Knowledge Graphs (KGs) are a collection of facts describing entities connected by relationships. KG embeddings map entities and relations into a vector space while preserving their relational semantics. This enables effective inference of missing knowledge from the embedding space. Most KG embedding approaches focused on triple-shaped KGs. A great amount of real-world knowledge, however, cannot simply be represented by triples. In this tutorial, we give a systematic introduction to KG embeddings that go beyond the triple representation. In particular, the tutorial will focus on temporal facts where the triples are enriched with temporal information, hyper-relational facts where the triples are enriched with qualifiers, n-ary facts describing relationships between multiple entities, and also facts that are augmented with literal and text descriptions. During the tutorial, we will introduce both fundamental knowledge and advanced topics for understanding recent embedding approaches for beyond-triple representations.

Answering complex queries on incomplete knowledge graphs is a challenging task where a model needs to answer complex logical queries in the presence of missing knowledge. Prior work in the literature has proposed to address this problem by designing architectures trained end-to-end for the complex query answering task with a reasoning process that is hard to interpret while requiring data and resource-intensive training. Other lines of research have proposed re-using simple neural link predictors to answer complex queries, reducing the amount of training data by orders of magnitude while providing interpretable answers. The neural link predictor used in such approaches is not explicitly optimised for the complex query answering task, implying that its scores are not calibrated to interact together. We propose to address these problems via CQD$^{\mathcal{A}}$, a parameter-efficient score \emph{adaptation} model optimised to re-calibrate neural link prediction scores for the complex query answering task. While the neural link predictor is frozen, the adaptation component -- which only increases the number of model parameters by $0.03\%$ -- is trained on the downstream complex query answering task. Furthermore, the calibration component enables us to support reasoning over queries that include atomic negations, which was previously impossible with link predictors. In our experiments, CQD$^{\mathcal{A}}$ produces significantly more accurate results than current state-of-the-art methods, improving from $34.4$ to $35.1$ Mean Reciprocal Rank values averaged across all datasets and query types while using $\leq 30\%$ of the available training query types. We further show that CQD$^{\mathcal{A}}$ is data-efficient, achieving competitive results with only $1\%$ of the complex training queries and robust in out-of-domain evaluations. Source code and datasets are available at https://github.com/EdinburghNLP/adaptive-cqd.

Neural link predictors are useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries containing logical conjunctions (∧), disjunctions (∨), and existential quantifiers (∃). We propose a framework for efficiently answering complex queries on in- complete Knowledge Graphs. We translate each query into an end-to-end differentiable objective, where the truth value of each atom is computed by a pre-trained neural link predictor. We then analyse two solutions to the optimisation problem, including gradient-based and combinatorial search. In our experiments, the proposed approach produces more accurate results than state-of-the-art methods — black-box models trained on millions of generated queries — without the need for training on a large and diverse set of complex queries. Using orders of magnitude less training data, we obtain relative improvements ranging from 8% up to 40% in Hits@3 across multiple knowledge graphs. We find that it is possible to explain the outcome of our model in terms of the intermediate solutions identified for each of the complex query atoms. All our source code and datasets are available online (https://github.com/uclnlp/cqd).

Knowledge Graphs (KG) are of vital importance for multiple applications on the web, including information retrieval, recommender systems, and metadata annotation.