There has recently been increasing interest in learning representations of temporal knowledge graphs (KGs), which record the dynamic relationships between entities over time. Temporal KGs often exhibit multiple simultaneous non-Euclidean structures, such as hierarchical and cyclic structures. However, existing embedding approaches for temporal KGs typically learn entity representations and their dynamic evolution in the Euclidean space, which might not capture such intrinsic structures very well. To this end, we propose Dy- ERNIE, a non-Euclidean embedding approach that learns evolving entity representations in a product of Riemannian manifolds, where the composed spaces are estimated from the sectional curvatures of underlying data. Product manifolds enable our approach to better reflect a wide variety of geometric structures on temporal KGs. Besides, to capture the evolutionary dynamics of temporal KGs, we let the entity representations evolve according to a velocity vector defined in the tangent space at each timestamp. We analyze in detail the contribution of geometric spaces to representation learning of temporal KGs and evaluate our model on temporal knowledge graph completion tasks. Extensive experiments on three real-world datasets demonstrate significantly improved performance, indicating that the dynamics of multi-relational graph data can be more properly modeled by the evolution of embeddings on Riemannian manifolds.
Knowledge Graph (KG) completion is an important task that greatly benefits knowledge discovery in many fields (e.g. biomedical research). In recent years, learning KG embeddings to perform this task has received considerable attention. Despite the success of KG embedding methods, they predominantly use negative sampling, resulting in increased computational complexity as well as biased predictions due to the closed world assumption. To overcome these limitations, we propose \textbf{KG-NSF}, a negative sampling-free framework for learning KG embeddings based on the cross-correlation matrices of…
Knowledge graph completion is the task of inferring missing facts based on existing data in a knowledge graph. Temporal knowledge graph completion (TKGC) is an extension of this task to temporal knowledge graphs, where each fact is additionally associated with a time stamp. Current approaches for TKGC primarily build on existing embedding models which are developed for (static) knowledge graph completion, and extend these models to incorporate time, where the idea is to learn latent representations for entities, relations, and timestamps and then use the learned representations to predict miss…
Peking University（北京大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；UC Berkeley（加州大学伯克利分校）
The task of completing knowledge triplets has broad downstream applications. Both structural and semantic information plays an important role in knowledge graph completion. Unlike previous approaches that rely on either the structures or semantics of the knowledge graphs, we propose to jointly embed the semantics in the natural language description of the knowledge triplets with their structure information. Our method embeds knowledge graphs for the completion task via fine-tuning pre-trained language models with respect to a probabilistic structured loss, where the forward pass of the languag…
Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones-a problem known as KG completion. KG embedding approaches have proved effective for KG completion, however, they have been developed mostly for static KGs. Developing temporal KG embedding models is an increasingly important problem. In this paper, we build novel models for temporal KG completion through equipping static models with a diachronic entity embeddi…
Computer Network Information Center, Chinese Academy of Sciences（中国科学院计算机网络信息中心）；University of Chinese Academy of Sciences（中国科学院大学）
Most researches for knowledge graph completion learn representations of entities and relations to predict missing links in incomplete knowledge graphs. However, these methods fail to take full advantage of both the contextual information of entity and relation. Here, we extract contexts of entities and relations from the triplets which they compose. We propose a model named AggrE, which conducts efficient aggregations respectively on entity context and relation context in multi-hops, and learns context-enhanced entity and relation embeddings for knowledge graph completion. The experiment resul…
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential f…
Predicting missing facts in a knowledge graph (KG) is a crucial task in knowledge base construction and reasoning, and it has been the subject of much research in recent works using KG embeddings. While existing KG embedding approaches mainly learn and predict facts within a single KG, a more plausible solution would benefit from the knowledge in multiple language-specific KGs, considering that different KGs have their own strengths and limitations on data quality and coverage. This is quite challenging, since the transfer of knowledge among multiple independently maintained KGs is often hinde…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院（EPFL））
Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on the family of translational models, whose performance has been lagging, and propose a model, dubbed HyperKG, which exploits the hyperbolic space in order to better reflect the topological properties of knowledge bases. We investigate the type of regularities that our model can capture and we show that it is a prominent candidate for effectively representing a…
Australian AI Institute（澳大利亚人工智能研究所）；University of Technology Sydney（悉尼科技大学）
Many graph embedding approaches have been proposed for knowledge graph completion via link prediction. Among those, translating embedding approaches enjoy the advantages of light-weight structure, high efficiency and great interpretability. Especially when extended to complex vector space, they show the capability in handling various relation patterns including symmetry, antisymmetry, inversion and composition. However, previous translating embedding approaches defined in complex vector space suffer from two main issues: 1) representing and modeling capacities of the model are limited by the t…
