Knowledge Graphs (KGs) are ubiquitous structures for information storagein
several real-world applications such as web search, e-commerce, social
networks, and biology. Querying KGs remains a foundational and challenging
problem due to their size and complexity. Promising approaches to tackle this
problem include embedding the KG units (e.g., entities and relations) in a
Euclidean space such that the query embedding contains the information relevant
to its results. These approaches, however, fail to capture the hierarchical
nature and semantic information of the entities present in the graph.
Additionally, most of these approaches only utilize multi-hop queries (that can
be modeled by simple translation operations) to learn embeddings and ignore
more complex operations such as intersection and union of simpler queries. To
tackle such complex operations, in this paper, we formulate KG representation
learning as a self-supervised logical query reasoning problem that utilizes
translation, intersection and union queries over KGs. We propose Hyperboloid
Embeddings (HypE), 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 Poincar\'e
ball. HypE models the positive first-order queries as geometrical translation,
intersection, and union. For the problem of KG reasoning in real-world
datasets, the proposed HypE model significantly outperforms the state-of-the
art results. We also apply HypE 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, we also visualize the learned HypE
embeddings in a Poincar\'e ball to clearly interpret and comprehend the
representation space.

本文介绍了利用 Hyperboloid Embeddings 学习知识图谱表示的自监督逻辑查询推理方法，并将其应用于真实世界数据集和异常检测任务中，取得了显著的性能提升。