## 3 Method
### AM-HDGAT for Text
#### 3.4.2 Hybrid-Dimensional Feature Extraction and Fusion  
As shown in Figure 2, a key innovation of our approach is the integration of complementary feature types through a mutual-attention mechanism, addressing the limitation of traditional methods that rely solely on semantic features. We extract two distinct categories of features for each document.  
**High-Dimensional Semantic Features (\(\mathbf{X_{h}}\)):** These features consist of the document vectors \(\mathbf{v}_{i}\) generated during graph construction, capturing deep semantic information:  
\[X_{h}=\{\mathbf{v}_{1},\mathbf{v}_{2},\ldots,\mathbf{v}_{N}\} \tag{10}\]  
**Low-Dimensional Statistical Features (\(\mathbf{X_{i}}\)):** These features complement semantic information with document-level statistics and metadata, including textual statistics such as vocabulary richness, average sentence length, readability indices (such as Flesch-Kincaid score), specific keyword frequencies, and capitalization ratios. When available, metadata  
Figure 2: AM-HDGAT architecture.  
features such as author information, publication channels, document length, and temporal information are also incorporated. These features form low-dimensional feature vectors \(\mathbf{s}_{i}\):  
\[X_{l}=\{\mathbf{s}_{1},\mathbf{s}_{2},\ldots,\mathbf{s}_{N}\} \tag{11}\]  
**Mutual-Attention Fusion:** We employ a mutual-attention mechanism to intelligently combine high-dimensional semantic features and low-dimensional statistical features. This mechanism allows the two feature types to query and complement each other, resulting in a unified and information-rich document representation \(Z\). The mutual-attention weights are computed as follows:  
\[\alpha_{h\to l}=\text{softmax}(X_{h}\mathbf{W}_{hl}X_{l}^{T}) \tag{12}\]  
\[\alpha_{l\to h}=\text{softmax}(X_{l}\mathbf{W}_{lh}X_{h}^{T}) \tag{13}\]  
where \(\mathbf{W}_{hl}\) and \(\mathbf{W}_{lh}\) are learnable transformation matrices. The fused representation is obtained through the following:  
\[Z=\text{Concat}(\alpha_{h\to l}X_{l},\alpha_{l\to h}X_{h})\mathbf{W}_{f} \tag{14}\]  
where \(\mathbf{W}_{f}\) is a projection matrix that maps the concatenated features to the desired dimensionality.  
**Module Interactions and Data Flow:** The fusion module serves as a critical bridge between feature extraction and subsequent processing stages. The data flow begins with the graph construction module providing document embeddings (\(X_{h}\)) and metadata (\(X_{l}\)) as inputs. These heterogeneous features are transformed through cross-dimensional attention mechanisms, where semantic features query statistical features and vice versa. The attention weights dynamically determine feature relevance, enabling adaptive information fusion. The resulting unified representation \(Z\) is then propagated to the graph attention network (GAT) module, where it serves as initial node features for neighborhood aggregation. Simultaneously, \(Z\) interfaces with the adversarial training module, where it becomes the primary target for perturbation generation during robust optimization.  
This bidirectional data flow ensures that (1) the fused representations incorporate both semantic and statistical characteristics before graph processing and (2) adversarial robustness is learned directly on the integrated feature space. The output \(Z\) thus forms the foundation for both structural processing in GAT and robustness optimization in adversarial training.