## 2 Previous Works  
Graph theory itself is said to have started when [PERSON] introduced it to one-stroke problems such as the Seven Bridges of Konigsberg. It is a field that is widely applied. A graph is a data structure represented by objects (nodes) and relationships (edges) between them. On the other hand, deep learning has mainly dealt with collections of individual data (vectors), data arranged in grids (images), and sequential data (text, voice). Therefore, it is a natural step to incorporate graph theory into DL and develop it. On the other hand, from the point of view of representation learning, nodes, edges, and subgraphs with low-dimensional vectors can be represented. In the area of graph analysis, traditional methods of machine learning rely on manually setting feature values, whereas graph-embedded methods can learn. DeepWalk, Skipgram model, node2 vec, LINE, and TADW are some examples [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. However, this approach also has its drawbacks: it is inefficient because parameters are not shared between nodes, and direct embedding lacks the ability to generalize. The matrix representation for treating graphs mathematically is as follows:  
1. Adjacency matrix \(A\) expresses whether there is a connection relationship between nodes. 2. The degree matrix \(D\) represents how many edges are connected to each node. The Laplacian matrix is a representation of these together: \(L=D-A\), as shown in Figure 1. A normalized Laplacian matrix is actually used. There are the following three types of networks:  
1. Graph Recurrent Networks (recurrent networks) In an early proposed model, information propagation is performed recursively using the same function. However, the low computational efficiency is considered a problem. 2. Graph Convolutional Networks (convolutional network, hereinafter referred to as GCN) GCN is a proposed model that is based on the mechanism of CNN, but parallel calculation is possible, so calculation efficiency is improved. Considering the type of convolution, these models can be divided into two types: the spectral method and spatial method. The former treats graphs as signal processing. The latter is more popular than the former because it is defined based on the relationships of the graph itself and is more intuitive than the former. 3. Graph Attention Networks (Attention-based networks) This model applies the mechanism of \"Attention\" to GNN. In the GCN model of (2), the node relationships are treated with the same importance, but by introducing \"Attention\", it is possible to assign importance scores to relationships, enabling more flexible judgment. Since GNN handles data composed of nodes and edges, it can be said that it is most suitable for processing objects that can be expressed in this format. For example, it is Thewidely applied in fields such as social network prediction, traffic/logistics prediction, recommendation systems, and compound/biomolecular analysis. Furthermore, even for data that cannot be expressed directly in graph form, such as document text, it is possible to use GNN by incorporating graphs of other areas (e.g., knowledge graphs) and applying them by assuming relationships. At the North American Chapter of the Association for Computational Linguistics (NAACL) international conference, many studies using GNN were presented. For example, some of the participants applied an utterance relation graph and an action graph to the abstract summarization of a conversation to reveal the structure of the conversation [19] or applied the GCN to sentiment analysis to reveal each aspect of the analyzed document. A model based on this GCN has been proposed [20]. Graph Neural Network processing is divided into three stages: aggregation of adjacent nodes (AGGREGATE), updating by aggregation of results (COMBINE), and aggregation of node features to obtain properties of the entire graph (READOUT).