## 6 Results and Discussion
Our results indicate that the use of the ENN algorithm in our framework significantly improves training time, a finding consistent with previous studies [27; 28; 29]. However, reducing the size of the training dataset does slightly impact the accuracy of our deep learning models. This is noteworthy because some Instance Reduction Techniques that remove noisy and borderline instances have been found to improve classification accuracy [27; 28]. The divergence in outcomes might be attributable to our use of subsets of encoded data, while previous studies used the original, unencoded data. Additionally, it is worth noting that those studies focused on simpler neural network architectures, making their findings less directly applicable to deep learning models that typically require large datasets for effective learning. Nonetheless, this limitation may be less serious than it appears, as collaborative learning often involves many clients--significantly more than the six we used in our experiments--thus making ample training data available. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**CNN**} & \multicolumn{4}{c}{**MLP**} \\ \cline{2-13}
**Dataset** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Validating**} & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Validating**} & \multicolumn{2}{c}{**Test**} \\ \cline{2-13}  & **Accuracy** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Loss** & **F-Score** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Time** & **Accuracy** & **Loss** & **F-Score** & **Time** \\ \hline
**MNIST** & _97.56\%_ & 99.39 s & _97.69\%_ & 5.30 s & 96\% & 0.175 & 96.43\% & 7.24 s & 99.44\% & 87.87\% & 99.44\% & 3.19 s & 97\% & 0.108 & 97.40\% & 3.99 s \\
**MNIST** & 96.41\% & 68.51 s & 96.68\% & 4.40 s & 84\% & 0.637 & 84.17\% & 7.14 s & 97.48\% & 57.85\% & 97.29\% & 2.85 s & 85\% & 0.626 & 85.14\% & 4.51 s \\
**EMNIST-Letters** & 73.94\% & 35.24 s & 77.87\% & 4.15 s & 82\% & 0.673 & 82.91\% & 9.80 s & 89.56\% & 9.18 s & 91.27\% & 1.00 s & 85\% & 0.530 & 85.60\% & 2.17 s \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The performance of CNN and MLP on MNIST, Fashion-MNIST, and EMNIST-Letters datasets in the privacy-preserving collaborative models experiments. Comparing our work with other Privacy-Preserving Deep Learning (PPDL) frameworks in terms of performance presents a challenge. Various studies may be specific to a particular application or domain, diverge in their implementation of privacy-preserving technology, differ in their learning framework configurations, utilize distinct deep learning architectures, or employ different datasets and parameters. Additionally, some studies assess the performance of different approaches by citing results from relevant papers, rather  
Figure 6: Comparative training times. Figure 7: Model reduction percentage. than re-executing the code on the same datasets [9]. However, we opted not to use this method for comparing the performance of privacy-preserving frameworks. In general, the existing Privacy-Preserving Deep Learning (PPDL) frameworks suffer from many performance issues like an unacceptable utility-privacy trade-off resulting from the practical implementations of differential privacy techniques [42]. Also, significant computation cost and communication overhead result from using many of the MPC-based and HE-based frameworks. For instance, the MPC-based framework detailed in [72] requires 80.5 h to train a simple neural network with two hidden layers on the MNIST dataset, largely due to extensive communication and interactions. Similarly, the use of Homomorphic Encryption (HE) increases communication overhead by generating large, encrypted representations of training instances [8]. In contrast, our framework minimizes communication overhead by transmitting a reduced subset of encodings, which are smaller than the original training sets.