Knowledge graphs (KGs) have gradually become valuable assets for many AI applications. In a KG, a node denotes an entity, and an edge (or link) denotes a relationship between the entities represented by the nodes. Knowledge graph completion infers and predicts missing edges in a KG automatically. Knowledge graph embeddings have shed light on addressing this task. Recent research embeds KGs in hyperbolic (negatively curved) space instead of conventional Euclidean (zero curved) space and is effective in capturing hierarchical structures. However, as multi-relational graphs, KGs are not structured uniformly and display intrinsic heterogeneous structures. They usually contain rich types of structures, such as hierarchical and cyclic typed structures. Embedding KGs in singlecurvature space, such as Euclidean or hyperbolic space, overlooks the intrinsic heterogeneous structures of KGs, and therefore cannot accurately capture their structures. To address this issue, we propose Mixed-Curvature Multi-Relational Graph Neural Network (M2GNN), a generic approach that embeds multi-relational KGs in a mixed-curvature space for knowledge graph completion. Specifically, we define and construct a mixed-curvature space through a product manifold combining multiple single-curvature spaces (e.g., spherical, hyperbolic, or Euclidean) with the purpose of modeling a variety of structures. However, constructing a mixed-curvature space typically requires manually defining the fixed curvatures, which needs domain knowledge and additional data analysis. Improperly defined curvature space also cannot capture the structures of KGs accurately. To address this problem, we set mixed-curvatures as trainable parameters to better capture the underlying structures of the KGs. Furthermore, we propose a Graph Neural Updater by leveraging the heterogeneous relational context in mixed-curvature space to improve the quality of the embedding. Experiments on three KG datasets demonstrate that the proposed M2GNN can out-perform its single geometry counterpart as well as state-of-the-art embedding methods on the KG completion task.
The majority of knowledge graph embedding techniques treat entities and predicates as separate embedding matrices, using aggregation functions to build a representation of the input triple. However, these aggregations are lossy, i.e. they do not capture the semantics of the original triples, such as information contained in the predicates. To combat these shortcomings, current methods learn triple embeddings from scratch without utilizing entity and predicate embeddings from pre-trained models. In this paper, we design a novel fine-tuning approach for learning triple embeddings by creating weak supervision signals from pre-trained knowledge graph embeddings. We develop a method for automatically sampling triples from a knowledge graph and estimating their pairwise similarities from pre-trained embedding models. These pairwise similarity scores are then fed to a Siamese-like neural architecture to fine-tune triple representations. We evaluate the proposed method on two widely studied knowledge graphs and show consistent improvement over other state-of-the-art triple embedding methods on triple classification and triple clustering tasks.
Knowledge Graph Embeddings (KGE) aim to map entities and relations to low dimensional spaces and have become the \textit{de-facto} standard for knowledge graph completion. Most existing KGE methods suffer from the sparsity challenge, where it is harder to predict entities that appear less frequently in knowledge graphs. In this work, we propose a novel framework KRACL to alleviate the widespread sparsity in KGs with graph context and contrastive learning. Firstly, we propose the Knowledge Relational Attention Network (KRAT) to leverage the graph context by simultaneously projecting neighboring triples to different latent spaces and jointly aggregating messages with the attention mechanism. KRAT is capable of capturing the subtle semantic information and importance of different context triples as well as leveraging multi-hop information in knowledge graphs. Secondly, we propose the knowledge contrastive loss by combining the contrastive loss with cross entropy loss, which introduces more negative samples and thus enriches the feedback to sparse entities. Our experiments demonstrate that KRACL achieves superior results across various standard knowledge graph benchmarks, especially on WN18RR and NELL-995 which have large numbers of low in-degree entities. Extensive experiments also bear out KRACL's effectiveness in handling sparse knowledge graphs and robustness against noisy triples.
This paper presents $\mu\text{KG}$, an open-source Python library for representation learning over knowledge graphs. $\mu\text{KG}$ supports joint representation learning over multi-source knowledge graphs (and also a single knowledge graph), multiple deep learning libraries (PyTorch and TensorFlow2), multiple embedding tasks (link prediction, entity alignment, entity typing, and multi-source link prediction), and multiple parallel computing modes (multi-process and multi-GPU computing). It currently implements 26 popular knowledge graph embedding models and supports 16 benchmark datasets. $\mu\text{KG}$ provides advanced implementations of embedding techniques with simplified pipelines of different tasks. It also comes with high-quality documentation for ease of use. $\mu\text{KG}$ is more comprehensive than existing knowledge graph embedding libraries. It is useful for a thorough comparison and analysis of various embedding models and tasks. We show that the jointly learned embeddings can greatly help knowledge-powered downstream tasks, such as multi-hop knowledge graph question answering. We will stay abreast of the latest developments in the related fields and incorporate them into $\mu\text{KG}$.
