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Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

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 knowledge graph completion and cannot be applied to the more challenging multi-hop reasoning task. Here we present Scalable Multi-hOp REasoning (SMORE), the first general framework for both single-hop and multi-hop reasoning in KGs. Using a single machine SMORE can perform multi-hop reasoning in Freebase KG (86M entities, 338M edges), which is 1,500x larger than previously considered KGs. The key to SMORE's runtime performance is a novel bidirectional rejection sampling that achieves a square root reduction of the complexity of online training data generation. Furthermore, SMORE exploits asynchronous scheduling, overlapping CPU-based data sampling, GPU-based embedding computation, and frequent CPU--GPU IO. SMORE increases throughput (i.e., training speed) over prior multi-hop KG frameworks by 2.2x with minimal GPU memory requirements (2GB for training 400-dim embeddings on 86M-node Freebase) and achieves near linear speed-up with the number of GPUs. Moreover, on the simpler single-hop knowledge graph completion task SMORE achieves comparable or even better runtime performance to state-of-the-art frameworks on both single GPU and multi-GPU settings.

Knowledge enhanced pre-trained language models (K-PLMs) are shown to be effective for many public tasks in the literature but few of them have been successfully applied in practice. To address this problem, we propose K-AID, a systematic approach that includes a low-cost knowledge acquisition process for acquiring domain knowledge, an effective knowledge infusion module for improving model performance, and a knowledge distillation component for reducing the model size and deploying K-PLMs on resource-restricted devices (e.g., CPU) for real-world application. Importantly, instead of capturing entity knowledge like the majority of existing K-PLMs, our approach captures relational knowledge, which contributes to better-improving sentence-level text classification and text matching tasks that play a key role in question answering (QA). We conducted a set of experiments on five text classification tasks and three text matching tasks from three domains, namely E-commerce, Government, and Film&TV, and performed online A/B tests in E-commerce. Experimental results show that our approach is able to achieve substantial improvement on sentence-level question answering tasks and bring beneficial business value in industrial settings.

We propose a knowledge-enhanced approach, ERNIE-ViL, to learn joint representations of vision and language. ERNIE-ViL tries to construct the detailed semantic connections (objects, attributes of objects and relationships between objects in visual scenes) across vision and language, which are essential to vision-language cross-modal tasks. Incorporating knowledge from scene graphs, ERNIE-ViL constructs Scene Graph Prediction tasks, i.e., Object Prediction, Attribute Prediction and Relationship Prediction in the pre-training phase. More specifically, these prediction tasks are implemented by predicting nodes of different types in the scene graph parsed from the sentence. Thus, ERNIE-ViL can model the joint representation characterizing the alignments of the detailed semantics across vision and language. Pre-trained on two large image-text alignment datasets (Conceptual Captions and SBU), ERNIE-ViL learns better and more robust joint representations. It achieves state-of-the-art performance on 5 vision-language downstream tasks after fine-tuning ERNIE-ViL. Furthermore, it ranked the 1st place on the VCR leader-board with an absolute improvement of 3.7%.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.

Knowledge graphs (KGs) serve as useful resources for various natural language processing applications. Previous KG completion approaches require a large number of training instances (i.e., head-tail entity pairs) for every relation. The real case is that for most of the relations, very few entity pairs are available. Existing work of one-shot learning limits method generalizability for few-shot scenarios and does not fully use the supervisory information; however, few-shot KG completion has not been well studied yet. In this work, we propose a novel few-shot relation learning model (FSRL) that aims at discovering facts of new relations with few-shot references. FSRL can effectively capture knowledge from heterogeneous graph structure, aggregate representations of few-shot references, and match similar entity pairs of reference set for every relation. Extensive experiments on two public datasets demonstrate that FSRL outperforms the state-of-the-art.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

Knowledge graphs are important resources for many artificial intelligence tasks but often suffer from incompleteness. In this work, we propose to use pre-trained language models for knowledge graph completion. We treat triples in knowledge graphs as textual sequences and propose a novel framework named Knowledge Graph Bidirectional Encoder Representations from Transformer (KG-BERT) to model these triples. Our method takes entity and relation descriptions of a triple as input and computes scoring function of the triple with the KG-BERT language model. Experimental results on multiple benchmark knowledge graphs show that our method can achieve state-of-the-art performance in triple classification, link prediction and relation prediction tasks.

Knowledge graphs capture structured information and relations between a set of entities or items. As such they represent an attractive source of information that could help improve recommender systems. However existing approaches in this domain rely on manual feature engineering and do not allow for end-to-end training. Here we propose knowledge-aware graph neural networks with label smoothness regularization to provide better recommendations. Conceptually, our approach computes user-specific item embeddings by first applying a trainable function that identifies important knowledge graph relationships for a given user. This way we transform the knowledge graph into a user-specific weighted graph and then applies a graph neural network to compute personalized item embeddings. To provide better inductive bias, we use label smoothness, which assumes that adjacent items in the knowledge graph are likely to have similar user relevance labels/scores. Label smoothness provides regularization over edge weights and we prove that it is equivalent to a label propagation scheme on a graph. Finally, we combine knowledge-aware graph neural networks and label smoothness and present the unified model. Experiment results show that our method outperforms strong baselines in four datasets. It also achieves strong performance in the scenario where user-item interactions are sparse.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.