Question
Fragment of a discussion from Course talk:CPSC532:StaRAI2020:Query2Box and Faithful Embeddings for Knowledge Base Queries.
Hi Lucca, here the problem is that they represent a set of entities using a weighted sum of entity vectors. So, they have similar logic to point-based embedding. You could say a point is a trivial convex set.
Also, when computing answers to a query like relation following, the top-k similar triplet embedding is generally the answer. But as k is the same for every query, it is not necessary this region will be convex(unlike in threshold-based system where this region will be a convex sphere with the center as centroid and radius equal to the threshold).