The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学）；National Institute of Informatics（国立信息学研究所）
Knowledge graph completion is an important task that aims to predict the missing relational link between entities. Knowledge graph embedding methods perform this task by representing entities and relations as embedding vectors and modeling their interactions to compute the matching score of each triple. Previous work has usually treated each embedding as a whole and has modeled the interactions between these whole embeddings, potentially making the model excessively expensive or requiring specially designed interaction mechanisms. In this work, we propose the multi-partition embedding interact…
Real-world knowledge graphs (KG) are mostly incomplete. The problem of recovering missing relations, called KG completion, has recently become an active research area. Knowledge graph (KG) embedding, a low-dimensional representation of entities and relations, is the crucial technique for KG completion. Convolutional neural networks in models such as ConvE, SACN, InteractE, and RGCN achieve recent successes. This paper takes a different architectural view and proposes ComDensE which combines relation-aware and common features using dense neural networks. In the relation-aware feature extraction…
Knowledge graphs are inherently incomplete. Therefore substantial research has been directed toward knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). KG embedding models (KGEs) have yielded promising results for KGC, yet any current KGE is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent patterns jointly (e.g., hierarchy and composition), and (3) providing an intuitive interpretation of captured patterns. In this work, we propose ExpressivE, a fully expressive s…
ConvD: Attention Enhanced Dynamic Convolutional Embeddings for Knowledge Graph Completion
College of Intelligence and Computing, Tianjin University（天津大学智能与计算学院）；Tianjin Key Laboratory of Cognitive Computing and Application（认知计算与应用重点实验室）；School of Economics and Management, Ningxia University（宁夏大学经济管理学院）；School of Computer Science and Technology, Beijing Institute of Technology（北京理工大学计算机科学与技术学院）
National University of Science and Technology（国立科技大学）；RheinMain University of Applied Sciences（莱茵美因应用科学大学）
We present a novel extension to embedding-based knowledge graph completion models which enables them to perform open-world link prediction, i.e. to predict facts for entities unseen in training based on their textual description. Our model combines a regular link prediction model learned from a knowledge graph with word embeddings learned from a textual corpus. After training both independently, we learn a transformation to map the embeddings of an entity's name and description to the graph-based embedding space. In experiments on several datasets including FB20k, DBPedia50k and our new datase…
Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-tra…
SOKENDAI (The Graduate University for Advanced Studies)（综合研究大学院大学）；National Institute of Informatics（国立信息学研究所）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
Knowledge graphs are useful for many artificial intelligence tasks but often have missing data. Hence, a method for completing knowledge graphs is required. Existing approaches include embedding models, the Path Ranking Algorithm, and rule evaluation models. However, these approaches have limitations. For example, all the information is mixed and difficult to interpret in embedding models, and traditional rule evaluation models are basically slow. In this paper, we provide an integrated view of various approaches and combine them to compensate for their limitations. We first unify state-of-the…
Beijing University of Posts and Telecommunications（北京邮电大学）
Static knowledge graph (SKG) embedding (SKGE) has been studied intensively in the past years. Recently, temporal knowledge graph (TKG) embedding (TKGE) has emerged. In this paper, we propose a Recursive Temporal Fact Embedding (RTFE) framework to transplant SKGE models to TKGs and to enhance the performance of existing TKGE models for TKG completion. Different from previous work which ignores the continuity of states of TKG in time evolution, we treat the sequence of graphs as a Markov chain, which transitions from the previous state to the next state. RTFE takes the SKGE to initialize the emb…
Recent interest in Knowledge Base Completion (KBC) has led to a plethora of approaches based on reinforcement learning, inductive logic programming and graph embeddings. In particular, rule-based KBC has led to interpretable rules while being comparable in performance with graph embeddings. Even within rule-based KBC, there exist different approaches that lead to rules of varying quality and previous work has not always been precise in highlighting these differences. Another issue that plagues most rule-based KBC is the non-uniformity of relation paths: some relation sequences occur in very fe…
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；College of Software Technology, Zhejiang University（浙江大学软件学院）
Knowledge graphs (KGs) that modelings the world knowledge as structural triples are inevitably incomplete. Such problems still exist for multimodal knowledge graphs (MMKGs). Thus, knowledge graph completion (KGC) is of great importance to predict the missing triples in the existing KGs. As for the existing KGC methods, embedding-based methods rely on manual design to leverage multimodal information while finetune-based approaches are not superior to embedding-based methods in link prediction. To address these problems, we propose a VisualBERT-enhanced Knowledge Graph Completion model (VBKGC fo…
Peoples' Friendship University of Russia (RUDN University)（俄罗斯人民友谊大学（卢蒙巴大学））；Joint Institute for Nuclear Research（联合核研究所）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Skövde（舍夫德大学）；Comenius University in Bratislava（布拉迪斯拉发夸美纽斯大学）；University of Bergen（卑尔根大学）
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.
