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On Understanding Knowledge Graph Representation

arXiv.org Machine Learning

Many methods have been developed to represent knowledge graph data, which implicitly exploit low-rank latent structure in the data to encode known information and enable unknown facts to be inferred. To predict whether a relationship holds between entities, their embeddings are typically compared in the latent space following a relation-specific mapping. Whilst link prediction has steadily improved, the latent structure, and hence why such models capture semantic information, remains unexplained. We build on recent theoretical interpretation of word embeddings as a basis to consider an explicit structure for representations of relations between entities. For identifiable relation types, we are able to predict properties and justify the relative performance of leading knowledge graph representation methods, including their often overlooked ability to make independent predictions.


Learning Representations of Entities and Relations

arXiv.org Artificial Intelligence

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.


Multi-relational Poincar\'e Graph Embeddings

arXiv.org Machine Learning

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 multi-relational Poincar\'e embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.


Analogies Explained: Towards Understanding Word Embeddings

arXiv.org Machine Learning

Word embeddings generated by neural network methods such as word2vec (W2V) are well known to exhibit seemingly linear behaviour, e.g. the embeddings of analogy "woman is to queen as man is to king" approximately describe a parallelogram. This property is particularly intriguing since the embeddings are not trained to achieve it. Several explanations have been proposed, but each introduces assumptions that do not hold in practice. We derive a probabilistically grounded definition of paraphrasing and show it can be re-interpreted as word transformation, a mathematical description of "$w_x$ is to $w_y$". From these concepts we prove existence of the linear relationship between W2V-type embeddings that underlies the analogical phenomenon, and identify explicit error terms in the relationship.


Uncovering divergent linguistic information in word embeddings with lessons for intrinsic and extrinsic evaluation

arXiv.org Artificial Intelligence

Following the recent success of word embeddings, it has been argued that there is no such thing as an ideal representation for words, as different models tend to capture divergent and often mutually incompatible aspects like semantics/syntax and similarity/relatedness. In this paper, we show that each embedding model captures more information than directly apparent. A linear transformation that adjusts the similarity order of the model without any external resource can tailor it to achieve better results in those aspects, providing a new perspective on how embeddings encode divergent linguistic information. In addition, we explore the relation between intrinsic and extrinsic evaluation, as the effect of our transformations in downstream tasks is higher for unsupervised systems than for supervised ones.