Link prediction based on knowledge graph embedding (KGE) aims to predict new triples to complete knowledge graphs (KGs) automatically. However, recent KGE models tend to improve performance by excessively increasing vector dimensions, which would cause enormous training costs and save storage in practical applications. To address this problem, we first theoretically analyze the capacity of low-dimensional space for KG embeddings based on the principle of minimum entropy. Then, we propose a novel knowledge distillation framework for knowledge graph embedding, utilizing multiple low-dimensional KGE models as teachers. Under a novel iterative distillation strategy, the MulDE model produces soft labels according to training epochs and student performance adaptively. The experimental results show that MulDE can effectively improve the performance and training speed of low-dimensional KGE models. The distilled 32-dimensional models are very competitive compared to some of state-or-the-art (SotA) high-dimensional methods on several commonly-used datasets.

Through the combination of crowdsourcing knowledge graph and teaching system, research methods to generate knowledge graph and its applications. Using two crowdsourcing approaches, crowdsourcing task distribution and reverse captcha generation, to construct knowledge graph in the field of teaching system. Generating a complete hierarchical knowledge graph of the teaching domain by nodes of school, student, teacher, course, knowledge point and exercise type. The knowledge graph constructed in a crowdsourcing manner requires many users to participate collaboratively with fully consideration of teachers' guidance and users' mobilization issues. Based on the three subgraphs of knowledge graph, prominent teacher, student learning situation and suitable learning route could be visualized. Personalized exercises recommendation model is used to formulate the personalized exercise by algorithm based on the knowledge graph. Collaborative creation model is developed to realize the crowdsourcing construction mechanism. Though unfamiliarity with the learning mode of knowledge graph and learners' less attention to the knowledge structure, system based on Crowdsourcing Knowledge Graph can still get high acceptance around students and teachers

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 (usually a vector space). Ultimately, the plausibility of the predicted links is measured by using a scoring function over the learned embeddings (vectors). Therefore, the capability in preserving graph characteristics including structural aspects and semantics highly depends on the design of the KGE, as well as the inherited abilities from the underlying geometry. Many KGEs use the flat 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 a smooth Riemannian manifold. We specifically parameterize ODEs by a neural network to represent various complex shape manifolds and more importantly complex shape vector fields on the manifold. Therefore, the underlying embedding space is capable of getting various geometric forms to encode complexity in subgraph structures with different motifs. Experiments on synthetic and benchmark dataset as well as social network KGs justify the ODE trajectories as a means to structure preservation and consequently avoiding wrong inferences over state-of-the-art KGE models.

There is an increasing interest in the use of automatic mathematical word problem (MWP) generation in educational assessment. Different from standard natural question generation, MWP generation needs to maintain the underlying mathematical operations between quantities and variables, while at the same time ensuring the relevance between the output and the given topic. To address above problem we develop an end-to-end neural model to generate personalized and diverse MWPs in real-world scenarios from commonsense knowledge graph and equations. The proposed model (1) learns both representations from edgeenhanced Levi graphs of symbolic equations and commonsense knowledge; (2) automatically fuses equation and commonsense knowledge information via a selfplanning module when generating the MWPs. Experiments on an educational gold-standard set and a large-scale generated MWP set show that our approach is superior on the MWP generation task, and it outperforms the state-of-the-art models in terms of both automatic evaluation metrics, i.e., BLEU-4, ROUGE-L, Self-BLEU, and human evaluation metrics, i.e, equation relevance, topic relevance, and language coherence. A mathematical word problem (MWP) is a coherent narrative that provides clues to the underlying correct mathematical equations and operations between variables and numerical quantities (Verschaffel et al., 2000; Cetintas et al., 2010; Moyer et al., 1984). Table 1 shows one such problem where students are asked to infer the counts of chickens and rabbits. Mathematical Word Problem Equations Solutions Chickens and rabbits were in the yard. Together they had 27 heads x y 27 x 11 and 86 legs. How many chickens and rabbits were in the yard? In this paper, our objective is to automatically generate well-formed MWPs.

