propose?
 

Minor comments:
- You should make sentences when using references with the author names format. Example: ... graph theory, Chung (1997) -> graph theory by Chung (1997)
- As Eq 2 -> As the minimization of Eq 2 (same with eq 4)
- Don't start sentences with And, or But


review_title: Interesting approach that should be better presented 

Meta-review: The authors make an experimental study of the relative merits of RNN-type approaches and graph-neural-network approaches to solving node-labeling problems on graphs.   They discuss various improvements in gnn constructions, such as residual connections.

This is a borderline paper.  On one hand, the reviewers feel that there is a place for this kind of empirical study, but on the other, there is agreement amongst the reviewers that the paper is not as well written as it could be.  Furthermore, some reviewers are worried about the degree of novelty (of adding residual connections to X).

I will recommend  rejection, but urge the authors to clarify the writing and expand on the empirical  study and resubmit. 
Decision: Reject