###### Abstract
As shown in Figure 1, the relationship between _[PERSON]_ and _[PERSON]_ can be mined through the facts of \([PERSON]\stackrel{{ Father of}}{{\rightarrow}}\)_[PERSON]_\(\stackrel{{ Spouse}}{{\rightarrow}}\)_[PERSON]_. Existing path construction methods attempt to capture the high-order connectivity of KGs using multi-step relationship chains [14]. However, the vast paths pose a significant computational complexity challenge for such methods. These methods can only perform path sampling or select approximate treatments for efficient path modeling. Our analysis reveals that such approximations can significantly impact the final model performance. (2) Explicitly modeling attribute information in KGs. There is a large amount of attribute information in real KGs, as shown in a statistic of [PERSON] et al. [15] on the English version of the DBpedia dataset (2016-04), in which attribute triples are three times as many as relation triples. Attribute triples (denoted as \((s,r,v)\), with \(v\) indicating attribute values) form a rich network of associations between entities that can characterize specific meanings of entities and relationships. As shown in Figure 1, attributes such as _Education_ and _Profile_ associated with the entity _[PERSON]_ can provide insights into his educational background and personal profile, facilitating the extraction of rich semantic information and enhancing the model's prediction and completion capabilities. Such information cannot be obtained from relationship quadruplets alone. Existing works have attempted to incorporate attribute information into TKGC models [16; 17]. However, they suffer from two limitations. On the one hand, some methods only utilize partial attribute information, such as AATE_E[17], that solely uses entity description information. On the other hand, both relational and attribute information are optimized in a unified framework, but the loss function must be balanced for both tasks. For instance, JAPE [15] adjusts hyperparameters to achieve the optimal balance between the two loss functions. The limitations of existing methods severely restrict the performance of the models. Given this, designing a model that can learn attribute information and high-order connectivity uniformly and efficiently is essential. Modeling high-order connectivity allows for the capturing of dependencies and semantic associations among entities, thus enabling a more comprehensive understanding of entity characteristics from multiple perspectives. Attribute information explicitly describes entity features and complements structural information, allowing the model to generalize better to unseen entities. The joint modeling of structure and attributes enables the learning of representations that fuse connectivity patterns and content features, leading to a more comprehensive understanding of entity characteristics. The combination of both approaches provides complementary benefits. Unlike existing approaches, HCAE computes entity-specific representations by weighting attribute information and performing embedding propagation based on high-order structural relationships. Specifically, HCAE elaborates on two improvement strategies. Firstly, recursive embedding propagation of relational quaternions using a GCN-based architecture aims at the real-time updating of entity embedding representations. Using a recursive embedding mechanism enables HCAE to learn high-order connectivity between entities with linear time complexity. Secondly, the automatic learning of the importance of different attributes to entity representation through the multi-attention mechanism, which adequately fuses structural and attribute information to enhance the ability to model entities from multiple perspectives. The main contributions of this work are as follows:  
* We emphasize the importance of attribute information and high-order connectivity in temporal knowledge graph completion, highlighting the complementary benefits of their combination.