## 5 Experiment
### Main Result  
To demonstrate that RGISQL can improve text-to-SQL accuracy, it was compared with the aforementioned baselines, and the results for the Spider dataset are shown in Tables 3 and 4. The bold entries represent the optimal experimental results. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Values** \\ \hline PLM & 512 \\ GNN layers & 8 \\ Dropout rate & 0.1 \\ Hidden state dimension & 512 \\ Inner layer dimension & 1024 \\ Relation embedding & 128 \\ Node embedding & 64 \\ Dropout probability & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model hyperparameter settings. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Models** & **Dev** & **Test** \\ \hline Global-GNN [18] & 52.7 & 47.4 \\ IRNet [24] & 64.9 & 55.0 \\ RATSQL+BERT [7] & 69.7 & 65.6 \\ ShadowGNN+RoBERTa-large [20] & 72.3 & 66.1 \\ RATSQL+ELECTRA+ASIFormer [28] & 74.6 & - \\ RASAT+PICARD [9] & 75.3 & 70.9 \\ LGESQL+ELECTRA [8] & 75.1 & 72.0 \\ S2 SQL+ELECTRA [31] & 76.4 & 72.1 \\
**RGISQL+ELECTRA** & **77.2** & **73.6** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The exact set match accuracy of different methods on the Spider dev and test sets. As shown in Table 3, RGISQL outperformed all baseline models on the Spider dataset. It is noteworthy that RGISQL+ELECTRA achieved 73.6% on the hidden test set and 77.2% on the development set, improving the exact set match accuracy by 1.5% and 0.8%, respectively, compared with the optimal baseline S\({}^{2}\)SQL+ELECTRA. Regarding the development and test sets, it can be observed that (1) the exact set match accuracy of RGISQL on both the development and test sets has significantly improved, indicating that RGISQL can generate SQL queries more accurately, demonstrating a clear enhancement in the model's understanding of natural language questions. (2) The model's accuracy on the unseen test set has also increased, suggesting a significant improvement in its generalization ability. As shown in Table 4, RGISQL+ELECTRA achieved 77.3% on the hidden test set and 82.6% on the development set, improving execution accuracy by 1.8% and 2.1%, respectively, compared with the optimal baseline RASAT+PICARD. The RGISQL model's execution accuracy on both the development and test sets has significantly improved, indicating that RGISQL can not only generate SQL queries more accurately but also produce SQL queries with more precise execution results. This suggests that the SQL queries generated by RGISQL meet the requirements more effectively and are better aligned with practical needs. We also compared the model's more fine-grained performance at different levels of complexity, as shown in Table 5. The experimental results indicate that RGISQL demonstrates higher performance and better generalization capabilities when handling datasets of varying complexity. Particularly, RGISQL achieved significant improvements over previous methods when handling datasets with complex grammatical structures and questions with diverse meanings, especially those containing long queries. This indicates that RGISQL has a clear advantage in processing complex and lengthy query problems. Additionally, as shown in Table 6, RGISQL also demonstrates significant improvements in robustness on the dataset Spider-Syn, indicating that the SQL queries generated by RGISQL exhibit strong robustness. This finding emphasizes our method's ability to handle various, complex real-world situations and highlights its stability and reliability when facing unknown or changing data, suggesting an enhancement in the model's generalization capability. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Models** & **Dev** & **Test** \\ \hline BRIDGE+BERT [32] & 70.3 & 68.3 \\ RaSaP+ELECTRA [33] & - & 70.0 \\ SmBoP+GraPra [17] & 75.0 & 71.1 \\ RATSQL+GAP+NatSQL [34] & 75.0 & 73.3 \\ RASAT+PICARD [9] & 80.5 & 75.5 \\
**RGISQL+ELECTRA** & **82.6** & **77.3** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The execution accuracy of different methods on the Spider dev and test sets.