# Cross-Modal Fake News Detection Method Based on Multi-Level Fusion Without Evidence
## 3 Methods
### Secondary Fusion
#### 3.5.2 Ambiguity Score Acquisition Network  
In the above process, the attentional weights are computed to measure the importance of different modalities in the task at hand. These weights are able to adaptively adjust the contribution of each modality. However, this weighting method may pose the following issues. First, the model's learning results may lack intuitive explanations, making it difficult to understand why a certain modality is assigned a higher weight. Second, in some cases, there may be ambiguity in the information between different modalities. This may lead to an irrational allocation of attention weights. Therefore, this paper proposes a symmetric KL divergence-based ambiguity score acquisition network. This network generates KL ambiguity score to assist in adjusting the attentional weights. Specifically, the symmetric KL score between two modalities is calculated as a measure of the degree of ambiguity between them. If the KL score is large, the difference between the two modalities is significant, indicating high ambiguity. In this case, the model should rely more on cross-modal features, and the value of \(a_{f}\) should be increased. Conversely, the model can rely more on unimodal features, and the values of \(a_{t}\) and \(a_{v}\) should be increased. During model training, the differences in cross-modal distributions across single samples were quantified by the following steps. First, conditional distributions \(q_{\phi_{t}}\) and \(q_{\phi_{v}}\) of latent variables are generated by the text encoder and image encoder. As shown in Equations (27) and (28). \[q_{\phi_{t}}(z_{1}\ |m^{t})=\mathcal{N}\left(z_{1};\mu_{t},\sigma_{t}^{2}\right) \tag{27}\]  
\[q_{\phi_{v}}(z_{2}\ |m^{v})=\mathcal{N}\left(z_{2};\mu_{v},\sigma_{v}^{2}\right) \tag{28}\]  
where \(\mu_{t}\), \(\sigma_{t}\), and \(\mu_{v}\), \(\sigma_{v}\) are the mean and variance of the text and image distributions, respectively. Then, the latent variables \(z_{1}\) and \(z_{2}\) were sampled from the text and image distributions, respectively, using the Reparameterization Trick, as shown in Equations (29) and (30). \[z_{1}=\mu_{t}+\epsilon\ \odot\sigma_{t}\,\epsilon\sim\mathcal{N}(0,1) \tag{29}\]\[z_{2}=\mu_{v}+e^{\prime}\ \odot\sigma_{v}\,e^{\prime}\ \sim\mathcal{N}(0,1) \tag{30}\]  
Next, in order to measure the difference between the two modal distributions, this paper approximates the single-sample KL divergence by Monte Carlo sampling method. This avoids the direct computation of integrals and improves the training efficiency. Specifically, the KL divergence is obtained by following steps: First, samples are drawn from each of the two distributions. Then, the log probabilities of these samples are calculated in the other distribution. Finally, the KL divergence is computed by taking the expectation of the difference between these log probabilities. The two-way KL divergences, \(k_{i}^{t\to v}\) and \(k_{i}^{v\to t}\), are calculated as shown in Equations (31) and (32). \[k_{i}^{t\to v}\approx\ log\ q_{\phi_{t}}(z_{1})-log\ q_{\phi_{v}}(z_{1}) \tag{31}\]  
\[k_{i}^{v\to t}\ \approx\ log\ q_{\phi_{v}}(z_{2})-log\ q_{\phi_{t}}(z_{2}) \tag{32}\]  
Subsequently, \(k_{i}^{t\to v}\) and \(k_{i}^{v\to t}\) are averaged to obtain a combined ambiguity measure. This measure is then passed through the Sigmoid activation function to normalize it to the range (0,1), representing the degree of ambiguity. The resulting ambiguity score is shown in Equation (33). \[k_{i}=\textit{sigmoid}\left(\frac{k_{i}^{v\to t}+k_{i}^{t\to v}}{2} \right)\ \in[0,\ 1] \tag{33}\]  
We obtain the cross-modal ambiguity scores \(k=\{[1-k_{i},1-k_{i},k_{i}]\}\) by calculating the bidirectional KL divergence, where \(k_{i}\) indicates the degree of ambiguity between image and text modalities, with higher values indicating greater ambiguity. In order to make the attention weights \(a=\left[a_{t},\ a_{v},\ a_{f}\ \right]\) closer to the ambiguity scores \(k\), a loss function \(\mathcal{L}_{ak}\) is introduced here.