Paper:
We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB. This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive enough to model multi-hop inferences, and scalable enough to use with realistically large KBs. The sparse-matrix reified KB can be distributed across multiple GPUs, can scale to tens of millions of entities and facts, and is orders of magnitude faster than naive sparse-matrix implementations. The reified KB enables very simple end-to-end architectures to obtain competitive performance on several benchmarks representing two families of tasks: KB completion, and learning semantic parsers from denotations.

Review:
The paper provides a way to represent symbolic KBs called sparse matrix reified. Relations and entities' types are modelled using sparse matrices. This modelization allows distributing the computation on many GPUs. A neural model is used to manage these matrices. The trained model can be used to perform multi-hop queries. The proposed system has been compared with related systems. The results show that it achieves hits@1 that are comparable with the others.
The proposed approach seems promising, however, I feel that the paper is not ready for publication. The experiments lack a scalability test with related systems, the scalability test included in the paper only takes into account other definitions of the system. Also, comparison on the run time should be performed to see if the lower performance in terms of hits@1 (which are good anyway) is balanced by a better run time.
Therefore, it is difficult to see whether the proposed system is good or not.
As for the description of the system, it seems to me to be quite foggy. In my opinion, the neural model should be better described to show how the sparse matrices are mapped into the model.
Also, how are the training and testing sentences created? How would the output of a query look?
After reading the paper I have the feeling that it was written in a bit of a hurry, without working on the details. There are several typos, parentheses not correctly opened or closed, out of place commas that make some sentences seem unrelated to the rest of the paragraph. However, here last problems are easily fixable.
To sum up, I am conflicted about the choice of the final score. On the one hand, the approach is interesting, on the other hand the article seems to me not mature enough and strong enough from the point of view of organization, contents and experimental results shown.
Minor problems
On page 4, the size of the matrices XM_k uses the factor b that is introduced later.
In the introduction, next to footnote 1, I suggest specifying that A is the first query, the one about Tarantino's movies.
Also, his surname is misspelt throughout the paper. The correct one is Tarantino.