## 2 Related Work
### Deep-Learning-Based Model  
Deep-learning-based models provide a flexible approach to extract hidden features of triples using popular frameworks such as convolutional neural networks (CNNs) or Graph Neural Networks (GNNs). A notable example is ConvE [36], which uses relation-specific filters to perform adaptive convolution on the entity transformation matrix, followed by scoring through a dot product of the output and tail embedding. HypER, proposed by [37], is a hypernetwork architecture that generates simplified specific relation convolutional filters. This approach combines tensor factorization techniques to enhance the performance of the model compared to traditional convolutional models like ConvE. GLSP [38] combines a GNN with an LSTM to effectively store temporal information. By leveraging both long- and short-term networks, GLSP can better capture the complex dynamics of temporal KGs and enhance the predictive ability. Recently, there has been an increasing trend of using attention mechanisms and Transformer [39] frameworks to extract potential connections between entities and relations. For instance, HitER [22] leverages neighbor information extensively and designs a masking and prediction mechanism for source entities to appropriately extract data from the structured Transformer module. The recent advancement in large-scale pre-trained models in the natural language processing field has inspired researchers to introduce text pre-training models such as BERT [40] to graph embedding. This approach leverages the text descriptions of entities to represent their embeddings, which enhances their semantic information and expressive ability. For example, MTL-KGC [21] introduces an effective multi-task learning method aimed at overcoming the limitations of BERT in the KG domain. By combining relation prediction and correlation sorting tasks with target link prediction, the method achieves stronger performance. StAR [41], on the other hand, proposes a structure-enhanced text representation learning framework for effective KG completion. PKGC [42] discusses the issue of the improper use of pre-trained language models in KG completion, proposing to transform each triplet and its supporting information into natural prompt sentences and further input them into pre-trained language models for classification. More recently, SimKGC [43] adopted a dual-encoder architecture utilizing two parallel BERT modules to model head-entity-relation combinations and tail entities. The model leverages three negative sampling mechanisms and introduces the InfoNCE loss function to make use of comparative learning. KGLM [44] generates a corpus by converting triples in the KG into text sequences, continuing to pre-train language models that have already been pre-trained on other large natural language corpora, and enhancing the model by adding additional entity/relation-type embedding layers to better understand the underlying graph structure. In fact, deep-learning-based models lack prior rules of feature construction, resulting in lower efficiency in utilizing triples compared to machine-learning-based models. As a result, deep-learning-based models require significant amounts of knowledge triples to learn effective feature construction methods. The RiQ-KGC proposed in this paper is a deep-learning-based model that integrates geometric information into a new hierarchical Transformer network architecture. It embeds entities into quaternion space and generalizes the rotation between entities using attention mechanism and innovative relation instantiation methods. With regard to embedding complex relations, RiQ-KGC can alleviate the associated difficulties better than machine-learning-based models. Additionally, compared to deep-learning-based models, RiQ-KGC demonstrates more efficient learning capabilities. We evaluated the performance by testing its ability to detect missing entities in triples using link prediction as a downstream task.