## 4 Experiments and Results
### Architecture Search
#### 4.2.2 Result of Architecture Search  
Table 2 shows the search cell performance for each number of clusters. If the number of clusters is four, too many skip connections are selected, and the number of skip connections is set to two. In other cases, there are 1-3 clusters, and skip connections were well-regulated. As shown in Table 3, the best case can be found when the number of clusters is three. For the architecture search, 0.22 GPU days (5.35 h) are consumed with 1 Tesla P100 GPU. Clustering is performed after finishing stage 1, and clustering is used to solve the vote dispersion problem. Based on the number of clusters, the final model performance can be described as follows: one cluster indicates that all operations are in the same cluster, and it is the same result produced by DARTS searching the architecture twice with 25 epochs. With a larger number of clusters, the final model performance increases and we found the best performance when the number of clusters was three, since more clusters led the same structure as the DARTS structure with unregulated operations. For example, seven clusters of operations create the same structure as that of DARTS without the effect of clustering. With our clusters, as we experienced, _skip_connect_ is not well-regulated; thus, too many _skip_connect_ were selected, which caused the collapse phenomenon [9]. It is clear that models with five _skip_connect_ operations out of eight will perform poorly, so two _skip_connect_ operations were selected manually as is performed by P-DARTS [7]. This model from DG-DARTS showed a test error of 2.71%, whereas the three-cluster model achieved a test error of 2.51%, which is the best results. We provide another result of our experiment for better verification of our strategy. Table 4 shows the effect of \(\alpha\). In our research, cluster 2, which has the largest sum of \(\alpha\), was selected for the next stage. Instead of choosing operation _sep_conv_3_ \(\times\) 3 from cluster 2, the operations from clusters 1 and 3 were chosen to prooove our strategy. Operation _skip_connect_ from cluster 1 had an accuracy of 97.06%, and operation _dil_conv_3_ \(\times\) 3 from cluster 3 had an accuracy of 96.94%. Operation _sep_conv_3_ \(\times\) 3 from cluster 1 achieved the best accuracy of 97.49% as intended by our strategy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Architecture** & **Test Error (\%)** & **Parameter (M)** & **Search Cost (GPU Days)** & **Search Method** \\ \hline DenseNet-BC [17] & 3.46 & 25.6 & - & manual \\ \hline NASNet-A [1] + cutout1  & 2.65 & 3.3 & 1800 & RL \\ \hline DARTS (1 st order) [3] + cutout & 3.00 & 3.3 & 1.5 & Gradient \\ DARTS (2 nd order) [3] + cutout & 2.76 & 3.3 & 4 & Gradient \\ SNAS (moderate) [18] + cutout & 2.83 & 2.8 & 1.5 & Gradient \\ ProxylessNAS [19] & 2.08 & 5.7 & 4 & Gradient \\ P-DARTS [7] + cutout & 2.50 & 3.4 & 0.3 & Gradient \\ PC-DARTS [8] + cutout & 2.57 & 3.6 & 0.1 & Gradient \\ DART+ [9] + cutout + AA2  & 2.20 & 4.3 & 0.4 & Gradient \\ StacNAS [11] + cutout & 2.33 & 3.9 & 0.8 & Gradient \\ \hline DG-DARTS (ours) + cutout & 2.51 & 3.8 & 0.2 & Gradient \\ DG-DARTS (ours) + cutout + AA2  & 2.21 & 3.8 & 0.2 & Gradient \\ \hline cutout1: apply cutout augmentation [20], AA2: apply AutoAugment [21].[ENDFOOTNOTE] & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of state-of-the-art architectures with on the CIFAR 10 data set. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Clusters** & **Number of Skip Connections** & **Final Model Test Error** \\ \hline
1 & 2 & 2.73\% \\
2 & 1 & 2.66\% \\
3 & 2 & **2.51\% (best)** \\
4 & 5 & 2.71\% * \\ \hline \hline \end{tabular}  
* The number of skip connections was forced to be set to 2.  
\end{table} 
Table 3: Performance of the final model with respect to the number of clusters. Implementation Details  
The model for the final evaluation was composed of 20 cells and 36 initial channels. A total of 20 cells were composed of 18 normal cells and 2 reduction cells.