## 3 Proposed Model
### Complex Question Decomposition
#### 3.2.2 Dependency Encoder  
The second part is the word dependency encoder. In contrast to the semantic encoder which needs to encode the word context representation vector, the dependency encoder needs to extract the dependency relations between words. Dependency parsing is a method of representing sentence structure based on word relations, which can connect the relations of distant constituents, and this type of relation across the order of words can reveal the dependency relations between words. The dependency-directed graph is commonly used to describe dependence relations, and the distance between nodes in the graph can reflect the strength of the dependency relations, which is what the dependency encoder needs to extract. Based on the dependency directed graph, the encoder generates \(\mathbf{W}_{dep}\in\mathbb{R}^{n^{\prime}n}\) reflecting the strength of the dependency relation between words. Figure 3 shows an example of producing \(\mathbf{W}_{dep}\) from the dependency graph, and the generation of \(\mathbf{W}_{dep}\) follows the rules stated below. Figure 3: Dependency matrix generation example, where \(\alpha=0.8\) and \(\varepsilon=0.3\). For the sentence “Which country is [PERSON] from”, there is a weak dependency between “is” and “[PERSON]” and a strong dependency between “is” and “from”. After generating the dependency matrix, we need to select the vectors corresponding to this topic entity, normalize the vectors by rows, and then average them by columns. 1. The \(d_{i,j}\) in the dependency matrix \(\mathbf{W}_{dep}\) represents how strongly or weakly the \(j\)th word has an impact on the \(i\)th word in the dependency relation. 2. When the \(i\)th word travels through the relation only once to reach the \(j\)th word, it indicates that they have a strong dependency such that \(d_{i,j}=1\). 3. When word \(w_{i}\) takes two or more hops to reach word \(w_{j}\), this indicates that they have weak dependency. At this point, \(d_{i,j}\) will decay according to the shortest path between \(w_{i}\) and \(w_{j}\) based on the distance (number of hops), that is, \(d_{i,j}=\alpha d_{i,j-1}\), where \(\alpha\) is the decay coefficient and \(w_{j-1}\) is the nearest word to \(w_{j}\) on the shortest path between \(w_{i}\) and word \(w_{j}\). 4. When \(w_{i}\) and \(w_{j}\) are not reachable, define \(d_{i,j}=\varepsilon\) and \(\varepsilon\) denotes the minimum dependency. Following the generation of \(\mathbf{W}_{dep}\), the vector corresponding to the topic entity is chosen, and the vector is normalized by row first and then averaged by column. The goal is to create the weight vector for the topic entity. The model employs the attention mechanism to merge the dependency information into the semantic information after the two encoders individually extract the semantic and dependency information. This procedure is described in Equation (6):  
\[\mathbf{t}_{i}=a_{i}\mathbf{e}_{i}^{FFN} \tag{6}\]  
where \(\mathbf{t}_{i}\) is the vector of \(w_{i}\) after information fusion, \(a_{i}\) is \(w_{i}\)'s weight information. \(\mathbf{T}=[\mathbf{t}_{1},\mathbf{t}_{2},\cdots,\mathbf{t}_{n}]\) is then passed into the sequence tagger for question tagging, which first reduces \(\mathbf{T}\in\mathbb{R}^{l^{\prime}n}\) to \(\mathbf{T}^{\prime}\in\mathbb{R}^{l^{\prime}2}\) before determining its probability on 0 or 1, where 1 denotes the word in the decomposed simple question and 0 indicates the word is not part of the simple question. Equation (7) shows the process of obtaining \(\mathbf{T}^{\prime}\):  
\[\mathbf{T}^{\prime}=\mathbf{T}\mathbf{W}_{F} \tag{7}\]  
where \(l\) is the length of the word vector, \(\mathbf{W}_{F}\in\mathbb{R}^{n^{\prime}m}\) represents the trainable matrix, and \(m\) represents the number of classification. Here \(m=2\),which means it is a binary classification problem. For the complex question decomposition task, we model it as a sequence tagging task and use cross entropy as the loss function.