Geometric relational embeddings map relational data as geometric objects that
combine vector information suitable for machine learning and
structured/relational information for structured/relational reasoning,
typically in low dimensions. Their preservation of relational structures and
their appealing properties and interpretability have led to their uptake for
tasks such as knowledge graph completion, ontology and hierarchy reasoning,
logical query answering, and hierarchical multi-label classification. We survey
methods that underly geometric relational embeddings and categorize them based
on (i) the embedding geometries that are used to represent the data; and (ii)
the relational reasoning tasks that they aim to improve. We identify the
desired properties (i.e., inductive biases) of each kind of embedding and
discuss some potential future work.

本文概述了基于几何关系嵌入的方法，将关系数据映射为适合于机器学习的矢量信息和适合于结构化 / 关系推理的结构化 / 关系信息，以低维度的方式组合。这种嵌入方法保留了关系结构和吸引人的属性和可解释性，已被应用于诸如知识图谱完成、本体和层次关系推理、逻辑查询回答和层次多标签分类等任务。本文对构成几何关系嵌入的方法进行了概述，并根据（i）用于表示数据的嵌入几何和（ii）旨在改进的关系推理任务对其进行分类。同时，本文确定了每类嵌入所需的期望属性（即归纳偏差），并讨论了一些潜在的未来研究方向。