## 3 Methodology
### Multi-View Stance Detection
#### 3.3.1 GCN Approach  
The text view captures the semantic representation of a post-target pair via a pre-trained BERT model. Specifically, each post \(p_{i}\) and its corresponding target \(t_{j}\) are concatenated with special tokens [CLS] and [SEP] and then encoded using BERT. The graph view models stance-related relationships using HSN, and the initial node representation for post nodes, target nodes, and entity nodes is obtained using BERT embeddings. Since the text view and the graph view serve distinct tasks, we employ two separate BERT instances, denoted as BERT\({}_{1}\) and BERT\({}_{2}\), to optimize performance for each specific objective:  
\[\mathbf{h}_{ij}^{\text{Text}}=\text{BERT}_{1}(\text{[CLS]}\ p_{i}\ \text{[SEP]}\ t_{j}\ \text{[SEP]}), \tag{6}\]  
\[\mathbf{h}_{u}^{(0)}= \begin{cases}\text{BERT}_{2}(\text{desc}(u)),&\text{if }u\in \mathcal{E}\cup\mathcal{T}\\ \text{BERT}_{2}(u),&\text{if }u\in\mathcal{P}\end{cases}  \tag{7}\]  
Figure 3: The three-step process for constructing a heterogeneous stance network from tweets using LLMs. Step 1 extracts entities, Step 2 determines stance relations, and Step 3 enhances nodes with descriptions. For clarity, prompts are simplified, omitting certain details. Full prompts are in Appendix A.  
where \(\mathbf{h}_{ij}^{\text{Text}}\in\mathbb{R}^{d}\) denotes the feature embedding of the post-target pair, and \(\mathbf{h}_{u}^{(0)}\in\mathbb{R}^{d}\) denotes the initial graph representation of node \(u\). Additionally, for nodes that lack textual descriptions, we use random initialization for their initial embeddings. To effectively propagate relational information, we employ relational graph convolutional network (RGCN) layers [37], updating node embeddings based on their neighbors:  
\[\mathbf{h}_{u}^{(l+1)}=\sigma\left(\sum_{s\in\mathcal{S}}\sum_{v\in\mathcal{N}_{ i}(u)}\frac{1}{c_{u,s}}\mathbf{W}_{r}^{(l)}\mathbf{h}_{v}^{(l)}+\mathbf{W}_{0}^{(l)}\mathbf{h}_{u}^{( l)}\right), \tag{8}\]  
where \(\mathbf{h}_{u}^{(l+1)}\in\mathbb{R}^{d}\) is the updated feature representation of node \(u\) at layer \(l+1\). Here, \(\mathcal{N}_{s}(u)\) represents the neighbors of node \(u\) connected via relation type \(s\), and \(c_{u,s}\) is a normalization factor. \(\mathbf{W}_{r}^{(l)}\) and \(\mathbf{W}_{0}^{(l)}\) are learnable weight matrices for the neighbor nodes and the self-connection of the node, respectively. \(\sigma\) is a non-linear activation function (e.g., ReLU [38]). We denote the final representation of node \(u\) as \(h_{u}^{\text{Graph}}\). To integrate both text-based and graph-based features, we begin by concatenating the graph representations of the post \(p_{i}\) and the target \(t_{j}\). This combined representation is then passed through a fully connected layer to generate a shared feature representation. Specifically, this process can be described by the following equation:  
\[\mathbf{h}_{ij}^{\text{Graph}}=\mathbf{W}_{1}\cdot\text{concat}(\mathbf{h}_{p_{i}}^{\text {Graph}},\mathbf{h}_{t_{j}}^{\text{Graph}})+\mathbf{b}_{1} \tag{9}\]  
where \(\mathbf{h}_{ij}^{\text{Graph}}\in\mathbb{R}^{d}\) is the resulting graph-based feature vector, while \(\mathbf{W}_{1}\) and \(\mathbf{b}_{1}\) are learnable weight and bias vectors, respectively. This operation serves to fuse the graph-based information from both the post and the target into a unified feature representation. To further refine the interaction between the textual and graph-based features and to capture potential dependencies between them, we employ a cross-attention mechanism. This mechanism allows the model to focus on the most relevant aspects of the textual and graph representations during fusion. The interaction is defined by  
\[\mathbf{h}_{ij}=\text{CrossAttention}(Q=\mathbf{h}_{ij}^{\text{Text}},K=V=\mathbf{h}_{ij}^ {\text{Graph}}), \tag{10}\]  
where \(\mathbf{h}_{ij}\in\mathbb{R}^{d}\) is the resulting fused feature vector, incorporating the most important interactions between the text and graph features.