# NDARTS: A Differentiable Architecture Search Based on the Neumann Series
## 3 Experiment
### Simulation Experiment
#### 3.1.5 Performance Experiment
The architecture search algorithm using random search as the baseline still exhibits certain search capabilities in the NAS-Bench-201 search space. The gradient-based method exhibits adaptive differences in the NAS-Bench-201 search space, while the GDAS algorithm, which performs poorly in the DARTS search space, exhibits good performance in \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Val Acc** & **Test Acc** & **Param** & **Search Space** & **Search** \\  & **(\%)** & **(\%)** & **(m)** & & **Method** \\ \hline RandomNAS & 16.53 & 15.63 & 0.4 & NAS-Bench-201 & Random \\ RL & 41.90 & 42.23 & 0.4 & NAS-Bench-201 & RL \\ ENAS & 16.43 & 16.32 & 0.1 & NAS-Bench-201 & RL \\ EA & 44.03 & 44.23 & 1.0 & NAS-Bench-201 & EA \\ \hline GDAS & 43.47 & 43.10 & 0.8 & NAS-Bench-201 & Gradient \\ SETN & 33.04 & 32.37 & 0.3 & NAS-Bench-201 & Gradient \\ DARTS & 16.43 & 16.32 & 0.1 & NAS-Bench-201 & Gradient \\ \hline NDARTS & 40.66 & 41.02 & 1.3 & NAS-Bench-201 & Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of NDARTS and other NAS algorithms on the ImageNet dataset (based on the NAS-Bench-201 search space). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Val Acc** & **Test Acc** & **Param** & **Search Space** & **Search** \\  & **(\%)** & **(\%)** & **(m)** & & **Method** \\ \hline RandomNAS & 72.42 & 76.10 & 0.4 & NAS-Bench-201 & Random \\ RL & 89.83 & 92.20 & 0.4 & NAS-Bench-201 & RL \\ ENAS & 39.77 & 54.30 & 0.1 & NAS-Bench-201 & RL \\ EA & 91.18 & 93.40 & 1.0 & NAS-Bench-201 & EA \\ \hline GDAS & 89.78 & 93.49 & 0.8 & NAS-Bench-201 & Gradient \\ SETN & 84.24 & 87.67 & 0.3 & NAS-Bench-201 & Gradient \\ DARTS & 39.77 & 54.30 & 0.1 & NAS-Bench-201 & Gradient \\ \hline NDARTS & 89.94 & 93.67 & 1.3 & NAS-Bench-201 & Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of NDARTS and other NAS algorithms on the CIFAR-10 dataset (based on the NAS-Bench-201 search space). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Val Acc** & **Test Acc** & **Param** & **Search Space** & **Search** \\  & **(\%)** & **(\%)** & **(m)** & & **Method** \\ \hline RandomNAS & 47.54 & 46.94 & 0.4 & NAS-Bench-201 & Random \\ RL & 68.72 & 67.80 & 0.4 & NAS-Bench-201 & RL \\ ENAS & 15.03 & 15.61 & 0.1 & NAS-Bench-201 & RL \\ EA & 70.88 & 71.00 & 1.0 & NAS-Bench-201 & EA \\ \hline GDAS & 71.28 & 70.28 & 0.8 & NAS-Bench-201 & Gradient \\ SETN & 58.81 & 58.87 & 0.3 & NAS-Bench-201 & Gradient \\ DARTS & 15.03 & 15.61 & 0.1 & NAS-Bench-201 & Gradient \\ \hline NDARTS & 71.37 & 70.91 & 1.3 & NAS-Bench-201 & Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of NDARTS and other NAS algorithms on the CIFAR-100 dataset (based on the NAS-Bench-201 search space). the NAS-Bench-201 search space. The model searched by the NDARTS algorithm achieves optimal performance or approaches optimal performance on the three datasets. The results of the CIFAR-10 dataset are shown in Table 4, and the results of 50 epochs intercepted using gradient-based methods are plotted in Figure 16. It can be seen that the methods based on RL and EA have shown good performance in the NAS-Bench-201 search space. DARTS experienced severe performance degradation, while GDAS, which performed poorly in the DARTS search space, maintained good model performance, while NDARTS had a slightly better test set accuracy of 93.67% than the 93.49% of GDAS. From Figure 16, it can be seen that DARTS is difficult to search for good architectures in the NAS-Bench-201 search space. The SETN [30] algorithm with good initial model performance has an unstable search process, while the GDAS and NDARTS algorithms can effectively search for better architectures.