# Cross-Modal Fake News Detection Method Based on Multi-Level Fusion Without Evidence
## 3 Methods
### Feature Fusion  
In order to realize the interactive fusion between aligned text features \(m^{t}\) and aligned image features \(m^{v}\), this paper designs a cross-modal feature fusion network based on bidirectional multi-head cross-attention. Its core is to capture cross-modal semantic associations through text-image and image-text bidirectional interactions, and eventually fused to generate a unified joint representation. The structure of this fusion network is shown in Figure 2, which consists of two parallel Multi-head Cross Attention Networks.  
The principle formula of the single-head attention mechanism is shown in Equation (13).  
\[\textbf{{head}}=Attention\ (\textbf{{Q}},\textbf{{K}},\textbf{{V}})=Softmax\left( \frac{\textbf{{Q}}\textbf{{K}}^{T}}{\sqrt{d_{k}}}\right)\textbf{{V}} \tag{13}\]  
where, \(\textbf{{Q}},\ \textbf{{K}}\) and \(\ \textbf{{V}}\) denote the input feature matrices, respectively. \(\sqrt{d_{k}}\) is the scaling factor, which is used to prevent the gradient from destabilizing due to overly large dot product results for the matrices.  
The multi-head attention mechanism segments features into several \"heads\". Each \"head\" can independently learn different semantic associations between text and image features. The computation of each attention head is shown in Equation (14).  
\[\textbf{{head}}_{i}=Attention\left(Q\textbf{{W}}_{i}^{\textbf{{Q}}},K\textbf{{ W}}_{i}^{\textbf{{K}}},V\textbf{{W}}_{i}^{\textbf{{V}}}\right) \tag{14}\]  
where, \(i\) indicates the \(i\)-th head of the attention mechanism. \(\textbf{{W}}_{i}^{\textbf{{Q}}},\ \textbf{{W}}_{i}^{\textbf{{K}}}\) and \(\textbf{{W}}_{i}^{\textbf{{V}}}\) are trainable weight matrices used to transform the input features into query, key and value vector representations, respectively.  
When all the \"heads\" have been calculated, the results are spliced. The output formula for multi-head attention is shown in Equation (15).  
\[MultiHeadAttention(Q,K,V)=Concat(\textbf{{head}}_{1},\textbf{{head}}_{2},\ldots, \textbf{{head}}_{h})\textbf{{W}}^{\textbf{{O}}} \tag{15}\]  
where, \(h\) is the number of attention heads and \(\textbf{{W}}^{\textbf{{O}}}\) is the trainable weight matrix.  
Based on the above computational process, in the feature fusion network, the first attention network takes the aligned text feature \(m^{t}\) as the query vector \(Q\) and the aligned image feature \(m^{v}\) as both the key vector \(K\) and the value vector \(V\). The text-to-image attention \(O_{txt-to-img}\) is computed as shown in Equation (16). Conversely, the second  
Figure 2: Schematic diagram of a two-way multi-head cross-attention fusion network.  
attention network takes \(m^{v}\) as \(Q\) and \(m^{t}\) as both \(K\) and \(V\). The image-to-text attention is computed as shown in Equation (17).  
\[\mathbf{O_{txt-to-img}}=MultiHeadAttention\big{(}m^{t},\ m^{v},\ m^{v}\big{)} \tag{16}\]  
\[\mathbf{O_{img-to-txt}}=MultiHeadAttention\big{(}m^{v},\ m^{t},\ m^{t}\big{)} \tag{17}\]  
Next, the two interaction results, \(O_{txt-to-img}\) and \(O_{img-to-txt}\), are spliced along the first dimension. The spliced features are then subjected to linear transformation, batch normalization and ReLu activation. Finally, the primary fusion feature \(m^{final}\) is obtained, as shown in Equations (18) and (19).  
\[C=\mathbf{O_{txt-to-img}}\oplus\mathbf{O_{img-to-txt}} \tag{18}\]  
\[m^{final}\ =ReLu\big{(}BN(C\mathbf{W}+b)\big{)} \tag{19}\]  
where, \(\oplus\) denotes the splicing operation, \(\mathbf{W}\) is the weight matrix of the linear layer, \(b\) is the bias vector of the linear layer, \(BN\) is the batch normalization layer, and \(ReLu\) is the activation function.