# NDARTS: A Differentiable Architecture Search Based on the Neumann Series
## 3 Experiment
### Simulation Experiment
#### 3.1.5 Performance Experiment
The results on the CIFAR-100 dataset are shown in Table 2, and the 50 epoch iteration curves of some algorithms are plotted in Figure 13. The results showed that NDARTS outperforms other gradient-methods with an error of 16.02%, while the performance of GDAS on the CIFAR-100 dataset drops to a Test Error of 18.38%. In addition, gradient-based methods are generally superior to other algorithms based on random search, RL, and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Vol Error (\%)** & **Test Error (\%)** & **Param (m)** & **Search Space** & **Search Method** \\ \hline RandomNAS * & — & 17.63 & 4.3 & DARTS & Random \\ NASNet-A * & — & 17.81 & 3.3 & NASNet & RL \\ PNAS * & — & 17.63 & 3.2 & DARTS & Sequential \\ \hline GDAS * & — & 18.38 & 3.4 & DARTS & Gradient \\ SETN * & — & 17.25 & 4.6 & DARTS & Gradient \\ PDARTS & 19.97 & 17.4 & 3.4 & DARTS & Gradient \\ PC-DARTS & 20.25 & 17.11 & 3.6 & DARTS & Gradient \\ DARTS & 21.42 & 17.54 & 3.4 & DARTS & Gradient \\ \hline NDARTS & 16.17 & 16.02 & 3.8 & DARTS & Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of NDARTS (based on DARTS search space) and other NAS algorithms on the CIFAR-100 dataset. Figure 12: Performance of different algorithms on the CIFAR-10 dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Top1** & **Top5** & **Param** & **Search** & **Search** \\  & **Test** & **Test** & **(m)** & **Space** & **Method** \\  & **Error (\%)** & **Error (\%)** & & & \\ \hline RandomNAS * & 27.1 & — & 4.3 & DARTS & Random \\ AmoebaNet-A * & 25.5 & 8.0 & 5.1 & NASNet & EA \\ NASNet-A * & 26.0 & 8.4 & 3.3 & NASNet & RL \\ PNAS * & 25.8 & 8.1 & 3.2 & DARTS & Sequential \\ \hline GDAS * & 26.0 & 8.5 & 3.4 & DARTS & Gradient \\ SETN * & 25.7 & 8.0 & 4.6 & DARTS & Gradient \\ SharpDARTS [42] & 25.1 & 7.8 & 4.9 & DARTS & Gradient \\ PDARTS * & 24.4 & 7.4 & 3.4 & DARTS & Gradient \\ PC-DARTS * & 25.1 & 7.8 & 3.6 & DARTS & Gradient \\ DARTS & 26.9 & 8.7 & 3.4 & DARTS & Gradient \\ \hline NDARTS & 24.3 & 7.3 & 3.8 & DARTS & Gradient \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of NDARTS (based on DARTS search space) and other NAS algorithms on the ImageNet dataset. other methods. From the iteration curve, it can be seen that NDARTS, PDARTS, and PC-DARTS have similar search speeds, they have faster search speeds and better performance than DARTS. The results on ImageNet are shown in Table 3. When extended to big data, the gradient method can no longer maintain its superiority over other methods in performance, but the NDARTS algorithm still achieved optimal performance with 24.3% and 7.3% TOP1 and TOP5 Test ERROR, respectively. Figures 14 and 15 showed the structures of Normal Cells and Reduction Cells searched by NDARTS in the DARTS search space. As we can see, there are four nodes between the outputs of units \(k-1,k-2\) and the output of unit \(k\). There are some operations on each edge. There are also some pooling operations in the Reduction cell, which can reduce the feature map height and width by a factor of two. Figure 14: Normal cell model found by NDARTS in DARTS search space. Figure 13: Performance of different algorithms on the CIFAR-100 dataset. Figure 15: Reduction cell model found by NDARTS in DARTS search space. The performance of the NDARTS algorithm and other NAS algorithms was tested in the NAS-Bench-201 search space. The results on CIFAR-10, CIFAR-100, and ImageNet datasets are shown in Tables 4-6, respectively. Among them, each algorithm searches for the optimal structural unit on the CIFAR-10 dataset and evaluates its performance on the CIFAR-100 and ImageNet datasets. Due to the simpler unit search space of NAS-Bench-201 than the DARTS search space, the algorithm performance generally decreases in the NAS-Bench-201 search space. Overall, due to the omission of a large amount of training and evaluation calculations in the NAS-Bench-201 search space, the RL- and EA-based methods have shown good performance.