Knowledge graph embedding research has mainly focused on learning continuous representations of knowledge graphs towards the link prediction problem. Recently developed frameworks can be effectively applied in research related applications. Yet, these frameworks do not fulfill many requirements of real-world applications. As the size of the knowledge graph grows, moving computation from a commodity computer to a cluster of computers in these frameworks becomes more challenging. Finding suitable hyperparameter settings w.r.t. time and computational budgets are left to practitioners. In addition, the continual learning aspect in knowledge graph embedding frameworks is often ignored, although continual learning plays an important role in many real-world (deep) learning-driven applications. Arguably, these limitations explain the lack of publicly available knowledge graph embedding models for large knowledge graphs. We developed a framework based on the frameworks DASK, Pytorch Lightning and Hugging Face to compute embeddings for large-scale knowledge graphs in a hardware-agnostic manner, which is able to address real-world challenges pertaining to the scale of real application. We provide an open-source version of our framework along with a hub of pre-trained models having more than 11.4 B parameters.
Knowledge graph embedding is a representation learning technique that projects entities and relations in a knowledge graph to continuous vector spaces. Embeddings have gained a lot of uptake and have been heavily used in link prediction and other downstream prediction tasks. Most approaches are evaluated on a single task or a single group of tasks to determine their overall performance. The evaluation is then assessed in terms of how well the embedding approach performs on the task at hand. Still, it is hardly evaluated (and often not even deeply understood) what information the embedding approaches are actually learning to represent. To fill this gap, we present the DLCC (Description Logic Class Constructors) benchmark, a resource to analyze embedding approaches in terms of which kinds of classes they can represent. Two gold standards are presented, one based on the real-world knowledge graph DBpedia and one synthetic gold standard. In addition, an evaluation framework is provided that implements an experiment protocol so that researchers can directly use the gold standard. To demonstrate the use of DLCC, we compare multiple embedding approaches using the gold standards. We find that many DL constructors on DBpedia are actually learned by recognizing different correlated patterns than those defined in the gold standard and that specific DL constructors, such as cardinality constraints, are particularly hard to be learned for most embedding approaches.
Knowledge graph embedding (KGE) models are an effective and popular approach to represent and reason with multi-relational data. Prior studies have shown that KGE models are sensitive to hyperparameter settings, however, and that suitable choices are dataset-dependent. In this paper, we explore hyperparameter optimization (HPO) for very large knowledge graphs, where the cost of evaluating individual hyperparameter configurations is excessive. Prior studies often avoided this cost by using various heuristics; e.g., by training on a subgraph or by using fewer epochs. We systematically discuss and evaluate the quality and cost savings of such heuristics and other low-cost approximation techniques. Based on our findings, we introduce GraSH, an efficient multi-fidelity HPO algorithm for large-scale KGEs that combines both graph and epoch reduction techniques and runs in multiple rounds of increasing fidelities. We conducted an experimental study and found that GraSH obtains state-of-the-art results on large graphs at a low cost (three complete training runs in total).
Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space, no matter the Euclidean space, hyperbolic space or hyperspheric space, cannot capture the complex structures of KGs accurately. To overcome this challenge, we propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Theoretically, our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities. Experimental results on three well-established knowledge graph completion benchmarks show that our GIE achieves the state-of-the-art performance with fewer parameters.
We study the effectiveness of Knowledge Graph Embeddings (KGE) for knowledge graph (KG) completion with rule mining. More specifically, we mine rules from KGs before and after they have been completed by a KGE to compare possible differences in the rules extracted. We apply this method to classical KGEs approaches, in particular, TransE, DistMult and ComplEx. Our experiments indicate that there can be huge differences between the extracted rules, depending on the KGE approach for KG completion. In particular, after the TransE completion, several spurious rules were extracted.
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.
