## 3 Method Design
### Dependency Information Fusion Attention Graph Convolutional Network
#### 3.2.3 Graph Convolution Layer  
Graph Convolutional Network (GCN) is a widely used architecture for encoding information in a graph. It convolves the features of neighboring nodes and also propagates the information of a node to the nearest neighboring node [21]. By overlaying GCN layers, GCN can extract the features of each node. Generally, the graph in the standard GCN model is constructed from word dependency and represented by the adjacency matrix \(\text{A}=(a_{i,j})_{n,n}\), with \(a_{i,j}=1\) when \(i=j\) or when there is an edge connection between two words \(x_{i}\) and \(x_{j}\), otherwise \(a_{i,j}=0\). Based on the adjacency matrix \(\text{A}\), for each word \(x_{i}\in X\), the first GCN layer aggregates the information carried by its contextual word in the sentence and computes the output representation of \(x_{i}\) by computing the output representation of \(h_{i}^{(l)}\) in the following way:  
\[h_{i}^{(l)}=\sigma(\sum_{j=1}^{n}a_{i,j}(W^{(l)}\cdot h_{j}^{(l-1)}+b^{(l)})) \tag{2}\]  
where \(h_{j}^{(l-1)}\) is the output of \(x_{j}\) of the GCN model at layer \((l-1)\), \(W^{(l)}\) and \(b^{(l)}\) are the trainable weight matrix and bias of the GCN at layer \(l\), respectively, and \(\sigma\) is the ReLU activation function. In Equation (2), the dependency connections between words are treated equally as \(a_{i,j}\) either 1 or 0. Therefore, the traditional GCN model cannot distinguish the importance of different connections. To solve this problem, we propose a graph convolutional network incorporating attention mechanism to calculate the weights of different dependency connections, which enables the model to distinguish important information and reduce the impact of distractive information. In order to calculate the weights, we need to use the dependency types between words in the dependency syntax tree. Specifically, we first construct dependency type matrix \(\text{D}=(d_{i,j})_{n\equiv n}\) to represent the dependency types in the dependency tree \(D_{x}\). Details of which are shown in Figure 6, where \(d_{i,j}\) are the dependency types of the directed dependency connections between \(x_{i}\) and \(x_{j}\) (e.g., \(nsubj\)). Next, each dependency type \(d_{i,j}\) is mapped to its embedding vector \(u_{i,j}^{d}\). At the \(l\)th GCN layer, the weights \(k_{i,j}^{(l)}\) of the dependency connections between \(x_{i}\) and \(x_{j}\) are computed:  
\[k_{ij}^{(l)}=\frac{a_{i,j}\cdot\exp(v_{i}^{(l)}\cdot v_{j}^{(l)})}{\sum_{j=1}^ {n}a_{i,j}\cdot\exp(v_{i}^{(l)}\cdot v_{j}^{(l)})} \tag{3}\]  
where \(a_{i,j}\in A\), \(v_{i  
The computation is obtained, which represents the output of the previous layer of GCN and the dependency type embedding vector for concatenating to incorporate dependency information into the model. After that, this paper applies weights \(k_{i,j}^{(l)}\) to the dependency connections between \(x_{i}\) and \(x_{j}\) to obtain the output representation of \(x_{i}\) as follows:  
\[h_{i}^{(l)}=\sigma(\sum_{j=1}^{n}k_{i,j}^{(l)}(W^{(l)}\cdot H_{j}^{(l-1)}+b^{(l )})) \tag{6}\]  
where \(\sigma\), \(W^{(l)}\) and \(b^{(l)}\) have the same meaning in Equation (2). \[H_{j}^{(l-1)}=h_{j}^{(l-1)}+W_{D}^{(l)}\cdot t_{i,j}^{d} \tag{7}\]  
\(W_{D}^{(l)}\) maps the dependency type embedding vector \(u_{i,j}^{d}\) into the same dimension as the \(h_{j}^{(l-1)}\). The original GCN was designed for undirected graphs. In this paper, we start from the dependency syntax tree, and in order to take into account the directedness of the dependency tree, this paper uses a bidirectional GCN model incorporating the attention mechanism to extract its structural features on this basis.