Link prediction on knowledge graphs (KGs) has been extensively studied on binary relational KGs, wherein each fact is represented by a triple. A significant amount of important knowledge, however, is represented by hyper-relational facts where each fact is composed of a primal triple and a set of qualifiers comprising a key-value pair that allows for expressing more complicated semantics. Although some recent works have proposed to embed hyper-relational KGs, these methods fail to capture essential inference patterns of hyper-relational facts such as qualifier monotonicity, qualifier implication, and qualifier mutual exclusion, limiting their generalization capability. To unlock this, we present ShrinkE, a geometric hyper-relational KG embedding method aiming to explicitly model these patterns. ShrinkE models the primal triple as a spatial-functional transformation from the head into a relation-specific box. Each qualifier “shrinks” the box to narrow down the possible answer set and, thus, realizes qualifier monotonicity. The spatial relationships between the qualifier boxes allow for modeling core inference patterns of qualifiers such as implication and mutual exclusion. Experimental results demonstrate ShrinkE’s superiority on three benchmarks of hyper-relational KGs.

Knowledge graphs mostly exhibit a mixture of branching relations, e.g., hasFriend, and complex structures, e.g., hierarchy and loop. Most knowledge graph embeddings have problems expressing them, because they model a specific relation r from a head h to tails by starting at the node embedding of h and transitioning deterministically to exactly one other point in the embedding space. We overcome this issue in our novel framework ItCAREToE by modeling relations between nodes by relation-specific, stochastic transitions. Our framework is based on stochastic ItCARETo processes, which operate on low-dimensional manifolds. ItCAREToE is highly expressive and generic subsuming various state-of-the-art models operating on different, also non-Euclidean, manifolds. Experimental results show the superiority of ItCAREToE over other deterministic embedding models with regard to the KG completion task.

Representation learning approaches for knowledge graphs have been mostly designed for static data. However, many knowledge graphs involve evolving data, e.g., the fact (The President of the United States is Barack Obama) is valid only from 2009 to 2017. This introduces important challenges for knowledge representation learning since the knowledge graphs change over time. In this paper, we present a novel time-aware knowledge graph embebdding approach, TeLM, which performs 4th-order tensor factorization of a Temporal knowledge graph using a Linear temporal regularizer and Multivector embeddings. Moreover, we investigate the effect of the temporal dataset’s time granularity on temporal knowledge graph completion. Experimental results demonstrate that our proposed models trained with the linear temporal regularizer achieve the state-of-the-art performances on link prediction over four well-established temporal knowledge graph completion benchmarks.

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. The capability of KGEs in preserving graph characteristics including structural aspects and semantics, highly depends on the design of their score function, as well as the inherited abilities from the underlying geometry. Many KGEs use the Euclidean 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 several manifolds. We specifically parameterize ODEs by a neural network to represent complex manifolds and complex vector fields on the manifolds. Therefore, the underlying embedding space is capable to assume the shape of various geometric forms to encode heterogeneous subgraphs. Experiments on synthetic and benchmark datasets using state-of-the-art KGE models justify the ODE trajectories as a means to enable structure preservation and consequently avoiding wrong inferences.

Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a low dimensional latent representation space. Existing KG embedding approaches model entities and relations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternion or 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 utilizes multivector representations and the geometric product to model entities and relations. Our framework subsumes several state-of-the-art KG embedding approaches and is advantageous with its ability of modeling various key relation patterns, including (anti-)symmetry, inversion and composition, rich expressiveness with higher degree of freedom as well as good generalization capacity. Experimental results on multiple benchmark knowledge graphs show that the proposed approach outperforms existing state-of-the-art models for link prediction.

In the last few years, there has been a surge of interest in learning representations of entities and relations in knowledge graph (KG). However, the recent availability of temporal knowledge graphs (TKGs) that contain time information for each fact created the need for reasoning over time 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 current time in the complex vector space. Specially, for facts involving time intervals, each relation is represented as a pair of dual complex embeddings to handle the beginning and the end of the relation, 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 inferring various relation patterns over time. Experimental results on three 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 has not been investigated in previous literature.