In recent years, Knowledge Graph (KG) development has attracted significant researches considering the applications in web search, relation prediction, natural language processing, information retrieval, question answering to name a few. However, often KGs are incomplete due to which Knowledge Graph Completion (KGC) has emerged as a sub-domain of research to automatically track down the missing connections in a KG. Numerous strategies have been suggested to work out the KGC dependent on different representation procedures intended to embed triples into a low-dimensional vector space. Given the difficulties related to KGC, researchers around the world are attempting to comprehend the attributes of the problem statement. This study intends to provide an overview of knowledge bases combined with different challenges and their impacts. We discuss existing KGC approaches, including the state-of-the-art Knowledge Graph Embeddings (KGE), not only on static graphs but also for the latest trends such as multimodal, temporal, and uncertain knowledge graphs. In addition, reinforcement learning techniques are reviewed to model complex queries as a link prediction problem. Subsequently, we explored popular software packages for model training and examine open research challenges that can guide future research.
Knowledge graph (KG) link prediction is a fundamental task in artificial intelligence, with applications in natural language processing, information retrieval, and biomedicine. Recently, promising results have been achieved by leveraging cross-modal information in KGs, using ensembles that combine knowledge graph embeddings (KGEs) and contextual language models (LMs). However, existing ensembles are either (1) not consistently effective in terms of ranking accuracy gains or (2) impractically inefficient on larger datasets due to the combinatorial explosion problem of pairwise ranking with deep language models. In this paper, we propose a novel tiered ranking architecture CascadER to maintain the ranking accuracy of full ensembling while improving efficiency considerably. CascadER uses LMs to rerank the outputs of more efficient base KGEs, relying on an adaptive subset selection scheme aimed at invoking the LMs minimally while maximizing accuracy gain over the KGE. Extensive experiments demonstrate that CascadER improves MRR by up to 9 points over KGE baselines, setting new state-of-the-art performance on four benchmarks while improving efficiency by one or more orders of magnitude over competitive cross-modal baselines. Our empirical analyses reveal that diversity of models across modalities and preservation of individual models' confidence signals help explain the effectiveness of CascadER, and suggest promising directions for cross-modal cascaded architectures. Code and pretrained models are available at https://github.com/tsafavi/cascader.
Knowledge graph embedding research has mainly focused on learning continuous representations of entities and relations tailored towards the link prediction problem. Recent results indicate an ever increasing predictive ability of current approaches on benchmark datasets. However, this effectiveness often comes with the cost of over-parameterization and increased computationally complexity. The former induces extensive hyperparameter optimization to mitigate malicious overfitting. The latter magnifies the importance of winning the hardware lottery. Here, we investigate a remedy for the first problem. We propose a technique based on Kronecker decomposition to reduce the number of parameters in a knowledge graph embedding model, while retaining its expressiveness. Through Kronecker decomposition, large embedding matrices are split into smaller embedding matrices during the training process. Hence, embeddings of knowledge graphs are not plainly retrieved but reconstructed on the fly. The decomposition ensures that elementwise interactions between three embedding vectors are extended with interactions within each embedding vector. This implicitly reduces redundancy in embedding vectors and encourages feature reuse. To quantify the impact of applying Kronecker decomposition on embedding matrices, we conduct a series of experiments on benchmark datasets. Our experiments suggest that applying Kronecker decomposition on embedding matrices leads to an improved parameter efficiency on all benchmark datasets. Moreover, empirical evidence suggests that reconstructed embeddings entail robustness against noise in the input knowledge graph. To foster reproducible research, we provide an open-source implementation of our approach, including training and evaluation scripts as well as pre-trained models in our knowledge graph embedding framework (https://github.com/dice-group/dice-embeddings).
Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities. Recently, some Euclidean KGE methods have been enhanced to model semantic hierarchies commonly found in KGs, improving the performance of link prediction. To embed hierarchical data, hyperbolic space has emerged as a promising alternative to traditional Euclidean space, offering high fidelity and lower memory consumption. Unlike Euclidean, hyperbolic space provides countless curvatures to choose from. However, it is difficult for existing hyperbolic KGE methods to obtain the optimal curvature settings manually, thereby limiting their ability to effectively model semantic hierarchies. To address this limitation, we propose a novel KGE model called $\textbf{Hyp}$erbolic $\textbf{H}$ierarchical $\textbf{KGE}$ (HypHKGE). This model introduces attention-based learnable curvatures for hyperbolic space, which helps preserve rich semantic hierarchies. Furthermore, to utilize the preserved hierarchies for inferring missing links, we define hyperbolic hierarchical transformations based on the theory of hyperbolic geometry, including both inter-level and intra-level modeling. Experiments demonstrate the effectiveness of the proposed HypHKGE model on the three benchmark datasets (WN18RR, FB15K-237, and YAGO3-10). The source code will be publicly released at https://github.com/wjzheng96/HypHKGE.
