## 3 Proposed Framework
### BiLSTM-Bgat-GCN Model  
Prior to integration into the graph convolutional neural network, the data traverse six distinct pathways. The initial two pathways remain as they were, one facilitating the generation of a new adjacency matrix \(R^{bh}\) via the biaffine attention mechanism. Another pathway utilizes the graph attention network to derive a new node feature table \(\hat{H}^{gat}\). Building on this, four additional pathways focus on linguistic features: syntactic dependency type, parts of speech combinations, syntactic tree-based distance, and positional relationships. Each of these pathways, respectively, results in four new adjacency matrices: \(R^{sdt}\), \(R^{psc}\), \(R^{tbd}\), and \(R^{rpd}\).  
The adjacency matrix \(R^{sdt}\), \(R^{psc}\), \(R^{tbd}\), and \(R^{rpd}\) obtained according to the four language features introduced above are, respectively, input into GCN to carry out repeated graph convolution operations. The new nodes represent \(H^{sdt}\), \(H^{psc}\), \(H^{tbd}\), and \(H^{rpd}\). Specific calculations are given in Equations (25)-(28):  
(1) Syntactic dependency types  
\[\hat{H}^{sdt}_{k}=\sigma(R^{sdt}_{:,:,k}HW_{k}+b_{k}) \tag{25}\]  
(2) Part-of-speech combination  
\[\hat{H}^{psc}_{k}=\sigma(R^{psc}_{:,:,k}HW_{k}+b_{k}) \tag{26}\]  
(3) Tree-based distance  
\[\hat{H}^{tbd}_{k}=\sigma(R^{tbd}_{:,:,k}HW_{k}+b_{k}) \tag{27}\](4) Relative position distance  
\[\hat{H}_{k}^{rpd}=\sigma(R_{:,:,k}^{rpd}HW_{k}+b_{k}) \tag{28}\]  
where \(R_{:,:,k}^{sdt}\in R^{n\times n}\), \(R_{:,:,k}^{psc}\in R^{n\times n}\), \(R_{:,:,k}^{tbd}\in R^{n\times n}\) and \(R_{:,:,k}^{rpd}\in R^{n\times n}\) said, respectively, according to the relationship between the first \(k\) type modeling of adjacency matrix; \(W_{k}\) and \(b_{k}\) are to learn the weights and bias; \(\sigma\) is the activation function. Then, the adjacency matrix modeled from all relationship types is aggregated to obtained through:  
\[\hat{H}^{sdt}=f(\hat{H}_{1}^{sdt},\hat{H}_{2}^{sdt},\cdots,\hat{H}_{m}^{sdt}) \tag{29}\]  
\[\hat{H}^{psc}=f(\hat{H}_{1}^{psc},\hat{H}_{2}^{psc},\cdots,\hat{H}_{m}^{sc}) \tag{30}\]  
\[\hat{H}^{tbd}=f(\hat{H}_{1}^{tbd},\hat{H}_{2}^{tbd},\cdots,\hat{H}_{m}^{tbd}) \tag{31}\]  
\[\hat{H}^{rpd}=f(\hat{H}_{1}^{rpd},\hat{H}_{2}^{rpd},\cdots,\hat{H}_{m}^{rpd}) \tag{32}\]  
where \(f\) represents the average pooling function.  
Similarly, input adjacency matrix \(R^{ba}\) from the BiLSTM-biaffine attention model into the graph convolutional neural network to obtain new node representation \(H^{ba}\) through:  
\[\hat{H}_{k}^{ba}=\sigma(R_{:,:,k}^{ba}HW_{k}+b_{k}) \tag{33}\]  
where \(R_{:,:,k}^{ba}\in R^{n\times n}\) are said to be according to the relationship between the first k type modeling by adjacency matrix; \(W_{k}\) and \(b_{k}\) are to learn the weights and bias; and \(\sigma\) is the activation function. Then, the adjacency matrix modeled by all relationship types is aggregated to obtain:  
\[\hat{H}^{ba}=f(\hat{H}_{1}^{ba},\hat{H}_{2}^{ba},\cdots,\hat{H}_{m}^{ba}) \tag{34}\]  
At the same time, input adjacency matrix \(R^{sdt}\) from BiLSTM-biaffine attention model into the graph convolutional neural network to obtain new node representation \(H^{sdt}\) through:  
\[\hat{H}_{k}^{sdt}=\sigma(R_{:,:,k}^{sdt}HW_{k}+b_{k}) \tag{35}\]  
\[\hat{H}^{sdt}=f(\hat{H}_{1}^{sdt},\hat{H}_{2}^{sdt},\cdots,\hat{H}_{m}^{sdt}) \tag{36}\]  
Finally, the final result is obtained through:  
\[H=f\Big{(}\hat{H}^{sdt},\hat{H}^{ba},\hat{H}^{sdt},\hat{H}^{psc},\hat{H}^{tbd },\hat{H}^{rpd}\Big{)} \tag{37}\]  
\[R=R^{ba}\oplus R^{sdt}\oplus R^{psc}\oplus R^{tbd}\oplus R^{rpd} \tag{38}\]  
where \(f\) represents the average pooling function.