Predicting answers to queries over knowledge graphs is called a complex reasoning task because answering a query requires subdividing it into subqueries. Existing query embedding methods use this decomposition to compute the embedding of a query as the combination of the embedding of the subqueries. This requirement limits the answerable queries to queries having a single free variable and being decomposable, which are called tree-form queries and correspond to the SROI- description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the ALCOIR description logic, propose a query embedding method for them, called DAGE, and a new benchmark to evaluate query embeddings on them. Given the computational graph of a DAG query, DAGE combines the possibly multiple paths between two nodes into a single path with a trainable operator that represents the intersection of relations and learns DAG-DL concepts from tautologies. We implement DAGE on top of existing query embedding methods, and we empirically measure the improvement of our method over the results of vanilla methods evaluated in tree-form queries that approximate the DAG queries of our proposed benchmark.

Heterogeneous networks contain multiple types of nodes and links, with some link types encapsulating hierarchical structure over entities. Hierarchical relationships can codify information such as subcategories or one entity being subsumed by another and are often used for organizing conceptual knowledge into a tree-structured graph. Hyperbolic embedding models learn node representations in a hyperbolic space suitable for preserving the hierarchical structure. Unfortunately, current hyperbolic embedding models only implicitly capture the hierarchical structure, failing to distinguish between node types, and they only assume a single tree. In practice, many networks contain a mixture of hierarchical and non-hierarchical structures, and the hierarchical relations may be represented as multiple trees with complex structures, such as sharing certain entities. In this work, we propose a new hyperbolic representation learning model that can handle complex hierarchical structures and also learn the representation of both hierarchical and non-hierarchic structures. We evaluate our model on several datasets, including identifying relevant articles for a systematic review, which is an essential tool for evidence-driven medicine and node classification.

The sparse interactions between users and items have aggravated the difficulty of their representations in recommender systems. Existing methods leverage tags to alleviate the sparsity problem but ignore prevalent logical relations among items and tags (e.g., membership, hierarchy, and exclusion), which can be leveraged to enhance the accuracy of modeling user preferences and conducting recommendations. To this end, we propose to extract logical relations among item tags from existing tag taxonomies and exploit the individual strengths of the Poincaré and the Lorentz models in hyperbolic space for logical relation modeling towards enhanced recommendations. Moreover, we find that the logical relations directly extracted from existing tag taxonomies can be inaccurate and coarse. Therefore, we further devise innovative consistency-based and granularity- based weighting mechanisms based on user behavior patterns for data-driven logical relation mining that can be jointly optimized along with recommendations in an end-to-end fashion. Extensive experiments on four real-world benchmark datasets show drastic performance gains brought by our proposed framework, which constantly achieves an average of 8.25% improvement over state-of-the-art competitors regarding both Recall and NDCG metrics. Insightful case studies further demonstrate that our automatically refined logical relations are highly accurate and interpretable.

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.

Graph Neural Networks (GNNs) generalize conventional neural networks to graph-structured data and have received considerable attention owing to their impressive performance. In spite of the notable successes, the performance of Euclidean models is inherently bounded and limited by the representation ability of Euclidean geometry, especially when it comes to datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution and a surge of works on either methods or novel applications have been seen. Unlike Euclidean space, which expands polynomially, hyperbolic space grows exponentially with its radius, making it more suitable for modeling complex real-world data. Hence, it gains natural advantages in abstracting tree-like graphs with a hierarchical organization or power-law distribution.

Medical decision-making processes can be enhanced by comprehensive biomedical knowledge bases, which require fusing knowledge graphs constructed from different sources via a uniform index system. The index system often organizes biomedical terms in a hierarchy to provide the aligned entities with fine-grained granularity. To address the challenge of scarce supervision in the biomedical knowledge fusion (BKF) task, researchers have proposed various unsupervised methods. However, these methods heavily rely on ad-hoc lexical and structural matching algorithms, which fail to capture the rich semantics conveyed by biomedical entities and terms. Recently, neural embedding models have proved effective in semantic-rich tasks, but they rely on sufficient labeled data to be adequately trained. To bridge the gap between the scarce-labeled BKF and neural embedding models, we propose HiPrompt, a supervision-efficient knowledge fusion framework that elicits the few-shot reasoning ability of large language models through hierarchy-oriented prompts. Empirical results on the collected KG-Hi-BKF benchmark datasets demonstrate the effectiveness of HiPrompt.

Recent knowledge graph (KG) embeddings have been advanced by hyperbolic geometry due to its superior capability for representing hierarchies. The topological structures of real-world KGs, however, are rather heterogeneous, i.e., a KG is composed of multiple distinct hierarchies and non-hierarchical graph structures. Therefore, a homogeneous (either Euclidean or hyperbolic) geometry is not sufficient for fairly representing such heterogeneous structures. To capture the topological heterogeneity of KGs, we present an ultrahyperbolic KG embedding (UltraE) in an ultrahyperbolic (or pseudo-Riemannian) manifold that seamlessly interleaves hyperbolic and spherical manifolds. In particular, we model each relation as a pseudo-orthogonal transformation that preserves the pseudo-Riemannian bilinear form. The pseudo-orthogonal transformation is decomposed into various operators (i.e., circular rotations, reflections and hyperbolic rotations), allowing for simultaneously modeling heterogeneous structures as well as complex relational patterns. Experimental results on three standard KGs show that UltraE outperforms previous Euclidean, hyperbolic, and mixed-curvature KG embedding approaches.

Knowledge graph (KG) alignment is to match entities in different KGs, which is important to knowledge fusion and integration. Temporal KGs (TKGs) extend traditional Knowledge Graphs (KGs) by associating static triples with specific timestamps (e.g., temporal scopes or time points). Moreover, open-world KGs (OKGs) are dynamic with new emerging entities and timestamps. While entity alignment (EA) between KGs has drawn increasing attention from the research community, EA between TKGs and OKGs still remains unexplored. In this work, we propose a novel Temporal Relational Entity Alignment method (TREA) which is able to learn alignment-oriented TKG embeddings and represent new emerging entities. We first map entities, relations and timestamps into an embedding space, and the initial feature of each entity is represented by fusing the embeddings of its connected relations and timestamps as well as its neighboring entities. A graph neural network (GNN) is employed to capture intra-graph information and a temporal relational attention mechanism is utilized to integrate relation and time features of links between nodes. Finally, a margin-based full multi-class log-loss is used for efficient training and a sequential time regularizer is used to model unobserved timestamps. We use three well-established TKG datasets, as references for evaluating temporal and non-temporal EA methods. Experimental results show that our method outperforms the state-of-the-art EA methods.