# Cognitive Diagnosis Method via Q-Matrix-Embedded Neural Networks
## 3 Experiments and Results
### Simulation Studies
#### 3.2.2 Results
Figure 4 serves the same purpose as Figure 3. The difference is that the simulated dataset was generated from the GDINA model with Q-matrix \(\mathbf{Q}_{2}\). Notably, Q-matrix \(\mathbf{Q}_{2}\) assessed five skills, and there were 26 skill interaction patterns according to Equation (3). In the experiment in Figure 4, we only set 10 random skill interaction patterns; that is, the interaction matrix \(\mathbf{Q}^{\prime}\) was a binary matrix with a dimension of \(10\times 5\) and no duplicate rows. The hyperparameter learning rates, batch size, and epochs for the trained models were 0.01, 128, and 100 for the high-quality dataset. However, the hyperparameters were adjusted to 0.005, 64, and 200 for the low-quality dataset. The findings presented in Figure 4 consistently align with those depicted in Figure 3. Dual Q-Net exhibited a pronounced advantage over MLP and ANN across loss, AAR, and PAR, particularly in the case of the low-quality data. The collective findings from Figures 3 and 4 demonstrate that our method maintained a reliable and robust performance when the number of questions and skills increased. This contrasts with the classical methods (e.g., DINA and GDINA; [25]), indicating that our approach can, to some extent, address this limitation inherent in classical methods. Figure 3: Training Dynamics: loss, AAR, and PAR values in neural networks on simulated data generated by the DINA model with Q-matrix \(\mathbf{Q}_{1}\). Subplots (**a–c**) show the results of the model training process for the high-quality dataset (i.e., \(P(0),1-P(1)\in\mathrm{U}(0,0.15)\)), and subfigures (**d–f**) show the results of the model training process for the low-quality dataset (i.e., \(P(0),1-P(1)\in\mathrm{U}(0.15,0.30)\)). Result II: Result comparison of different methods on simulated datasets  
The objective of the previous analysis was to discuss the changing trends in the accuracy of the MLP, ANN, and Dual Q-Net models during the training process. The main purpose of this section is to compare the performance of our proposed method with the classical methods on the various datasets, to better evaluate the effectiveness of our method. The section is structured as follows: First, we present the related experimental parameter settings and datasets, followed by the parameterized optimal baseline model for each dataset. Before the analysis of some typical experimental results, the results of each model on different datasets are reviewed. The simulated experimental dataset shown in Table 1 was created so that a clearer experimental analysis could be performed. With reference to existing studies and after several experiments [26], it was found that DINA was better at generating simulated data when the number of examined attributes was small. And when more attributes were examined, GDINA was better. For example, the first dataset HSD1 is the simulation data generated by the DINA model. Where the Q-matrix contains 10 items and 3 attributes (i.e., \(\mathbf{Q}_{1}\in\mathbb{R}^{10\times 3}\)), while the guesses and sleeps are at a low level (i.e., \(g,s\in\mathrm{U}[0,0.15]\)). To evaluate the model performance, we produced simulated datasets for each condition and sampled four sub-datasets with sample sizes \(N\) of 100, 200, 300, and 500. To make the evaluation more comprehensive and unbiased, we selected the most representative classical methods as reference benchmarks. These included parametric cognitive diagnosis