Knowledge graph (KG) refinement mainly aims at KG completion and correction (i.e., error detection). However, most conventional KG embedding models only focus on KG completion with an unreasonable assumption that all facts in KG hold without noises, ignoring error detection which also should be significant and essential for KG refinement.In this paper, we propose a novel support-confidence-aware KG embedding framework (SCEF), which implements KG completion and correction simultaneously by learning knowledge representations with both triple support and triple confidence. Specifically, we build …
DELE: Deductive $\mathcal{EL}^{++}$ Embeddings for Knowledge Base Completion
Mathematical Sciences \& Engineering Division, King Abdullah University of Science；KAUST Center of Excellence for Smart Health, King Abdullah University of Science；KAUST Center of Excellence for Generative AI, King Abdullah University of Science
Spectal Harmonics: Bridging Spectral Embedding and Matrix Completion in Self-Supervised Learning
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院（AIRI））；Skolkovo Institute of Science and Technology (Skoltech)（斯科尔科沃科学技术学院（Skoltech））
With the large volume of new information created every day, determining the validity of information in a knowledge graph and filling in its missing parts are crucial tasks for many researchers and practitioners. To address this challenge, a number of knowledge graph completion methods have been developed using low-dimensional graph embeddings. Although researchers continue to improve these models using an increasingly complex feature space, we show that simple changes in the architecture of the underlying model can outperform state-of-the-art models without the need for complex feature enginee…
We study the non-convex matrix factorization approach to matrix completion via Riemannian geometry. Based on an optimization formulation over a Grassmannian manifold, we characterize the landscape based on the notion of principal angles between subspaces. For the fully observed case, our results show that there is a region in which the cost is geodesically convex, and outside of which all critical points are strictly saddle. We empirically study the partially observed case based on our findings.
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；NAVER LABS Europe（NAVER LABS 欧洲实验室）；University College London（伦敦大学学院）；Bloomsbury AI
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real sq…
Knowledge graphs (KGs) capture knowledge in the form of head--relation--tail triples and are a crucial component in many AI systems. There are two important reasoning tasks on KGs: (1) single-hop knowledge graph completion, which involves predicting individual links in the KG; and (2), multi-hop reasoning, where the goal is to predict which KG entities satisfy a given logical query. Embedding-based methods solve both tasks by first computing an embedding for each entity and relation, then using them to form predictions. However, existing scalable KG embedding frameworks only support single-hop…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to decompose a partially observed matrix into the superposition of a low-rank matrix and a sparse matrix, where the sparse matrix captures the grossly corrupted entries of the matrix. A widely used approach to tackle RMC is to consider a convex formulation, which minimizes the nuclear norm of the low-rank matrix (to promote low-rankness) and the l1 norm of the sparse…
Cranberry-Lemon University（蔓越莓柠檬大学）；University of the Witwatersrand（金山大学）
Knowledge graph completion aims to predict the new links in given entities among the knowledge graph (KG). Most mainstream embedding methods focus on fact triplets contained in the given KG, however, ignoring the rich background information provided by logic rules driven from knowledge base implicitly. To solve this problem, in this paper, we propose a general framework, named EM-RBR(embedding and rule-based reasoning), capable of combining the advantages of reasoning based on rules and the state-of-the-art models of embedding. EM-RBR aims to utilize relational background knowledge contained i…
New Jersey Institute of Technology（新泽西理工学院）；Central Michigan University（中密歇根大学）
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and different levels of sparsity. Current non-linear tensor completion algorithms tend to learn noisy embedding and incur overfitting. This paper focuses on the embedding learning aspect of the tensor completion problem and proposes a new multi-layer neural network architecture for tensor factorization and completion (MLCTR). The network architecture entails multiple…
In Human-Robot Interaction (HRI) systems, a challenging task is sharing the representation of the operational environment, fusing symbolic knowledge and perceptions, between users and robots. With the existing HRI pipelines, users can teach the robots some concepts to increase their knowledge base. Unfortunately, the data coming from the users are usually not enough dense for building a consistent representation. Furthermore, the existing approaches are not able to incrementally build up their knowledge base, which is very important when robots have to deal with dynamic contexts. To this end, …
McGill University（麦吉尔大学）；MILA（MILA研究所）；University of Montreal（蒙特利尔大学）
Reasoning in a temporal knowledge graph (TKG) is a critical task for information retrieval and semantic search. It is particularly challenging when the TKG is updated frequently. The model has to adapt to changes in the TKG for efficient training and inference while preserving its performance on historical knowledge. Recent work approaches TKG completion (TKGC) by augmenting the encoder-decoder framework with a time-aware encoding function. However, naively fine-tuning the model at every time step using these methods does not address the problems of 1) catastrophic forgetting, 2) the model's i…
University of Southern California（南加州大学）；Stanford University（斯坦福大学）
Commonsense knowledge graph (CKG) is a special type of knowledge graph (KG), where entities are composed of free-form text. However, most existing CKG completion methods focus on the setting where all the entities are presented at training time. Although this setting is standard for conventional KG completion, it has limitations for CKG completion. At test time, entities in CKGs can be unseen because they may have unseen text/names and entities may be disconnected from the training graph, since CKGs are generally very sparse. Here, we propose to study the inductive learning setting for CKG com…
University of Liège（列日大学）；University of Cambridge（剑桥大学）
We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a novel Riemannian metric that is tailored to the least-squares cost. Numerical comparisons suggest that R3MC robustly outperforms state-of-the-art algorithms across different problem instances, especially those that combine scarcely sampled and ill-conditioned data.
