## 3 Results
\[Accuracy=\frac{true\,\,positive+true\,\,negative}{true\,\,positive+true\,\, negative+false\,\,positive+false\,\,negative} \tag{31}\]  
To address class imbalance and provide a more nuanced view of detection capability, recall (also known as sensitivity or _true positive_ rate) was utilized. Equation (32) defines recall as the proportion of actual positive cases correctly identified by the model. This metric is particularly important in intrusion detection scenarios, where false negatives (i.e., undetected attacks) can result in severe security breaches. High recall ensures that the model effectively identifies attack instances, which is critical in minimizing risk in IIoT and edge deployments. \[Recall=\frac{true\,\,positive}{true\,\,positive+false\,\,negative} \tag{32}\]  
We further evaluated the models using the area under the curve (_AUC_), as described in Equation (33). _AUC_ provides a comprehensive view of the model's discriminatory ability across all possible threshold settings. By integrating the receiver operating characteristic (_ROC_) curve over all classification thresholds, this metric captures the trade-off between _true positive_ and _false positive_ rates. _AUC_ is particularly valuable in binary and multiclass intrusion detection, as it is less affected by class distribution and reflects the model's robustness across different operating conditions. \[AUC=\int_{0}^{1}ROC(t)dt \tag{33}\]where \(ROC(t)\) is \(ROC\) curve at threshold \(t\). To analyze the training behavior and convergence characteristics of each model, we also computed the root mean square error (\(RMSE\)) during training epochs, as given in Equation (34). \(RMSE\) quantifies the deviation between predicted values and actual values in terms of their squared differences. In the context of our model, \(RMSE\) was applied to monitor the reconstruction quality of the \(AE\) and the output of the generator network. Lower \(RMSE\) indicates better convergence and learning stability, providing insight into whether the model is effectively minimizing reconstruction and adversarial loss over time. \[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}[y_{i}-\hat{y}_{i}]^{2}}, \tag{34}\]  
where \(y_{i}\) is the observed value and \(\hat{y}_{i}\) is the calculated value. We also examined the variance of results across multiple independent runs and the convergence behavior during training to evaluate the robustness and stability of each model. Variance reflects the degree of sensitivity a model has to changes in initialization, stochastic components (e.g., random sampling, noise vectors), or hyperparameter tuning. A lower variance across repeated executions indicates that the model's performance is stable and less prone to randomness, which is particularly important in security-critical applications where predictability and reproducibility are essential. Furthermore, the convergence trend, as monitored through metrics such as \(RMSE\) and loss curves over epochs, provides insight into the training dynamics. Smooth and rapid convergence suggests that the model is learning effectively and optimizing the objective functions efficiently. In contrast, oscillatory or plateaued convergence patterns can reveal issues such as vanishing gradients, adversarial instability, or suboptimal parameter initialization. In addition to the above metrics, we recorded the execution time of each model as a proxy for computational efficiency and measured the variance of performance across multiple experimental runs to evaluate consistency and generalizability. These supplementary criteria help assess not only the accuracy of predictions but also the practical feasibility and stability of each method when deployed in resource-constrained or real-time environments. Hyperparameter tuning plays a critical role in determining the final performance and stability of DI models, especially in complex hybrid architectures such as Transformer-GAN-AE.