## 5 Conclusions  
CNNs are a powerful method for making predictions, not only for classification problems but also for regression concerns. In regression, the focus is on understanding the relationship between continuous-number scores and data. The prediction network seeks to bring the estimated output closer to the actual scores by minimizing the average value of the loss function over the data related to the network weights. However, A CNN-regression-based model developed for FBP may face challenges if it relies solely on traditional loss functions. These challenges stem from biases naturally embedded in facial-beauty data, leading to an uneven distribution of data. For instance, preferences toward certain beauty scores, ethnicities, or age groups can introduce biases that impede the model's ability to generalize effectively across various situations. Accordingly, a new ensemble average loss function composed of three distinct regression-loss functions (L2 loss, L1 loss, and Log-cosh) was introduced by this work. and then integrated within various pretrained CNN architectures, namely AlexNet, VGG16-Net, and FIAC-Net. Its efficacy in \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Method**} & \multicolumn{2}{c}{**SCUT-FBP**} & \multicolumn{3}{c}{**SCUT-FBP 5500**} & \multicolumn{3}{c}{**ME Beauty**} \\ \hline  & \(\uparrow\)**PC** & \(\downarrow\)**MAE** & \(\downarrow\)**RMSE** & \(\uparrow\)**PC** & \(\downarrow\)**MAE** & \(\downarrow\)**RMSE** & \(\uparrow\)**PC** & \(\downarrow\)**MAE** & \(\downarrow\)**RMSE** \\ \hline VGG16 + Bayesian Ridge & 0.857 & 0.2595 & 0.3397 & N/A & N/A & N/A & N/A & N/A & N/A \\ Regression [29] & **0.95** & 0.2314 & 0.2885 & 0.9055 & 0.2236 & 0.2954 & N/A & N/A & N/A \\ HMNTet [32] & 0.897 & N/A & N/A & 0.8783 & 0.2501 & 0.3263 & N/A & N/A & N/A \\ ResNet-18 biased P-aNet [48] & 0.9103 & 0.2224 & 0.2816 & 0.9055 & 0.2236 & 0.2954 & N/A & N/A & N/A \\ Cascade fine-tuned CNN [24] & 0.88 & N/A & N/A & N/A & N/A & N/A & N/A & N/A & N/A \\ REIX-INCEP [35] & N/A & N/A & N/A & 92.18 & 0.2052 & 0.2698 & N/A & N/A & N/A \\ CNN-ER [49] & N/A & N/A & N/A & 0.9250 & **0.2009** & 0.2650 & N/A & N/A & N/A \\ VGGFace2+ Ensemble Stack [50] & 0.8898 & 0.2409 & 0.3105 & 0.9112 & 0.2304 & 0.2951 & N/A & N/A & N/A \\ Ensemble CNN [28] & 0.8795 & 0.226 & 0.330 & 0.886 & 0.242 & 0.320 & 0.888 & **0.365** & 0.600 \\ AlexNet + proposed & & 0.9038 & 0.2635 & 0.3482 & 0.9141 & 0.2449 & 0.3097 & 0.8977 & 0.4764 & 0.6097 \\ VGG16-Net + proposed & & & & & & & & & \\ ensemble loss & 0.9059 & 0.2229 & 0.2920 & **0.9309** & 0.2183 & 0.2792 & 0.9079 & 0.5121 & 0.6363 \\ FIAC-Net + proposed & & & & & & & & & \\ ensemble loss & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance comparison with FBP state-of-the-arts. predicting facial-image beauty scores was evaluated across three FBP benchmarks: SCUT-FBP, SCUT-FBP5500, and MEBeauty. It demonstrated its superiority when compared to the state-of-the-art. Additionally, our approach can potentially improve model performance by providing a significant correlation between machine- and human-predicted beauty scores and a low error rate. These findings highlight the effectiveness of the proposed ensemble cost function for regression tasks and suggest its potential use in improving CNN models. Conceptualization, J.N.S. ; Methodology, J.N.S. ; Writing--original draft, J.N.S. ; Supervision, A.M.A. and D.A.I. All authors have read and agreed to the published version of the manuscript. This research received no external funding.