# Beyond Classical AI: Detecting Fake News with Hybrid Quantum Neural Networks
## 3 Results
### Confusion Matrix Analysis  
The confusion matrices presented in Figure 5 offer a comparative visualization of the classification performance of both the HQDNN configurations, one using TF-IDF representations and the other enhanced with DistilBERT embeddings and a quantum layer.  
In the TF-IDF-based model (left matrix), the HQDNN successfully identifies a large portion of the positive class (i.e., fake news), with 661 true positives and only 53 false negatives, corresponding to a high recall score of 0.9258. However, the model also generates a significant number of false positives (477), meaning that a considerable number of true news items were misclassified as fake. This reflects a precision-recall trade-off, where the model prioritizes capturing all the fake news instances, even at the expense of mislabeling some true news.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Value** \\ \hline Accuracy & 0.5817 \\ Precision & 0.5808 \\ Recall & 0.9258 \\ F1 Score & 0.7138 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Test set results of HQDNN with TF-IDF model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Value** \\ \hline Accuracy & 0.5652 \\ Precision & 0.5780 \\ Recall & 0.9450 \\ F1 Score & 0.7176 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test set results of HQDNN with DistillBert model.  
In contrast, the DistilBERT with Quantum variant (right matrix) further improves the performance by reducing both types of error. Specifically, it lowers the number of false negatives to 40 and increases the number of true positives to 674, pushing the recall score to 0.944. While the number of false positives remains high (492), the slight improvement in precision and the consistently high recall value (F1 score: 0.7176) indicate a more stable and generalizable model behavior.  
This side-by-side comparison reaffirms the design choice of adopting a recall-oriented optimization strategy for both the configurations. Such a strategy is especially justified in domains like fake news detection, where the cost of missing a harmful instance is significantly higher than misclassifying a benign one. Overall, both the confusion matrices underscore the models' effectiveness in identifying the positive class, with the transformer-based variant demonstrating slightly enhanced sensitivity and robustness.  
To further evaluate the performance of the proposed HQDNN model, we present a Receiver Operating Characteristic (ROC) curve and a precision-recall (PR) curve based on its predictions with the test set. As shown in Figure 6, the ROC curve demonstrates a strong discriminative capability, with an Area Under the Curve (AUC) of 0.72, indicating that the model is generally able to distinguish between fake and real news effectively. Similarly, the precision-recall curve highlights the model's superior recall behavior, with a smooth trade-off curve and a relatively high area under the PR curve. These curves confirm the model's tendency to prioritize sensitivity over specificity, which is particularly valuable in critical fake news detection scenarios, where missing false information can be more harmful than occasionally flagging real content. Overall, the graphical evaluation complements the numerical results and supports the claim that HQDNN provides high-recall, robust detection in binary fake news classification.  
Figure 5: Comparison of confusion matrices for HQDNN model with TF-IDF (**left**) and DistilBERT (**right**) input representations.  
Figure 6: The ROC and precision–recall curves of the HQDNN model on the test set.