  Some of the most successful knowledge graph embedding (KGE) models for link
prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based
models. Under this perspective they are not amenable for exact
maximum-likelihood estimation (MLE), sampling and struggle to integrate logical
constraints. This work re-interprets the score functions of these KGEs as
circuits -- constrained computational graphs allowing efficient
marginalisation. Then, we design two recipes to obtain efficient generative
circuit models by either restricting their activations to be non-negative or
squaring their outputs. Our interpretation comes with little or no loss of
performance for link prediction, while the circuits framework unlocks exact
learning by MLE, efficient sampling of new triples, and guarantee that logical
constraints are satisfied by design. Furthermore, our models scale more
gracefully than the original KGEs on graphs with millions of entities.
