Paper:
Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks
Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationary structures on user/item graphs, and the number of parameters to learn is linear w.r.t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines a novel multi-graph convolutional neural network that can learn meaningful statistical graph-structured patterns from users and items, and a recurrent neural network that applies a learnable diffusion on the score matrix. Our neural network system is computationally attractive as it requires a constant number of parameters independent of the matrix size. We apply our method on several standard datasets, showing that it outperforms state-of-the-art matrix completion techniques.

Review:
This paper generalizes a recent NIPS 2016 paper [10] by allowing convolutional neural network (CNN) models to work on multiple graphs.  It extracts local stationary patterns from signals defined on the graphs simultaneously.  In particular, it is applied to recommender systems by considering the graphs defined between users and between items.  The multi-graph CNN model is followed by a recurrent neural network (RNN) with long short-term memory (LSTM) cells to complete the score matrix.
Strengths of the paper:
* The proposed deep learning architecture is novel for solving the matrix completion problem in recommender systems with the relationships between users and the relationships between items represented as two graphs.
* The proposed method has relatively low computational complexity.
* The proposed method has good performance in terms of accuracy.
Weaknesses of the paper:
* The multi-graph CNN part of the proposed method is explained well, but the RNN part leaves open many questions.  Apart from illustrating the process using an example in Figure 3, there is not much discussion to explain why it can be regarded as a matrix diffusion process.  Does the process correspond to optimizing with respect to some criterion?  What is the effect of changing the number of diffusion steps on the completed matrix and how is the number determined?  This needs more detailed elaboration.
In addition, to demonstrate that incorporating the pairwise relationships between users or items helps, you may add some degenerate versions of RMGCNN or sRMGCNN by removing one or both graphs while keeping the rest of the architecture unchanged (including the RNN part).
Minor comments (just some examples of the language errors):
#18: “Two major approach”
#32: “makes well-defined”
#66: “Long-Short Term Memory”
#76: “turns out an NP-hard combinatorial problem”
#83-84: “to constraint the space of solutions”
#104-105: “this representation … often assumes”
#159: “in details”
Table 1 & Table 2: strictly speaking you should show the number of parameters and complexity using the big-O notation.
The reference list contains many arXiv papers.  For those papers that have already been accepted, the proper sources should be listed instead.