## 5 Experiments
### Ablation Studies
\begin{table}
\begin{tabular}{l l l c} \hline \hline
**Backbone** & **With 3D** & **Loss Functions** & **PE3D Testing** \\ \hline \hline \multirow{2}{*}{Res18 [84]} & N & \(Loss_{ce}\) & 57.2 \\  & Y & \(Loss_{ce}+Loss_{dua}\) & 59 \\ \hline \hline \multirow{2}{*}{Res50} & N & \(Loss_{ce}\) & 62.3 \\  & Y & \(Loss_{ce}+Loss_{dua}\) & 64.9 \\ \hline \hline \multirow{2}{*}{SCN [49]} & N & \(Loss_{ce}\) & 64.3 \\  & 3D + Fuzzy [52] & Y & - & **81.3** \\ \hline \hline \end{tabular}  
* Highest accuracy is highlighted in bold.  
\end{table} 
Table 9: Evaluation of different training data. In our experiments, we compared various models under identical hyperparameter settings. Additionally, we evaluated the models' performance with and without the application of 3D labels. The Validation Data (VD) in FER+ is used for training, while the model's accuracy was assessed using the FER+ Testing Data. Experiments with SCN: The Self-Attention Convolutional Network (SCN) [49], an enhancement of traditional CNNs, incorporates a self-attention mechanism for importance weighting alongside a ranking regularization layer and a relabeling optimization approach. In our implementation, we use the same hyper-parameters and methods described in the original paper with several modifications: we process images directly from the dataset without data augmentation; a single Nvidia RTX 3090 GPU is used for training purposes; we initiate relabeling of the training data after the first 20 epochs and set the mini-batch to 128. The experiments indicate that when the SCN achieves 81% accuracy on the FER+ testing set. Integrating PE3D 3D labels into SCN enhances the testing accuracy by an additional 0.2%. Moreover, combining both PE3D and PST and their subsequent integration into SCN leads to a further accuracy improvement of 0.8%. This enhancement can likely be attributed to the robustness of the 3D labels and the distances to the centers, which offer both interpretable and more dataset-independent features. Experiments with ESR-9: ESR-9 [25] denoted as 'Ensembles with Shared Representations,' is an ensemble model comprising nine convolutional branches. Our experiment seamlessly integrated the 3D labels and \(Loss_{dis}\) into each network branch. We used the same experiment settings introduced in [52]. The results indicate that ESR-9 outperforms the other models by achieving an 87.2% higher accuracy. Utilizing PST allows the ESR-9 model to reach an 88.3% accuracy rate. Despite these enhancements, the gains are relatively modest, which could be attributed to the model's high performance. Experiments with EmoFAN: EmoFAN [24] represents an end-to-end model incorporating an embedded face alignment network to produce facial landmarks. It outputs emotion labels and valence and arousal values for input faces. We applied the same training and testing settings as [52]. The results demonstrate that EmoFAN achieved an accuracy of 79.6% on FER+, which is noteworthy considering the model was not trained on FER+, as indicated in the referenced paper. In Table 12, the highest accuracy obtained was 80.3% through integrating PE3D labels and \(Loss_{dis}\), marking a 0.7% improvement over the baseline model. Notably, implementing PST led to an accuracy increase of over 1%, surpassing the enhancements seen with ESR-9 and SCN. This significant improvement can be attributed to the original model's lower baseline performance and the robust characteristics of 3D labels from PE3D. These enhancements further attest to our module's superior performance on unseen data compared to existing methods, underscoring its potential for broad real-world application. Figure 16 shows the final confusion matrix of three FER models combined with our method. Figure 16: Confusion matrix of three FER models combined with our method on FER+. All the models are integrated with PE3D and PST modules and trained with \(Loss_{ce}+Loss_{dis}\). (**a**) Confusion matrix of EmoFAN. (**b**) Confusion matrix of SCN. (**c**) Confusion matrix of ESR-9.