## 6 Results and Discussion
### Ablation Studies  
In this section, we present the ablation studies for the proposed model.  
To verify the effects of the multiband attention and quantized question embedding, we conducted comparative experiments with and without them on the Assist09 and Assist17 datasets. As shown in Table 3, the network equipped with multiband attention and quantized question embedding outperformed the one without them, thereby indicating the effectiveness of the proposed embedding modules.  
We conducted experiments to optimize the hyperparameters of the proposed model, such as the number of the bands and the size of the codebook, on the Assist09 and Assist17 datasets. Using various hyperparameters, we trained and tested multiple neural network models. For each model, we evaluated its performance using RMSE and AUC. Table 4 demonstrates the impact of selecting varying numbers of bands in the multiband attention module on the final performance, while keeping all other settings the same. Table 5 exhibits the effect of choosing different codebook sizes in the quantized question embedding module on the overall performance, while maintaining consistent settings in all other aspects. From Tables 4 and 5, it can be observed that different hyperparameter selections have minimal impact on the overall performance of the model, indicating that our model is relatively stable. The hyperparameters yielding optimal performance are the band set to 8 and the codebook size set to 1024.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Metric** & **4** & **8** & **16** & **32** \\ \hline \multirow{2}{*}{Assist09} & RMSE & 40.71 & 40.25 & 40.32 & 40.98 \\  & AUC & 81.26 & 81.82 & 81.63 & 80.91 \\ \hline \multirow{2}{*}{Assist17} & RMSE & 37.79 & 37.36 & 37.44 & 37.96 \\  & AUC & 85.21 & 85.75 & 85.62 & 85.03 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The performance comparison of the proposed model with 4, 8, 16, and 32 bands on the Assist09 and Assist17 datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **Metric** & **DKT** & **DKT+** & **DKVMN** & **SAKT** & **AKT** & **CL4 KT** & **Ours** \\ \hline \multirow{2}{*}{Algebra05} & RMSE & 37.85 & 36.42 & 34.63 & 34.57 & 34.91 & 38.65 & 34.12 \\  & AUC & 75.14 & 71.63 & 78.37 & 78.48 & 77.61 & 78.49 & 79.26 \\ \hline \multirow{2}{*}{Bridge06} & RMSE & 40.91 & 39.56 & 39.01 & 39.77 & 36.26 & 36.10 & 34.27 \\  & AUC & 71.82 & 74.07 & 74.65 & 74.43 & 76.18 & 76.65 & 77.41 \\ \hline \multirow{2}{*}{Assist09} & RMSE & 43.27 & 41.19 & 41.53 & 41.71 & 41.86 & 41.59 & 40.25 \\  & AUC & 79.25 & 78.16 & 78.64 & 77.52 & 78.81 & 79.30 & 81.82 \\ \hline \multirow{2}{*}{Assist17} & RMSE & 45.06 & 46.71 & 45.38 & 46.62 & 43.48 & 42.27 & 37.36 \\  & AUC & 68.98 & 65.37 & 70.29 & 67.21 & 74.95 & 78.06 & 85.75 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The overall performance comparison of the four datasets. Our model outperformed other baseline models (especially the assist17 dataset).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Metric** & **Baseline** & **+MBA** & **+MBA + QQE** \\ \hline \multirow{2}{*}{Assist09} & RMSE & 42.84 & 41.13 & 40.25 \\  & AUC & 78.75 & 80.58 & 81.82 \\ \hline \multirow{2}{*}{Assist17} & RMSE & 43.62 & 41.15 & 37.36 \\  & AUC & 74.80 & 78.26 & 85.75 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The performance comparison of our framework with and without MBA, as well as of the QQE modules on the Assist09 and Assist17 datasets.