## 4 Experimental Process and Analysis
### Prediction of Dye Formulas and Ultrasonic Pretreatment Power
#### 4.4.3 Comparative Analysis of Experimental Results
As shown in Figures 12 and 13, the proposed SAT Fusion-Gated BiLSTM model outperformed traditional models, achieving the highest predictive performance with an \(R^{2}\) value of 0.8999 and \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\) values of 0.0547, 4.8005, 4.3340, and 0.0280, respectively, all of which are the best among the models considered. In contrast, the worst-performing model, SVR, achieved an \(R^{2}\) value of only 0.5885, with \(RMSE\), \(RPIQ\), \(RPD\), and \(MAE\) values of 0.1314, 1.9973, 1.8032, and 0.0782, respectively. The proposed model exhibited a high performance while requiring only 5.7683 s to execute, a significantly faster processing time than that of traditional deep learning models, including GRU, CNNs, LSTM, and BiLSTM. Although the running time of the proposed model was slightly higher than that of the SVR, RF, and AT Fusion-Gated BiLSTM models, the performance metrics of the proposed model, including \(R^{2}\), \(RPIQ\), \(RPD\), \(RMSE\), and \(MAE\), demonstrated a notable enhancement, with the proposed model exhibiting an optimal balance between running efficiency and prediction accuracy. The reported runtime excludes data preprocessing and focuses solely on model construction, training, and evaluation. The significant performance improvement of the SAT Fusion-Gated BiLSTM model over BiLSTM, LSTM, and other conventional deep learning models is primarily due to the integration of the Separable Attention Feature Fusion (SAT Fusion) module, which combines SDIIM and SCIIM based on separable cross-attention mechanisms. Additionally, the model incorporates Gated Linear Units (GLUs) and gated BiLSTM units to enhance computational efficiency through an optimized information flow. SDIIM and SCIIM are designed to extract differential and shared information from multimodal data, respectively, facilitating efficient feature fusion. By enabling key feature interactions, they preserve the benefits of parallel processing while improving feature representation and integration. This lightweight strategy reduces redundant feature generation and mitigates the sequential dependency typical of recurrent networks, significantly shortening runtime. SAT Fusion's hierarchical feature fusion effectively captures multimodal relationships, improving both feature extraction and computational efficiency. During fusion, SDIIM extracts differential information from spectral reflectance data, spectral characteristic parameters, and spectral similarity metric parameters using separable cross attention. SCIIM integrates shared information from these datasets, reducing redundancy and information loss and avoiding the low feature utilization seen in concatenated multi-spectral data. The SAT Fusion module dynamically leverages each modality's strengths, generating richer feature representations and enhancing the understanding of multimodal spectral data. These structural optimizations enable SAT Fusion-Gated BiLSTM to achieve significant runtime reductions without compromising model depth or feature representation. The GLU and gated BiLSTM units further optimize information flow. Specifically, GLUs apply layer normalization, with inputs processed through two parallel channels--a linear transformation and a sigmoid transformation. The outputs are fused via element-wise multiplication and added back to the normalized input through a residual connection, allowing the model to focus on critical information while retaining the original input. The gated BiLSTM unit extends the traditional BiLSTM by incorporating a parallel linear layer to capture global patterns, in addition to sequential features. These outputs are fused through element-wise multiplication, adjusting feature importance and suppressing redundancy, a process which enhances computational efficiency and feature representation without sacrificing expressive power. Table 3 illustrates the effect of removing or adding each module within the SAT Fusion-Gated BiLSTM architectural framework.