  Link prediction on knowledge graphs (KGs) has been extensively studied on
binary relational KGs, wherein each fact is represented by a triple. A
significant amount of important knowledge, however, is represented by
hyper-relational facts where each fact is composed of a primal triple and a set
of qualifiers comprising a key-value pair that allows for expressing more
complicated semantics. Although some recent works have proposed to embed
hyper-relational KGs, these methods fail to capture essential inference
patterns of hyper-relational facts such as qualifier monotonicity, qualifier
implication, and qualifier mutual exclusion, limiting their generalization
capability. To unlock this, we present \emph{ShrinkE}, a geometric
hyper-relational KG embedding method aiming to explicitly model these patterns.
ShrinkE models the primal triple as a spatial-functional transformation from
the head into a relation-specific box. Each qualifier ``shrinks'' the box to
narrow down the possible answer set and, thus, realizes qualifier monotonicity.
The spatial relationships between the qualifier boxes allow for modeling core
inference patterns of qualifiers such as implication and mutual exclusion.
Experimental results demonstrate ShrinkE's superiority on three benchmarks of
hyper-relational KGs.
