Graphs are fundamental data structures required to model many important realworld data, from knowledge graphs, physical and social interactions to molecules and proteins. In this paper, we study the problem of learning generative models of graphs from a dataset of graphs of interest. After learning, these models can be used to generate samples with similar properties as the ones in the dataset. Such models can be useful in a lot of applications, e.g. drug discovery and knowledge graph construction. The task of learning generative models of graphs, however, has its unique challenges. In particular, how to handle symmetries in graphs and ordering of its elements during the generation process are important issues. We propose a generic graph neural net based model that is capable of generating any arbitrary graph. We study its performance on a few graph generation tasks compared to baselines that exploit domain knowledge. We discuss potential issues and open problems for such generative models going forward.
The paper introduces a generative model for graphs. The three main decision functions in the sequential process are computed with neural nets. The neural nets also compute node embeddings and graph embeddings and the embeddings of the current graph are used to compute the decisions at time step T. The paper is well written but, in my opinion, a description of the learning framework should be given in the paper. Also, a summary of the hyperparameters used in the proposed system should be given. It is claimed that all possible types of graphs can be learned which seems rather optimistic. For instance, when learning trees, the system is tweaked for generating trees. Also, it is not clear whether models for large graphs can be learned. The paper contain many interesting contributions but, in my opinion, the model is too general and the focus should be given on some retricted classes of graphs. Therefore, I am not convinced that the paper is ready for publication at ICLR'18.
* Introduction. I am not convinced by the discussion on graph grammars in the second paragraph. It is known that there does not exist a definition of regular grammars in graph (see Courcelle and Engelfriet, graph structure and monadic second-order logic ...). Moreover, many problems are known to be undecidable. For weighted automata, the reference Droste and Gastin considers weighted word automata and weighted logic for words. Therefore I does not seem pertinent here. A more complete reference is "handbook of weighted automata" by Droste. Also, many decision problems for wighted automata are known to be undecidable. I am not sure that the paragraph is useful for the paper. A discussion on learning as in footnote 1 shoud me more interesting.
* Related work. I am not expert in the field but I think that there are recent references which could be cited for probablistic models of graphs.
* Section 3.1. Constraints can be introduced to impose structural properties of the generated graphs. This leads to the question of cheating in the learning process.
* Section 3.2. The functions f_m and g_m for defining graph embedding are left undefined. As the graph embedding is used in the generating process and for learning, the functions must be defined and their choice explained and justified.
* Section 3. As said before, a general description of the learning framework should be given. Also, it is not clear to me how the node and graph embeddings are initialized and how they evolve along the learning process. Therefore, it is not clear to me why the proposed updating framework for the embeddings allow to generate decision functions adapted to the graphs to be learned.  Consequently, it is difficult to see the influence of T. Also, it should be said whether the node embeddings and graph embeddings for the output graph can be useful.
* Section 3. A summary of all the hyperparameters should be given.
* Section 4.1. The number of steps is not given. Do you present the same graph multiple times. Why T=2 and not 1 or 10 ?
* Section 4.2. From table 2, it seems that all permutations are used for training which is rather large for molecules of size 20. Do you use tweaks in the generation process.
* Section 4.3. The generation process is adapted for generating trees which seems to be cheating. Again the choice of T seems ad hoc and based on computational burden.
* Section 5 should contain a discussion on complexity issues because it is not clear how the model can learn large graphs.
* Section 5. The discussion on the difficulty of training shoud be emphasized and connected to the --missing-- description of the model architecture and its hyperparameters.
* acronyms should be expansed at their first use