# Knowledge Graph Completion Based on Entity Descriptions in Hyperbolic Space
###### Abstract  
Hyperbolic space has received extensive attention because it can accurately and concisely represent hierarchical data. Currently, for knowledge graph completion tasks, the introduction of exogenous information of entities can enrich the knowledge representation of entities, but there is a problem that entities have different levels under different relations, and the embeddings of different entities in Euclidean space often requires high dimensional space to distinguish. Therefore, in order to solve the above problem, we propose a method that use entity descriptions to complete the knowledge graph in the Poincare ball model of hyperbolic space. In this method, the text representation of entity descriptions is in Euclidean space and mapped to hyperbolic space through exponential map. Next, the triple embeddings are initialized in hyperbolic space, and the structured representation of the triple is trained by the hyperbolic model. Finally, the text representation and the structured representation of the entity are cross-fused in hyperbolic space, and then the balance factors are used to adjust the unbalanced energy function. Experimental results show that, compared with baseline models, the proposed method can improve the performance of knowledge graphs completion. hyperbolic space; entity descriptions; structured representation; text representation; knowledge graph completion +
Footnote †: journal: _Sci._  
0000-0001-5000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-0000-00000-00000-0000-00000-00000-00000-00000-00000-00000-00  
years, hyperbolic models have gradually attracted attention in hyperbolic space [15; 16]. [PERSON] et al. [17] have proved that Poincare ball embeddings in hyperbolic geometry has great advantages in hierarchical data, and can accurately and concisely represent hierarchical data. [PERSON] et al. [18] have proved that hyperbolic embeddings are better than Euclidean embeddings at lower dimensionality in hyperbolic Poincare ball link prediction. Compared with hyperbolic space, some research results show that models of Euclidean space can not well reflect complex data structures [19; 20]. For a knowledge graph with a tree-like hierarchical structure, its volume (with a node as the center and the number of nodes within a certain radius) grows exponentially with the radius, while the volume of balls in Euclidean space grows polynomially with the radius, while the volume of balls in hyperbolic space grows exponentially with the radius [21]. It can be seen that embedding knowledge graph into Euclidean space will lead to high distortion embeddings, while embedding knowledge graph into hyperbolic space may show high fidelity performance. In addition, in order to expand the knowledge graph better, the models of Euclidean space usually integrate the external descriptions of entities. Some models of Euclidean space integrate entity descriptions, and use rich external information and structured information of entities to train together to mine more entity semantic information [22; 23; 24; 25]. For hyperbolic space, [PERSON] et al. [18] and [PERSON] et al. [26; 27] find that using the natural properties of hyperbolic space, data hierarchy can be modeled, and semantic information of entities can be expressed in lower dimensions. Currently, according to previous research results, hyperbolic embeddings are better than Euclidean embeddings in learning space. In knowledge representation, fusing entity descriptions can improve the representation ability of entities. Inspired by [PERSON] et al. [18] and [PERSON] et al. [22], this paper completes the knowledge graph in the Poincare ball models of hyperbolic space by combining the structured information of triples and the text descriptions of entities. The text descriptions of entities can find the semantic correlation between entities and provide accurate semantic expression. The characteristics of hyperbolic space can not only try to express the embeddings of entities with low dimensions, but also model the hierarchical information of data.