The flourishing of knowledge graph (KG) applications has driven the need for entity alignment (EA) across KGs. However, the heterogeneity of practical KGs, characterized by differing scales, structures, and limited overlapping entities, greatly surpasses that of existing EA datasets. This discrepancy highlights an oversimplified heterogeneity in current EA datasets, which obstructs the exploration of the EA application. In this paper, we study the performance of EA methods on the alignment of highly heterogeneous KGs (HHKGs). Firstly, we address the oversimplified heterogeneity settings of current datasets and propose two new HHKG datasets that closely mimic practical EA scenarios. Then, based on these datasets, we conduct extensive experiments to evaluate previous representative EA methods. Our findings reveal that, in aligning HHKGs, valuable structure information can hardly be exploited, which leads to inferior performance of existing EA methods, especially those based on GNNs. These findings shed light on the potential problems associated with the conventional application of GNN-based methods as a panacea for all EA datasets. Consequently, to elucidate what EA methodology is genuinely beneficial in practical scenarios, we undertake an in-depth analysis by implementing a simple but effective approach: Simple-HHEA. Our experiment results conclude that the key to the future EA model design in practice lies in their adaptability and efficiency to varying information quality conditions, as well as their capability to capture patterns across HHKGs. The datasets and source code are available at https://github.com/IDEA-FinAI/Simple-HHEA.

Temporal relation prediction in incomplete temporal knowledge graphs (TKGs) is a popular temporal knowledge graph completion (TKGC) problem in both transductive and inductive settings. Traditional embedding-based TKGC models (TKGE) rely on structured connections and can only handle a fixed set of entities, i.e., the transductive setting. In the inductive setting where test TKGs contain emerging entities, the latest methods are based on symbolic rules or pre-trained language models (PLMs). However, they suffer from being inflexible and not time-specific, respectively. In this work, we extend the fully-inductive setting, where entities in the training and test sets are totally disjoint, into TKGs and take a further step towards a more flexible and time-sensitive temporal relation prediction approach SST-BERT,incorporating Structured Sentences with Time-enhanced BERT. Our model can obtain the entity history and implicitly learn rules in the semantic space by encoding structured sentences, solving the problem of inflexibility. We propose to use a time masking MLM task to pre-train BERT in a corpus rich in temporal tokens specially generated for TKGs, enhancing the time sensitivity of SST-BERT. To compute the probability of occurrence of a target quadruple, we aggregate all its structured sentences from both temporal and semantic perspectives into a score. Experiments on the transductive datasets and newly generated fully-inductive benchmarks show that SST-BERT successfully improves over state-of-the-art baselines.

In the last few years, the solution to Knowledge Graph (KG) completion via learning embeddings of entities and relations has attracted a surge of interest. Temporal KGs(TKGs) extend traditional Knowledge Graphs (KGs) by associating static triples with timestamps forming quadruples. Different from KGs and TKGs in the transductive setting, constantly emerging entities and relations in incomplete TKGs create demand to predict missing facts with unseen components, which is the extrapolation setting. Traditional temporal knowledge graph embedding (TKGE) methods are limited in the extrapolation setting since they are trained within a fixed set of components. In this paper, we propose a Meta-Learning based Temporal Knowledge Graph Extrapolation (MTKGE) model, which is trained on link prediction tasks sampled from the existing TKGs and tested in the emerging TKGs with unseen entities and relations. Specifically, we meta-train a GNN framework that captures relative position patterns and temporal sequence patterns between relations. The learned embeddings of patterns can be transferred to embed unseen components. Experimental results on two different TKG extrapolation datasets show that MTKGE consistently outperforms both the existing state-of-the-art models for knowledge graph extrapolation and specifically adapted KGE and TKGE baselines.

Recent years, Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a Knowledge Graph (KG) into a geometric space and thus have gained increasing attentions. In addition, many recent Knowledge Graphs involve evolving data, e.g., the fact (Obama, PresidentOf, USA) is valid only from 2009 to 2017. This introduces important challenges for knowledge representation learning since such temporal KGs change over time. In this work, we strive to move beyond the complex or hypercomplex space for KGE and propose a novel geometric algebra based embedding approach, GeomE, which uses multivector representations and the geometric product to model entities and relations. GeomE subsumes several state-of-the-art KGE models and is able to model diverse relations patterns. On top of this, we extend GeomE to TGeomE for temporal KGE, which performs 4th-order tensor factorization of a temporal KG and devises a new linear temporal regularization for time representation learning. Moreover, we study the effect of time granularity on the performance of TGeomE models. Experimental results show that our proposed models achieve the state-of-the-art performances on link prediction over four commonly-used static KG datasets and four well-established temporal KG datasets across various metrics.

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.