Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a general framework based on a view of relations as regions, which allows us to study the compatibility between ontological knowledge and different types of vector space embeddings. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding methods are not capable of modelling even very simple types of rules, which in particular also means that they are not able to learn the type of dependencies captured by such rules. Second, we study a model in which relations are modelled as convex regions. We show particular that ontologies which are expressed using so-called quasi-chained existential rules can be exactly represented using convex regions, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.
Various approaches to KG completion have been proposed that are based on neural network architectures @cite_4 @cite_26 @cite_6 . Interestingly, some of these approaches can be seen as special cases of the extended convex geometric models considered in Section . For example, in the E-MLP model @cite_4 , to predict whether @math is a valid triple, the concatenation of the vectors @math and @math is fed into a two-layer neural network.
@cite_26 @cite_4 @cite_6
2767382887 2073587810 2774837955 2555231795
Knowledge Graphs (KGs) have been applied to many tasks including Web search, link prediction, recommendation, natural language processing, and entity linking. However, most KGs are far from complete and are growing at a rapid pace. To address these problems, Knowledge Graph Completion (KGC) has been proposed to improve KGs by filling in its missing connections. Unlike existing methods which hold a closed-world assumption, i.e., where KGs are fixed and new entities cannot be easily added, in the present work we relax this assumption and propose a new open-world KGC task. As a first attempt to solve this task we introduce an open-world KGC model called ConMask. This model learns embeddings of the entity's name and parts of its text-description to connect unseen entities to the KG. To mitigate the presence of noisy text descriptions, ConMask uses a relationship-dependent content masking to extract relevant snippets and then trains a fully convolutional neural network to fuse the extracted snippets with entities in the KG. Experiments on large data sets, both old and new, show that ConMask performs well in the open-world KGC task and even outperforms existing KGC models on the standard closed-world KGC task. The representation of a knowledge graph (KG) in a latent space recently has attracted more and more attention. To this end, some proposed models (e.g., TransE) embed entities and relations of a KG into a "point" vector space by optimizing a global loss function which ensures the scores of positive triplets are higher than negative ones. We notice that these models always regard all entities and relations in a same manner and ignore their (un)certainties. In fact, different entities and relations may contain different certainties, which makes identical certainty insufficient for modeling. Therefore, this paper switches to density-based embedding and propose KG2E for explicitly modeling the certainty of entities and relations, which learn the representations of KGs in the space of multi-dimensional Gaussian distributions. Each entity relation is represented by a Gaussian distribution, where the mean denotes its position and the covariance (currently with diagonal covariance) can properly represent its certainty. In addition, compared with the symmetric measures used in point-based methods, we employ the KL-divergence for scoring triplets, which is a natural asymmetry function for effectively modeling multiple types of relations. We have conducted extensive experiments on link prediction and triplet classification with multiple benchmark datasets (WordNet and Freebase). Our experimental results demonstrate that our method can effectively model the (un)certainties of entities and relations in a KG, and it significantly outperforms state-of-the-art methods (including TransH and TransR). We introduce a novel embedding method for knowledge base completion task. Our approach advances state-of-the-art (SOTA) by employing a convolutional neural network (CNN) for the task which can capture global relationships and transitional characteristics. We represent each triple (head entity, relation, tail entity) as a 3-column matrix which is the input for the convolution layer. Different filters having a same shape of 1x3 are operated over the input matrix to produce different feature maps which are then concatenated into a single feature vector. This vector is used to return a score for the triple via a dot product. The returned score is used to predict whether the triple is valid or not. Experiments show that ConvKB achieves better link prediction results than previous SOTA models on two current benchmark datasets WN18RR and FB15k-237. A quaternionic extension of feed forward neural network, for processing multi-dimensional signals, is proposed in this paper. This neural network is based on the three layered network with random weights, called Extreme Learning Machines (ELMs), in which iterative least-mean-square algorithms are not required for training networks. All parameters and variables in the proposed network are encoded by quaternions and operations among them follow the quaternion algebra. Neurons in the proposed network are expected to operate multi-dimensional signals as single entities, rather than real-valued neurons deal with each element of signals independently. The performances for the proposed network are evaluated through two types of experiments: classifications and reconstructions for color images in the CIFAR-10 dataset. The experimental results show that the proposed networks are superior in terms of classification accuracies for input images than the conventional (real-valued) networks with similar degrees of freedom. The detailed investigations for operations in the proposed networks are conducted. HighlightsA feedforward neural network for accepting three- or four-dimension is proposed.Quaternions, which are a four-dimensional hypercomlex numbers, are used for encoding neuronal parameters.Its performances are evaluated through the classification and autoencoding for CIFAR-10 dataset.