Paper:
Many methods have been developed to represent knowledge graph data, which implicitly exploit low-rank latent structure in the data to encode known information and enable unknown facts to be inferred. To predict whether a relationship holds between entities, their embeddings are typically compared in the latent space following a relation-specific mapping. Whilst link prediction has steadily improved, the latent structure, and hence why such models capture semantic information, remains unexplained. We build on recent theoretical interpretation of word embeddings to derive an explicit structure for the representations of relations between entities. From this we explain properties and justify the relative performance of leading knowledge graph representation methods for identifiable relation types, including their often overlooked ability to make independent predictions.

Review:
This paper proposes to provide a detailed study on the explainability of link prediction (LP) models by utilizing a recent interpretation of word embeddings. More specifically, the authors categorize the relations in KG into three categories (R, S, C) using the correlation between the semantic relation between two words and the geometric relationship between their embeddings. The authors utilize this categorization to provide a better understanding of LP models’ performance through several experiments.
This paper reads well and the results appear sound. I personally believe that works on better understanding KGC models are a very essential direction which is mostly ignored in this field of study. Moreover, the provided experiments support the authors’ intuition and arguments.
As for the drawbacks, I find the technical novelty of the paper is somewhat limited, as the proposed method consists of a mostly straightforward combination of existing methods. Further, I believe this work needs more experimental results and decisive conclusions identifying future directions to achieve better performance on link prediction. My concerns are as follows:
•    I am wondering about the reason for omitting Max/Avg path for two of the relations in WN18RR? Further, the average of 15.2 for the shortest path between entities with “also_see” relation appears to be a mistake?
•    Was there any specific reason in choosing WN18RR and NELL-995 KGs for the experiments?
•    It would be interesting to see the length of paths between entities for train and test data separately. 
•    I suggest providing a statistical significance evaluation for each experiment to better validate the conclusions.
•    I find the provided study in section 4.2 very similar to the triple classification task in KGs. Can you elaborate on the differences and potential advantages of your setting?
•    I am wondering how you identified the “Other True” triples for WN18RR KG in section 4.2 experiments?
On overall, although I find the proposed study very interesting and enlightening, I believe that the paper needs more experimental results and decisive conclusions.