Knowledge graphs store facts using relations between pairs of entities. In this work, we address the question of link prediction in knowledge hypergraphs where each relation is defined on any number of entities. While there exist techniques (such as reification) that convert the non-binary relations of a knowledge hypergraph into binary ones, current embedding-based methods for knowledge graph completion do not work well out of the box for knowledge graphs obtained through these techniques. Thus we introduce HSimplE and HypE, two embeddingbased methods that work directly with knowledge hypergraphs in which the representation of an entity is a function of its position in the relation. We also develop public benchmarks and baselines for this task and show experimentally that the proposed models are more effective than the baselines. Our experiments show that HypE outperforms HSimplE when trained with fewer parameters and when tested on samples that contain at least one entity in a position never encountered during training.
This paper proposes two new embedding strategies for the task of knowledge graph completion, with special attention on generalizations that support hypergraphs.  The first method, HSimplE, learns an embedding for entities that directly contains multiple positional representations; these are shifted depending on the relation they're used in.  The second method, HypE, disentangles entity embeddings and positional convolutional filters, allowing stronger positional generalization.  Experiments on standard benchmarks demonstrate that the approaches work well.
I think this paper should be accepted.  While the ideas are so simple that they border on being trivial generalizations of previous work, the paper is well written, and the results seem solid.  I think this is work that needs to be done, so I favor accepting it.
On the positive side:
* The ideas underlying HSimplE and HypE are natural and clear - we basically want to learn better embeddings for hypergraphs, and there are a couple of obvious ways to do that.  Both of these seem clear.
* The experiments are nicely done, and show a consistent (if unsurprising) benefit to the approach.
* The paper is well written and well situated in the literature.
* I expect that other researchers in this area will be able to reproduce and build upon this work without any difficulty.
On the negative side:
* The ideas are obvious; the results are unsurprising; the paper lacks "deep insight".  It is a contribution in the sense that someone needed to do this work, and I'm glad that it's been done (and done well), but it's not earth-shattering.
* It doesn't seem like this is quite the best version of this idea.  I really like the idea of HypE, but it seems strange that entity embeddings are modulated based on position *only*, without regard to relation -- that is, it seems like a given entity in position #2 might need to be represented in very different ways depending on which relation is being used.