# Integration of Multi-Branch GCNs Enhancing Aspect Sentiment Triplet Extraction
## 3 Framework of MBGCN
### Multi-Branch GCN  
Except for encoding text as semantic feature maps, it also can be represented in the linguistic feature types. Furthermore, the most widely utilized type is the syntax dependency graph, where the feature is formed in a graph \(G=(V,E)\). \(V\) is the vertex (i.e., node or word), and \(E\) is the edge (i.e., dependency or syntactic relation) between two nodes. Generally, we usually denote this kind of relation through a matrix, namely adjacent matrix \(A\). \(A_{\tau,\xi}=1\) if the relation between \(w_{\xi}\) and \(w_{\tau}\) exists, and \(A_{\tau,\xi}=0\) otherwise. In addition, in this paper, we also introduce three other types of linguistic features for each word pair to enhance the contextual representation of the sentence, which are the part-of-speech combination, tree-based distance, and relative position distance (Figure 4). Beforefeeding them into the GCN, they are all encoded in the fashion of adjacency matrices. Then, these four types of linguistic features are integrated with semantic features, respectively. For instance, we apply the GCN to integrate the \(R^{ba}\) with \(R^{sdt}\) encoded from syntactic dependency type tensor \(E_{sdt}\), and the process is depicted as follows:  
\[R^{sdt}_{\tau,\xi}=\sigma(E_{sdt}), \tag{13}\]  
\[H^{f1}_{\tau,\xi}=f((R^{ba}_{\tau,\xi}\oplus R^{sdt}_{\tau,\xi})H^{Bert}_{\tau, \xi}), \tag{14}\]  
where \(H^{Bert}\) is obtained from the original contextual representation \(h^{l}\) through a dense layer and a \(ReLU\) activation layer; \(\sigma\) is the function \(softmax\). Furthermore, \(f(\cdot)\) is an average pooling function applied on the node hidden representations of all channels. To make the extracted relations more accurate, a refining strategy is employed to enhance the relations among words, which can be described as  
\[R^{F}_{\tau,\xi}=h^{l}_{\tau,\xi}\oplus E^{sdt}_{\tau,\xi}, \tag{15}\]  
\[\hat{F}^{G(\tau,\xi)}_{ba+sdt}=R^{F}_{\tau,\xi}\oplus R^{F}_{\xi,\xi}\oplus R^{ F}_{\tau,\tau}\oplus H^{f1}_{\tau}\oplus H^{f1}_{\tau}, \tag{16}\]  
\[F^{G(\tau,\xi)}_{ba+sdt}=\sigma(LN(\hat{F}^{G(\tau,\xi)}_{ba+sdt})), \tag{17}\]  
we use \(\oplus\) to concatenate contextual representation \(h^{l}_{\tau,\xi}\) and syntactic dependency type tensor \(E^{sdt}_{\tau,\xi}\). Furthermore, in Equation (16), \(R^{F}_{\tau,\tau}\) and \(R^{F}_{\xi,\xi}\) are the main diagonal and vice diagonal, which are used to refine the representation \(\hat{F}^{G(\tau,\xi)}_{ba+sdt}\). Finally, with the operations of a linear layer and a softmax layer, the distribution of probabilities on ten defined relations between \(\tau\) and \(\xi\) is obtained, which is denoted as \(F^{G(\tau,\xi)}_{ba+sdt}\).  
Similarly, we integrate \(R^{ba}_{\tau,\xi}\) with \(E^{psc}_{\tau,\xi}\), \(E^{tbd}_{\tau,\xi}\), and \(E^{rpd}_{\tau,\xi}\) via different branches of the GCN to obtain the refined feature representations \(F^{G(\tau,\xi)}_{ba+psc}\), \(F^{G(\tau,\xi)}_{ba+tbd}\) and \(F^{G(\tau,\xi)}_{ba+tpd}\), respectively. Through the operations described in this part, we enhance the contextual feature \(R^{ba}_{\tau,\xi}\) with four types linguistic features, respectively.