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.
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.
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively simple but powerful linear model based on Tucker decomposition of the binary tensor representation of knowledge graph triples. TuckER outperforms all previous state-of-the-art models across standard link prediction datasets. We prove that TuckER is a fully expressive model, deriving the bound on its entity and relation embedding dimensionality for full expressiveness which is several orders of magnitude smaller than the bound of previous state-of-the-art models ComplEx and SimplE. We further show that several previously introduced linear models can be viewed as special cases of TuckER.
Knowledge graphs are large graph-structured databases of facts, which typically suffer from incompleteness. Link prediction is the task of inferring missing relations (links) between entities (nodes) in a knowledge graph. We propose to solve this task by using a hypernetwork architecture to generate convolutional layer filters specific to each relation and apply those filters to the subject entity embeddings. This architecture enables a trade-off between non-linear expressiveness and the number of parameters to learn. Our model simplifies the entity and relation embedding interactions introduced by the predecessor convolutional model, while outperforming all previous approaches to link prediction across all standard link prediction datasets.
Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily assessed, whereas judging that from their spelling is often impossible (e.g. cat /feline) and to predetermine and store similarities between all words is prohibitively time-consuming, memory intensive and subjective. We focus on word embeddings learned from text corpora and knowledge graphs. Several well-known algorithms learn word embeddings from text on an unsupervised basis by learning to predict those words that occur around each word, e.g. word2vec and GloVe. Parameters of such word embeddings are known to reflect word co-occurrence statistics, but how they capture semantic meaning has been unclear. Knowledge graph representation models learn representations both of entities (words, people, places, etc.) and relations between them, typically by training a model to predict known facts in a supervised manner. Despite steady improvements in fact prediction accuracy, little is understood of the latent structure that enables this. The limited understanding of how latent semantic structure is encoded in the geometry of word embeddings and knowledge graph representations makes a principled means of improving their performance, reliability or interpretability unclear. To address this: 1. we theoretically justify the empirical observation that particular geometric relationships between word embeddings learned by algorithms such as word2vec and GloVe correspond to semantic relations between words; and 2. we extend this correspondence between semantics and geometry to the entities and relations of knowledge graphs, providing a model for the latent structure of knowledge graph representation linked to that of word embeddings.