# A Deep Fusion Matching Network Semantic Reasoning Model
## 3 Methods
### Design of Reasoning Model Based on Deep Fusion Matching Network
#### 3.2.3 Syntactic Structure Modeling Based on d-TBCNN  
The semantic fusion depth matching network designed in this paper uses a dependency tree convolution network (d-TBCNN) to collect sentence syntactic structure reasoning information and improve inference information.  
As shown in Figure 3, the dependency convolution network will perform a convolution operation on each subtree according to the result of the dependency analysis tree of the sentence, extract the syntactic structure features of the subtree, and then splice all the syntactic structure features to form the syntactic structure inference information of the sentence. The specific calculation steps are as follows:  
Figure 3: Schematic diagram of dependency convolution network.  
1. Firstly, the natural language parser [24] proposed by Stanford University is used to transform sentences into a dependency syntax tree. Taking the premise sentence as an example, each node in the syntax tree corresponds to a word in the sentence. The arc between nodes indicates that the node (child node) and node (parent node) have a dependency relationship, and the arc is marked with the syntax relationship between the two nodes [25]. Because there are too many dependencies between words, some are meaningless for inferring sentence structure information. Therefore, referring to the work of [PERSON] [26], the dependency convolution layer only retains 34 grammatical relationships that are frequently used and are more important. Some of the dependencies are shown in Table 3.
2. (Then, the syntactic structure features corresponding to the subtree are extracted along with the dependency subtree. The feature extractor adopts a double-layer convolution layer [27]. Suppose that the child nodes connected to the parent node \(n_{p_{d}}\) are \(n_{c_{i}}(i=1,2,\ldots,m_{c})\), in which \(m_{c}\) represents the total number of child nodes. For each subtree \(y_{c}\), the extracted local sentence structure features are as follows: \[y_{p_{i}}^{c}=f(W_{p_{d}}^{d}.p_{d}+\sum_{j=1}^{n}W_{r[c_{j}]}^{d}.c_{j}+b^{d})\] (19)  
Among them, the structural feature \(y_{c}\in R^{m_{c}}\), \(p_{d}\) is the word embedding vector corresponding to the parent node, and the word embedding vector corresponding to the \(j\)-th child node is \(c_{j}\). The word vector representations in the dependency tree are obtained by pretraining in the coding layer. \(W_{p}^{d}\in R^{m_{c}\times n_{e}}\) is the weight corresponding to the node, the weight assigned according to the dependency type between words is \(W_{r[c_{i}]}^{d}\in R^{m_{c}\times n_{e}}\), \(b^{d}\in R^{m_{c}}\) is the offset vector, in which \(r[c_{j}]\) represents the dependency relationship between nodes \(p\) and \(c_{j}\).
3. By pooling the structural features of each subtree in the sentence \(p\), the syntactic structure features of the sentence \(p\) are shown in Formula (20), and the syntactic structure features \(u_{q}\) of the sentence \(q\) are shown in Formula (21). \[u_{p}=(y_{p_{1}}^{c},y_{p_{i}}^{c},\ldots,y_{p_{m}})\] (20) \[u_{q}=(y_{q_{1}}^{c},y_{q_{j}}^{c},\ldots,y_{q_{n}}^{c})\] (21)