What is: Hyperboloid Embeddings?

Hyperboloid Embeddings (HypE) is a novel self-supervised dynamic reasoning framework, that utilizes positive first-order existential queries on a KG to learn representations of its entities and relations as hyperboloids in a Poincaré ball. HypE models the positive first-order queries as geometrical translation (t), intersection ($\cap$), and union ($\cup$). For the problem of KG reasoning in real-world datasets, the proposed HypE model significantly outperforms the state-of-the art results. HypE is also applied to an anomaly detection task on a popular e-commerce website product taxonomy as well as hierarchically organized web articles and demonstrate significant performance improvements compared to existing baseline methods. Finally, HypE embeddings can also be visualized in a Poincaré ball to clearly interpret and comprehend the representation space.