## 5 Experimental Investigations
### Ablation Study  
In this section, a series of ablation experiments were designed to assess the individual contributions of various components in the proposed method to the performance of intent detection. The following conclusions can be drawn from Table 6.  
(1) After removing the Chinese BERT pre-training model, the overall accuracy of the Auto-HPIF model on CADS decreases by 0.9%. This is because the Chinese BERT can convert the input text into a high-dimensional vector representation containing rich semantic information and contextual relationships, and these vectors are used as the input of the subsequent model to help improve the accuracy of multi-intent detection. (2) Omitting the Gaussian prior attention mechanism results in a decrease of 0.37% and 1.38% in the overall accuracy of the Auto-HPIF model on CADS and MixATIS, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**CADS**} & \multicolumn{3}{c}{**MixATIS**} \\ \cline{2-7}  & **Slot (F1)** & **Intent (Acc)** & **Overall (OA)** & **Slot (F1)** & **Intent (Acc)** & **Overall (OA)** \\ \hline (w/o) Chinese BERT encoder & 95.90 & 90.57 & 86.26 & - & - & - \\ (w/o) Gaussian attention & 96.43 & 90.38 & 87.17 & 87.27 & 76.69 & 46.25 \\ mechanism & & & & & & \\ (w/o) & 96.37 & 90.53 & 87.02 & 87.49 & 76.84 & 46.89 \\ Multilabel\_crossentropy (w/o) Interaction mechanism & 94.59 & 89.92 & 84.96 & 78.10 & 76.36 & 41.07 \\ Auto-HPIF (ours) & **96.80** & **90.61** & **87.94** & **88.41*** & **77.60*** & **47.63*** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ablation study on MixATIS and CADS datasets (%). The numbers marked with an asterisk (*) indicate that the experimental results on the MixATIS dataset were obtained after removing the Chinese BERT pre-training model (%). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**MixATIS**} & \multicolumn{3}{c}{**MixSNIPS**} \\ \cline{2-7}  & **Overall (Acc)** & **Slot (F1)** & **Intent (Acc)** & **Overall (Acc)** & **Slot (F1)** & **Intent (Acc)** \\ \hline Attention BiRNN [30] & 39.1 & 86.4 & 74.6 & 59.5 & 89.4 & 95.4 \\ Slot-Gated [31] & 35.5 & 87.7 & 63.9 & 55.4 & 87.9 & 94.6 \\ Bi-Model [32] & 34.4 & 83.9 & 70.3 & 63.4 & 90.7 & 95.6 \\ SF-ID [33] & 34.9 & 87.4 & 66.2 & 59.9 & 90.6 & 95.0 \\ Stack-Propagation [34] & 40.1 & 87.8 & 72.1 & 72.9 & 94.2 & 96.0 \\ Joint Multiple ID-SF [4] & 36.1 & 84.6 & 73.4 & 62.9 & 90.6 & 95.1 \\ AGIF [5] & 40.8 & 86.7 & 74.4 & 74.2 & 94.2 & 95.1 \\ GL-GIN [16] & 43.5 & 88.3 & 76.3 & 75.4 & 94.9 & 95.7 \\ SDIN [35] & 44.6 & 88.2 & 77.1 & 75.7 & 94.4 & **96.5** \\ Auto-HPIF & **47.6** & **88.4** & **78.4** & **76.4** & **95.1** & 96.0 \\ (w/o Chinese-BERT) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluating multiple-intent detection and slot-filling performance on MixATIS and MixSNIPS datasets (%). This indicates that the Gaussian prior attention mechanism plays a crucial role in enabling the model to distinguish the importance of different parts of text input and focus on critical information more effectively. (3) Replacing the multi-label classification cross-entropy loss function, the overall accuracy of the Auto-HPIF model on CADS and MixATIS decreases by 0.43% and 0.74%, respectively, which indicates that the multi-label classification cross-entropy loss function is more effective when applied to the Auto-HPIF model, and its advantage is that it does not require special adjustment of the loss values of class weights and thresholds, which can improve the model stability and reliability of the model. (4) Removing the heterogeneous network interaction layer from the model and utilizing only the intent-aware slot-filling decoder for the one-way transfer of slot information to intent information results in a decrease of 2.98% and 6.56% in the overall accuracy of the Auto-HPIF model on CVDS and MixATIS, respectively.