## 3 Materials and Methods
### Proposed Method
#### 3.3.3 Time-Series and Space Fusion Module  
The time-series and space fusion module is designed to effectively integrate temporal features (e.g., stock prices and text sequences) with spatial features (e.g., images), leveraging  
Figure 2: Sliding-window attention mechanism. a combination of local perception, sliding-window attention, and a feed-forward network (FFN) to achieve deep multimodal feature fusion, as shown in Figure 3.  
The module, as illustrated in the figure, consists of three main components: sliding-window attention, a local perception unit, and a feed-forward network. In the input stage, assume the temporal features are represented as \(\mathbf{F}_{i}\in\mathbb{R}^{N_{t}\times C_{t}}\), and the spatial features are represented as \(\mathbf{M}_{i}\in\mathbb{R}^{H_{s}\times W_{s}\times C_{s}}\), where \(N_{t}\) and \(C_{t}\) denote the length and number of channels of the temporal features, respectively, and \(H_{s}\), \(W_{s}\), and \(C_{s}\) represent the height, width, and number of channels of the spatial features. To enable interaction between these features, a channel alignment operation is first applied to unify the channel dimensions to \(d\):  
\[\mathbf{F}_{i}^{\prime}=\mathbf{W}_{t}\mathbf{F}_{i},\quad\mathbf{M}_{i}^{ \prime}=\mathbf{W}_{s}\mathbf{M}_{i}, \tag{29}\]  
where \(\mathbf{W}_{t}\in\mathbb{R}^{C_{t}\times d}\) and \(\mathbf{W}_{s}\in\mathbb{R}^{C_{s}\times d}\) are linear transformation matrices. The sliding-window attention mechanism serves as the core of this module and is used to capture the correlation between temporal and spatial features. Specifically, both \(\mathbf{F}_{i}^{\prime}\) and \(\mathbf{M}_{i}^{\prime}\) are first normalized using LayerNorm, followed by the projection of query (Q), key (K), and value (V) vectors:  
\[\mathbf{Q}_{t}=\mathbf{W}_{q}^{t}\mathbf{F}_{i}^{\prime},\quad\mathbf{K}_{s}= \mathbf{W}_{t}^{s}\mathbf{M}_{i}^{\prime},\quad\mathbf{V}_{s}=\mathbf{W}_{p}^ {s}\mathbf{M}_{i}^{\prime}, \tag{30}\]  
where \(\mathbf{W}_{q^{\prime}}^{t}\), \(\mathbf{W}_{k^{\prime}}^{s}\) and \(\mathbf{W}_{p}^{s}\in\mathbb{R}^{d\times d}\) are projection matrices. This mechanism explicitly models the relationships between temporal and spatial features, enabling effective capture of multimodal data interactions. In the local perception unit, the extracted features are further enhanced through depthwise separable convolution operations, which focus on local feature enhancement. Given the input features \(\mathbf{O}_{ts}\), a \(3\times 3\) depthwise separable convolution is applied to extract local features:  
\[\mathbf{L}=\text{Conv}_{3\times 3}(\mathbf{O}_{ts}), \tag{31}\]  
where this convolution operation efficiently captures local spatial information while maintaining computational efficiency. Finally, the fused features are transformed non-linearly using a feed-forward network. The FFN comprises two fully connected layers, where the first layer increases the feature dimension and the second layer reduces it back:  
\[\mathbf{F}_{\text{output}}=\text{ReLU}(\mathbf{W}_{1}\mathbf{L})\mathbf{W}_ {2}, \tag{32}\]  
where \(\mathbf{W}_{1}\in\mathbb{R}^{d\times 4d}\) and \(\mathbf{W}_{2}\in\mathbb{R}^{4d\times d}\) are the weight matrices. This design has several advantages. The sliding-window attention mechanism captures long-range dependencies between temporal and spatial features, while the local perception unit enhances the representation of local spatial details. The FFN further improves feature expressiveness, ensuring robust performance in complex tasks. In the context of this study, the fusion  
Figure 3: Time-series and space fusion module. module effectively integrates the characteristics of temporal and spatial data, allowing the model to capture both local and global information simultaneously. As a result, the module demonstrates superior accuracy and robustness in multimodal data processing tasks.