  Detecting events and their evolution through time is a crucial task in
natural language understanding. Recent neural approaches to event temporal
relation extraction typically map events to embeddings in the Euclidean space
and train a classifier to detect temporal relations between event pairs.
However, embeddings in the Euclidean space cannot capture richer asymmetric
relations such as event temporal relations. We thus propose to embed events
into hyperbolic spaces, which are intrinsically oriented at modeling
hierarchical structures. We introduce two approaches to encode events and their
temporal relations in hyperbolic spaces. One approach leverages hyperbolic
embeddings to directly infer event relations through simple geometrical
operations. In the second one, we devise an end-to-end architecture composed of
hyperbolic neural units tailored for the temporal relation extraction task.
Thorough experimental assessments on widely used datasets have shown the
benefits of revisiting the tasks on a different geometrical space, resulting in
state-of-the-art performance on several standard metrics. Finally, the ablation
study and several qualitative analyses highlighted the rich event semantics
implicitly encoded into hyperbolic spaces.