We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on the product space of the factor matrices of the low-rank tensor in the polyadic decomposition form. This new metric is designed using an approximation of the diagonal blocks of the Hessian of the tensor completion cost function, thus has a preconditioning effect on these algorithms. We prove that the proposed Riemannian gradient descent algorithm globally converges to a stationary point of the tensor completion problem…
Knowledge bases contribute to many web search and mining tasks, yet they are often incomplete. To add missing facts to a given knowledge base, various embedding models have been proposed in the recent literature. Perhaps surprisingly, relatively simple models with limited expressiveness often performed remarkably well under today's most commonly used evaluation protocols. In this paper, we explore whether recent models work well for knowledge base completion and argue that the current evaluation protocols are more suited for question answering rather than knowledge base completion. We show tha…
Pretrained (language) embeddings are versatile, task-agnostic feature representations of entities, like words, that are central to many machine learning applications. These representations can be enriched through retrofitting, a class of methods that incorporate task-specific domain knowledge encoded as a graph over a subset of these entities. However, existing retrofitting algorithms face two limitations: they overfit the observed graph by failing to represent relationships with missing entities; and they underfit the observed graph by only learning embeddings in Euclidean manifolds, which ca…
Hong Kong University of Science and Technology（香港科技大学）
The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn considerable attention. Numerous fast algorithms, including the Riemannian gradient descent (RGrad), have been proposed for the TT-format tensor completion. However, the theoretical guarantees of these algorithms are largely missing or sub-optimal, partly due to the complicated and recursive algebraic operations in TT-format decomposition. Moreover, existin…
The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed g…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic geometry. However, going beyond embedding spaces of constant sectional curvature, while potentially more representationally powerful, proves to be challenging as one can easily lose the appeal of computationally tractable tools such as geodesic distances or Riemannian gradients. Here, we explore computationally efficient matrix manifolds, showcasing how to l…
In this paper we generalize single-relation pseudo-Riemannian graph embedding models to multi-relational networks, and show that the typical approach of encoding relations as manifold transformations translates from the Riemannian to the pseudo-Riemannian case. In addition we construct a view of relations as separate spacetime submanifolds of multi-time manifolds, and consider an interpolation between a pseudo-Riemannian embedding model and its Wick-rotated Riemannian counterpart. We validate these extensions in the task of link prediction, focusing on flat Lorentzian manifolds, and demonstrat…
A fundamental task for knowledge graphs (KGs) is knowledge graph completion (KGC). It aims to predict unseen edges by learning representations for all the entities and relations in a KG. A common concern when learning representations on traditional graphs is degree bias. It can affect graph algorithms by learning poor representations for lower-degree nodes, often leading to low performance on such nodes. However, there has been limited research on whether there exists degree bias for embedding-based KGC and how such bias affects the performance of KGC. In this paper, we validate the existence …
Heidelberg Institute for Theoretical Studies（海德堡理论研究所）；Heidelberg University（海德堡大学）；Stanford University（斯坦福大学）
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. This enables us to introduce a new method, the use of Finsler metrics integrated in a Riemannian optimization scheme, that better adapts to dissimilar structures in the graph. We develop a tool to analyze the embeddings and infer structural properties of the data sets. For implementation, we…
The University of Hong Kong（香港大学）；Zhejiang University（浙江大学）
Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks such as recommendation systems, genotype imputation and image inpainting. While the dual-graph regularization contributes a major part of the success, computational costly hyper-parameter tunning is usually involved. To circumvent such a drawback and improve the completion performance, we propose a novel Bayesian learning algorithm that automatically learns t…
