# Analysis of Score-Level Fusion Rules for Deepfake Detection
## 5 Discussion and Conclusions  
In this paper, we investigated the effectiveness of score-level fusion in deepfake detection as an attempt to exploit the complementarity of six different state-of-the-art detectors. In particular, we explored various fusion methods, which can be roughly categorized into non-parametric fusion, fusion based on the weighted average and fusion based on classification models (Figure 2). Therefore, we compared a battery of fusion methods through a common experimental setup in intra-dataset and cross-dataset scenarios. This allowed us to study different application contexts: the intra-dataset scenario simulated a context in which the designer knows the characteristics of the data (the resolution, size and compression levels) and the possible manipulations in input to the system; the cross-dataset scenario simulated a more unfavorable application context in which the data characteristics and manipulations were unknown. In general, the obtained results confirmed our initial hypothesis that a suitable fusion method can help in improving the performance, and hence the robustness, with respect to a single deepfake detection classifier. This was possible since all the considered models were trained with the exact same samples from the FF++ dataset (except for ResNet, trained on ad hoc samples), allowing us to highlight the strengths of each fusion model. The most important considerations are those that help the designer during the system implementation phase. First, the difference in performance between non-parametric and \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Fusion Time (\(\mu\)s)**} \\ \hline
**Fusion Method** & **2 Models** & **3 Models** & **4 Models** & **5 Models** & **6 Models** \\ \hline Avg & 7.872 & 7.891 & 7.825 & 7.853 & 8.132 \\ Bayes & 13.149 & 13.231 & 13.617 & 13.960 & 14.649 \\ Prod & 4.701 & 4.701 & 4.711 & 4.691 & 4.719 \\ Max & 4.280 & 4.290 & 4.306 & 4.576 & 4.315 \\ Min & 4.344 & 4.333 & 4.319 & 4.341 & 4.352 \\ Accuracy-based Avg & 1.823 & 2.259 & 2.672 & 3.117 & 3.622 \\ Correlation-based Avg & 1.693 & 2.056 & 2.434 & 2.810 & 3.270 \\ MI-based Avg & 1.828 & 2.255 & 2.672 & 3.103 & 3.646 \\ Complement NB & **0.528** & **0.524** & **0.525** & **0.517** & **0.534** \\ MLP & 1.180 & 1.206 & 1.221 & 1.251 & 1.292 \\ Perceptron & 0.613 & 0.625 & 0.640 & 0.658 & 0.646 \\ SVM & 204.975 & 190.043 & 172.928 & 175.817 & 127.683 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average inference time of the fusion methods on a single sample for two to six fused modules (the lowest values for each number of fused models are reported in bold). Figure 8: Inference time of fusion methods for various numbers of fused models. parametric fusion rules suggests that the approaches related to the latter are inherently more robust to the influence of networks that do not perform well on the data on which these fusion methods are fitted, as with ResNet in our case (e.g., Figures 9b and 10a). As a result, based on the analyzed sample, a detector might be weighted by parametric techniques more heavily than another, regardless of overall accuracy, as illustrated in Figure 10b, where the ResNet network, while not the best performing, guides the decision of most of the machine-learning models, such as the Complement NB. This evidence is crucial in designing an ensemble of deepfake detectors since we cannot know in advance which types of detectors could be more suitable for a specific type of fake in a real-world scenario. In contrast, the parametric rules appear to be more influenced by the presence of a detection system showing relatively poor performance. In particular, in contrast with the other models, the ResNet employed a different training technique, which could be the cause of the lowest performance. Thus, the evaluation of this model should always be considered to be related to a cross-dataset scenario.