Encoding facts as representations of entities and binary relationships
between them, as learned by knowledge graph representation models, is useful
for various tasks, including predicting new facts, question answering, fact
checking and information retrieval. The focus of this thesis is on (i)
improving knowledge graph representation with the aim of tackling the link
prediction task; and (ii) devising a theory on how semantics can be captured in
the geometry of relation representations. Most knowledge graphs are very
incomplete and manually adding new information is costly, which drives the
development of methods which can automatically infer missing facts. The first
contribution of this thesis is HypER, a convolutional model which simplifies
and improves upon the link prediction performance of the existing convolutional
state-of-the-art model ConvE and can be mathematically explained in terms of
constrained tensor factorisation. The second contribution is TuckER, a
relatively straightforward linear model, which, at the time of its
introduction, obtained state-of-the-art link prediction performance across
standard datasets. The third contribution is MuRP, first multi-relational graph
representation model embedded in hyperbolic space. MuRP outperforms all
existing models and its Euclidean counterpart MuRE in link prediction on
hierarchical knowledge graph relations whilst requiring far fewer dimensions.
Despite the development of a large number of knowledge graph representation
models with gradually increasing predictive performance, relatively little is
known of the latent structure they learn. We generalise recent theoretical
understanding of how semantic relations of similarity, paraphrase and analogy
are encoded in the geometric interactions of word embeddings to how more
general relations, as found in knowledge graphs, can be encoded in their
representations.

本文提出了三种知识图谱表征模型，分别是 HypER、TuckER 和 MuRP，它们都能够自动预测缺失的关系，并且在性能方面不断取得进步。同时，该文还将最新的理论研究成果推广到了知识图谱的领域，探讨了如何在这些模型中编码不同种类的关系。

学习实体和关系的表征

Learning Representations of Entities and Relations

Hyperbolic embeddings have recently gained attention in machine learning due
to their ability to represent hierarchical data more accurately and succinctly
than their Euclidean analogues. However, multi-relational knowledge graphs
often exhibit multiple simultaneous hierarchies, which current hyperbolic
models do not capture. To address this, we propose a model that embeds
multi-relational graph data in the Poincar\'e ball model of hyperbolic space.
Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific
parameters to transform entity embeddings by M\"obius matrix-vector
multiplication and M\"obius addition. Experiments on the hierarchical WN18RR
knowledge graph show that our Poincar\'e embeddings outperform their Euclidean
counterpart and existing embedding methods on the link prediction task,
particularly at lower dimensionality.

本研究提出了一种称为 MuRP 的多关系泊松球模型，用于在 Poincaré 空间中嵌入多关系图数据，并学习关系特定参数以通过 Möbius 矩阵 - 向量乘法和 Möbius 相加来转换嵌入，实验表明 Poincare 嵌入在链接预测任务中比欧几里得模型和现有嵌入方法的效果更好，特别是在低维度的情况下。