## 3 Results and Discussion
### Model Interpretation  
To elucidate the decision-making process of our final model, PLM-FRP, we employed SHapley Additive exPlanations (SHAP) [46]. The SHAP framework provides a robust method for interpreting machine learning models by quantifying the contribution of each feature to an individual prediction. By leveraging principles from cooperative game theory, SHAP fairly allocates the impact of each feature on the model's output, thereby offering a comprehensive understanding of feature importance. To visualize the feature space and the effectiveness of our selection strategy, we first employed t-Distributed Stochastic Neighbor Embedding (t-SNE) [47]. As shown in Figure 7, the t-SNE plots reveal a markedly improved separation between positive (FRPs) and negative (non-FRPs) samples after feature selection. This observation underscores the efficacy of our feature selection pipeline in identifying a highly discriminative feature subset that enhances the model's ability to distinguish between the two classes. To further examine the relationships between the most predictive features, a correlation heatmap was also generated (Figure 8). To further analyze the impact of individual features, we generated a SHAP summary plot for the top 20 features from the optimized DDE + ESM2 combination (Figure 9). This plot illustrates both the magnitude and direction of each feature's influence on the model's output. Features with positive SHAP values push the prediction towards the FRP class, while negative values push it towards the non-FRP class. The color intensity indicates the feature's value, providing deeper insight into its behavior. Figure 7: Comparison before and after feature selection. (**a**) Before feature selection. (**b**) After feature selection. To further elucidate the impact of individual features on the model's predictions, we analyzed the SHAP values for the top 20 features derived from the DDE + ESM2 feature combination, as depicted in Figure 9. This visualization provides insights into the direction and magnitude of each feature's influence on the model's output. Features with positive SHAP values contribute to a higher prediction score (FRPs), while features with negative SHAP values contribute to a lower prediction score (non-FRPs). The color intensity reflects the magnitude of the feature's impact. To gain further insights into the interactions between features, we generated a SHAP decision plot for the 216-dimensional feature set extracted from the combined DDE + ESM2 features. This plot illustrates the cumulative contribution of each feature to the model's decision-making process, highlighting the most influential features and their interactions (Figure 10). Figure 8: Correlation heatmap of top 15 features and target variable. Figure 9: SHAP summary plot for top 20 features from DDE + ESM2. While SHAP analysis effectively quantifies individual feature contributions, directly mapping high-importance features from the combined DDE and ESM2 set to specific biological motifs presents inherent challenges. This difficulty arises from the abstract, high-dimensional nature of ESM2 embeddings, which capture complex, non-linear dependencies, and the statistical derivation of DDE features. Nevertheless, the significant contributions of these features strongly suggest that our model leverages underlying biological signals. For instance, the importance of DDE features indicates the model's sensitivity to local amino acid environments, while the prominent role of ESM2 embeddings highlights the capture of global protein characteristics crucial for FRP prediction. This demonstrates that PLM-FRP effectively learns sophisticated biological patterns, even if they are not immediately interpretable as discrete biological units. Through this comprehensive analysis, we have gained a deeper understanding of the model's decision-making process, revealing the interplay among key features and their influence on FRP prediction.