Meta-Learning Based Knowledge Extrapolation for Temporal Knowledge Graph

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.

Ultrahyperbolic Knowledge Graph Embeddings

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- and hyperbolic-based approaches.

TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.

Time-aware Graph Neural Networks for Entity Alignment between Temporal Knowledge Graphs

Entity alignment aims to identify equivalent entity pairs between different knowledge graphs (KGs). Recently, the availability of temporal KGs (TKGs) that contain time information created the need for reasoning over time in such TKGs. Existing embedding-based entity alignment approaches disregard time information that commonly exists in many large-scale KGs, leaving much room for improvement. In this paper, we focus on the task of aligning entity pairs between TKGs and propose a novel Time-aware Entity Alignment approach based on Graph Neural Networks (TEA-GNN). We embed entities, relations and timestamps of different KGs into a vector space and use GNNs to learn entity representations. To incorporate both relation and time information into the GNN structure of our model, we use a time-aware attention mechanism which assigns different weights to different nodes with orthogonal transformation matrices computed from embeddings of the relevant relations and timestamps in a neighborhood. Experimental results on multiple real-world TKG datasets show that our method significantly outperforms the state-of-the-art methods due to the inclusion of time information.

Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion

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 (\textit{Obama}, \textit{PresidentOf}, \textit{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.

Geometric Algebra based Embeddings for Staticand Temporal Knowledge Graph Completion

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 (\textit{Obama}, \textit{PresidentOf}, \textit{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.

Multiple Run Ensemble Learning withLow-Dimensional Knowledge Graph Embeddings

Among the top approaches of recent years, link prediction using knowledge graph embedding (KGE) models has gained significant attention for knowledge graph completion. Various embedding models have been proposed so far, among which, some recent KGE models obtain state-of-the-art performance on link prediction tasks by using embeddings with a high dimension (e.g. 1000) which accelerate the costs of training and evaluation considering the large scale of KGs. In this paper, we propose a simple but effective performance boosting strategy for KGE models by using multiple low dimensions in different repetition rounds of the same model. For example, instead of training a model one time with a large embedding size of 1200, we repeat the training of the model 6 times in parallel with an embedding size of 200 and then combine the 6 separate models for testing while the overall numbers of adjustable parameters are same (6*200=1200) and the total memory footprint remains the same. We show that our approach enables different models to better cope with their expressiveness issues on modeling various graph patterns such as symmetric, 1-n, n-1 and n-n. In order to justify our findings, we conduct experiments on various KGE models. Experimental results on standard benchmark datasets, namely FB15K, FB15K-237 and WN18RR, show that multiple low-dimensional models of the same kind outperform the corresponding single high-dimensional models on link prediction in a certain range and have advantages in training efficiency by using parallel training while the overall numbers of adjustable parameters are same.

TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation

In the last few years, there has been a surge of interest in learning representations of entitiesand relations in knowledge graph (KG). However, the recent availability of temporal knowledgegraphs (TKGs) that contain time information for each fact created the need for reasoning overtime in such TKGs. In this regard, we present a new approach of TKG embedding, TeRo, which defines the temporal evolution of entity embedding as a rotation from the initial time to the currenttime in the complex vector space. Specially, for facts involving time intervals, each relation isrepresented as a pair of dual complex embeddings to handle the beginning and the end of therelation, respectively. We show our proposed model overcomes the limitations of the existing KG embedding models and TKG embedding models and has the ability of learning and inferringvarious relation patterns over time. Experimental results on four different TKGs show that TeRo significantly outperforms existing state-of-the-art models for link prediction. In addition, we analyze the effect of time granularity on link prediction over TKGs, which as far as we know hasnot been investigated in previous literature.

Knowledge Graph Embeddings in Geometric Algebras

Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor Octonion) representations, all of which are subsumed into a geometric algebra. In this work,we introduce a novel geometric algebra-based KG embedding framework, GeomE, which uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.

Motif Learning in Knowledge Graphs Using Trajectories Of Differential Equations

Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space (usually a vector space). Ultimately, the plausibility of the predicted links is measured by using a scoring function over the learned embeddings (vectors). Therefore, the capability in preserving graph characteristics including structural aspects and semantics highly depends on the design of the KGE, as well as the inherited abilities from the underlying geometry. Many KGEs use the flat geometry which renders them incapable of preserving complex structures and consequently causes wrong inferences by the models. To address this problem, we propose a neuro differential KGE that embeds nodes of a KG on the trajectories of Ordinary Differential Equations (ODEs). To this end, we represent each relation (edge) in a KG as a vector field on a smooth Riemannian manifold. We specifically parameterize ODEs by a neural network to represent various complex shape manifolds and more importantly complex shape vector fields on the manifold. Therefore, the underlying embedding space is capable of getting various geometric forms to encode complexity in subgraph structures with different motifs. Experiments on synthetic and benchmark dataset as well as social network KGs justify the ODE trajectories as a means to structure preservation and consequently avoiding wrong inferences over state-of-the-art KGE models.