Knowledge graph completion aims to perform link prediction between entities. In this paper, we consider the approach of knowledge graph embeddings. Recently, models such as TransE and TransH build entity and relation embeddings by regarding a relation as translation from head entity to tail entity. We note that these models simply put both entities and relations within the same semantic space. In fact, an entity may have multiple aspects and various relations may focus on different aspects of entities, which makes a common space insufficient for modeling. In this paper, we propose TransR to build entity and relation embeddings in separate entity space and relation spaces. Afterwards, we learn embeddings by first projecting entities from entity space to corresponding relation space and then building translations between projected entities. In experiments, we evaluate our models on three tasks including link prediction, triple classification and relational fact extraction. Experimental results show significant and consistent improvements compared to state-of-the-art baselines including TransE and TransH. The source code of this paper can be obtained from https://github.com/mrlyk423/relation_extraction.
Ontology matching is a core task when creating interoperable and linked open datasets. In this paper, we explore a novel structure-based mapping approach which is based on knowledge graph embeddings: The ontologies to be matched are embedded, and an approach known as absolute orientation is used to align the two embedding spaces. Next to the approach, the paper presents a first, preliminary evaluation using synthetic and real-world datasets. We find in experiments with synthetic data, that the approach works very well on similarly structured graphs; it handles alignment noise better than size and structural differences in the ontologies.
Semantic matching models -- which assume that entities with similar semantics have similar embeddings -- have shown great power in knowledge graph embeddings (KGE). Many existing semantic matching models use inner products in embedding spaces to measure the plausibility of triples and quadruples in static and temporal knowledge graphs. However, vectors that have the same inner products with another vector can still be orthogonal to each other, which implies that entities with similar semantics may have dissimilar embeddings. This property of inner products significantly limits the performance of semantic matching models. To address this challenge, we propose a novel regularizer -- namely, DUality-induced RegulArizer (DURA) -- which effectively encourages the entities with similar semantics to have similar embeddings. The major novelty of DURA is based on the observation that, for an existing semantic matching KGE model (primal), there is often another distance based KGE model (dual) closely associated with it, which can be used as effective constraints for entity embeddings. Experiments demonstrate that DURA consistently and significantly improves the performance of state-of-the-art semantic matching models on both static and temporal knowledge graph benchmarks.
Knowledge Graph Embedding models have become an important area of machine learning.Those models provide a latent representation of entities and relations in a knowledge graph which can then be used in downstream machine learning tasks such as link prediction. The learning process of such models can be performed by contrasting positive and negative triples. While all triples of a KG are considered positive, negative triples are usually not readily available. Therefore, the choice of the sampling method to obtain the negative triples play a crucial role in the performance and effectiveness of Knowledge Graph Embedding models. Most of the current methods fetch negative samples from a random distribution of entities in the underlying Knowledge Graph which also often includes meaningless triples. Other known methods use adversarial techniques or generative neural networks which consequently reduce the efficiency of the process. In this paper, we propose an approach for generating informative negative samples considering available complementary knowledge about entities. Particularly, Pre-trained Language Models are used to form neighborhood clusters by utilizing the distances between entities to obtain representations of symbolic entities via their textual information. Our comprehensive evaluations demonstrate the effectiveness of the proposed approach on benchmark Knowledge Graphs with textual information for the link prediction task.
Motivated by recent findings from cognitive neural science, we advocate the use of a dual-level model for concept representations: the embodied level consists of concept-oriented feature representations, and the symbolic level consists of concept graphs. Embodied concept representations are modality specific and exist in the form of feature vectors in a feature space. Symbolic concept representations, on the other hand, are amodal and language specific, and exist in the form of word / knowledge-graph embeddings in a concept / knowledge space. The human conceptual system comprises both embodied representations and symbolic representations, which typically interact to drive conceptual processing. As such, we further advocate the use of dual embodied-symbolic concept representations for deep learning. To demonstrate their usage and value, we discuss two important use cases: embodied-symbolic knowledge distillation for few-shot class incremental learning, and embodied-symbolic fused representation for image-text matching. Dual embodied-symbolic concept representations are the foundation for deep learning and symbolic AI integration. We discuss two important examples of such integration: scene graph generation with knowledge graph bridging, and multimodal knowledge graphs.
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.