We demonstrate the complementary natures of neural knowledge graph embedding, fine-grain entity type prediction, and neural language modeling. We show that a language model-inspired knowledge graph embedding approach yields both improved knowledge graph embeddings and fine-grain entity type representations. Our work also shows that jointly modeling both structured knowledge tuples and language improves both.

The current knowledge system of macroeconomics is built on interactions among a small number of variables, since traditional macroeconomic models can mostly handle a handful of inputs. Recent work using big data suggests that a much larger number of variables are active in driving the dynamics of the aggregate economy. In this paper, we introduce a knowledge graph (KG) that consists of not only linkages between traditional economic variables but also new alternative big data variables. We extract these new variables and the linkages by applying advanced natural language processing (NLP) tools on the massive textual data of academic literature and research reports. As one example of the potential applications, we use it as the prior knowledge to select variables for economic forecasting models in macroeconomics. Compared to statistical variable selection methods, KG-based methods achieve significantly higher forecasting accuracy, especially for long run forecasts.

In the Open Data era, a large number of table resources have been made available on the Web and data portals. However, it is difficult to directly utilize such data due to the ambiguity of entities, name variations, heterogeneous schema, missing, or incomplete metadata. To address these issues, we propose a novel approach, namely TabEAno, to semantically annotate table rows toward knowledge graph entities. Specifically, we introduce a "two-cells" lookup strategy bases on the assumption that there is an existing logical relation occurring in the knowledge graph between the two closed cells in the same row of the table. Despite the simplicity of the approach, TabEAno outperforms the state of the art approaches in the two standard datasets e.g, T2D, Limaye with, and in the large-scale Wikipedia tables dataset.

In recent years, many efforts have been made to complete knowledge graphs (KGs) by various graph embedding methods, most of which only focus on static KGs (SKGs) without considering the time dependency of facts. However, KGs in reality are dynamic and there exists correlations between facts with different timestamps. Due to the sparsity of temporal KGs (TKGs), SKG embedding methods cannot be directly applied to TKGs. And existing methods of TKG embedding suffer from two issues: (1) they follow the pattern of SKG embedding where all facts need to be retrained when a new timestamp appears; (2) they don't provide a general way to transplant SKG embedding methods to TKGs and therefore lack extensibility. In this paper, we propose a novel Recursive Temporal Fact Embedding Framework (RTFE) to transplant translation-based or graph neural network-based SKG embedding methods to TKGs. In the recursive way, timestamp parameters provide a good starting point for the next future timestamp. And existing SKG embedding models can be used as components. Experiments on TKGs show that our proposed framework (1) outperforms the state-of-the-art baseline model in the entity prediction task on fact datasets; (2) achieves similar performance compared with the state-of-the-art baseline model in relation prediction task on fact datasets; and (3) shows performance in the entity prediction task on event datasets.

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 translation function with rigorous multiplication of two complex numbers; and 2) embedding ambiguity caused by one-to-many relations is not explicitly alleviated. In this paper, we propose a relation-adaptive translation function built upon a novel weighted product in complex space, where the weights are learnable, relation-specific and independent to embedding size. The translation function only requires eight more scalar parameters each relation, but improves expressive power and alleviates embedding ambiguity problem. Based on the function, we then present our Relation-adaptive translating Embedding (RatE) approach to score each graph triple. Moreover, a novel negative sampling method is proposed to utilize both prior knowledge and self-adversarial learning for effective optimization. Experiments verify RatE achieves state-of-the-art performance on four link prediction benchmarks.

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 hindered by the insufficiency of alignment information and the inconsistency of described facts. In this paper, we propose KEnS, a novel framework for embedding learning and ensemble knowledge transfer across a number of language-specific KGs. KEnS embeds all KGs in a shared embedding space, where the association of entities is captured based on self-learning. Then, KEnS performs ensemble inference to combine prediction results from embeddings of multiple language-specific KGs, for which multiple ensemble techniques are investigated. Experiments on five real-world language-specific KGs show that KEnS consistently improves state-of-the-art methods on KG completion, via effectively identifying and leveraging complementary knowledge.