Question

I'm trying to visualize the regions defined by EmQL. Quick question: are those regions convex?

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).