# A Brief Survey on Deep Learning-Based Temporal Knowledge Graph Completion
## 3 Deep Learning-Based TKGC Methods
### GNN-Based Methods  
A graph neural network (GNN) [60] is an effective model that operates directly on graph-structured data, such as social networks [61] and road networks [62]. It follows a recursive neighborhood aggregation (or message passing) scheme, where the feature vector of a node (i.e., entity) is computed by recursively aggregating and transforming embeddings of its neighboring nodes. Formally, the computation of the feature vector of each node can be described as:  
\[\begin{split}& m_{v}^{(k)}=AGGREGATE^{(k)}(\{h_{u}^{(k-1)}:u\in N(v)\}), \\ & h_{v}^{(k)}=UPDATE^{(k)}(h_{v}^{(k-1)},m_{v}^{(k)}),\end{split} \tag{6}\]  
where \(m_{v}^{(k)}\) and \(h_{v}^{(k)}\) stand for the message vector and the feature vector of node \(v\) at the \(k\)-th layer, respectively. \(AGGREGATE()\) and \(UPDATE()\) are the aggregation function (e.g., mean, average, and max pooling) and the update function (e.g., linear-layer combination) [63], respectively.  
TGAP [37] views timestamps as properties of relations between entities and has an encoder-decoder architecture. In the encoder, a temporal GNN is introduced to aggregate query-related (a query is a incomplete quadruple) information from the local neighborhood of each entity, focusing on encoding the temporal displacement between the timestamp of the input query and each relation being encoded. In addition, a decoder based on attention propagation is proposed. Different from the score function decoder, the attention propagation decoder propagates attention through existing edges (i.e., relations) in the graph and determines the plausibility of facts based on the attention values. It naturally allows multi-hop reasoning, and the inferred attention distribution provides better interpretability.  
[PERSON] et al. [38] propose a semantic-driven, time-aware relational GNN model, named STRGNN, for the TKGC task, which consists of a semantic-enhanced encoder and a convolution-based decoder. In the encoder, it first abstracts a subgraph for the givensubject entity \(s\) (given an incomplete quadruple \((s,r,7,t)\) as an example) according to both its temporal neighborhoods and semantically similar neighborhoods. Then, it generates time-aware representation vectors for the temporal neighbors and performs aggregation. In the decoder, after updating the time-aware representation of the subject entity \(s\) at timestamp \(t\), a convolution-based decoder is introduced to calculate the score of each candidate object entity.  
HyGNet [39] exploits hyperbolic geometry to model temporal knowledge graphs, which comprises two key components: the Hyperbolic Gated Graph Neural Network (HGGNN) and the Hyperbolic Convolutional Neural Network (HCNN). HGGNN aggregates neighborhood information in hyperbolic space, aiming to capture the contextual information and dependencies between entities. HCNN interacts with embeddings in hyperbolic space to model the complex interactions among entities, relations, and timestamps. Finally, a distance-based score function is introduced to measure the plausibility of facts.  
Methods in this category use GNN to model the graph structure in TKGs, assuming that similar entities have similar graph structures. However, relying solely on structural information limits the completion performance. Therefore, methods in this category usually combine with other mechanisms to model information other than structural information in TKGs, such as relations, entity descriptions, and attributes, etc., for TKGC.