  Knowledge Graph Embeddings (KGEs) have shown promising performance on link
prediction tasks by mapping the entities and relations from a knowledge graph
into a geometric space (usually a vector space). Ultimately, the plausibility
of the predicted links is measured by using a scoring function over the learned
embeddings (vectors). Therefore, the capability in preserving graph
characteristics including structural aspects and semantics highly depends on
the design of the KGE, as well as the inherited abilities from the underlying
geometry. Many KGEs use the flat geometry which renders them incapable of
preserving complex structures and consequently causes wrong inferences by the
models. To address this problem, we propose a neuro differential KGE that
embeds nodes of a KG on the trajectories of Ordinary Differential Equations
(ODEs). To this end, we represent each relation (edge) in a KG as a vector
field on a smooth Riemannian manifold. We specifically parameterize ODEs by a
neural network to represent various complex shape manifolds and more
importantly complex shape vector fields on the manifold. Therefore, the
underlying embedding space is capable of getting various geometric forms to
encode complexity in subgraph structures with different motifs. Experiments on
synthetic and benchmark dataset as well as social network KGs justify the ODE
trajectories as a means to structure preservation and consequently avoiding
wrong inferences over state-of-the-art KGE models.
