# NDARTS: A Differentiable Architecture Search Based on the Neumann Series
## 3 Experiment
### Simulation Experiment
#### 3.1.5 Performance Experiment
The results of the CIFAR-100 dataset are shown in Table 5, and the results of intercepting 50 epochs using gradient-based methods are plotted in Figure 17. It can be seen that on the CIFAR-100 dataset, NDARTS performed with an accuracy of 70.91%, almost approaching the optimal performance of 71.00% achieved by EA, while GDAS also maintained a good performance of 70.28%. However, DARTS and ENAS [14] methods even have poorer performance compared to methods based on random search. In Figure 17, when comparing the results of the gradient method, GDAS and NDARTS have similar performance and are superior to DARTS and SETN. The results of the ImageNet dataset are shown in Table 6, and the results of intercepting 50 epochs using gradient-based methods are plotted in Figure 18. It can be seen that on the ImageNet dataset, the evolutionary algorithm-based method achieved the best performance with an accuracy of 44.23%, while the reinforcement learning-based method also achieved an accuracy of 42.23%. In gradient-based methods, GDAS achieves the best accuracy with 43.10%, while NDARTS performs slightly worse with 41.02%. The methods based on evolutionary algorithms and reinforcement learning can achieve good performance with the support of a large amount of computing resources. The NAS-Bench-201 search space uses a table query form for performance evaluation, especially on large datasets such as ImageNet, which saves a lot of computation. Therefore, the methods based on EA and RL  
Figure 16: Performance of different algorithms on the CIFAR-10 dataset in the NAS-Bench-201 search space. have shown good performance on the NAS-Bench-201 search space and ImageNet dataset. The gradient-based methods has significant performance differences in the NAS-Bench-201 search space and ImageNet dataset. Specifically, as shown in Figure 18, GDAS and NDARTS perform better than SETN and DARTS. Although GDAS and NDARTS have poor initial states, they can still quickly optimize to better models, while SETN has a slower search speed and unstable search process, DARTS makes it difficult to search for better models in the NAS-Bench-201 search space. Figure 17: Performance of different algorithms on the CIFAR-100 dataset in the NAS-Bench-201 search space. Figure 18: Performance of different algorithms on the ImageNet dataset in the NAS-Bench-201 search space. To compare the performance of NDARTS and GDAS in detail, the results of all epochs on the three datasets were plotted as shown in Figure 19. It can be seen that NDARTS has a faster search speed than GDAS. When approaching stability, NDARTS and GDAS search for the same model for a long time but ultimately stop at different architectures. At this time, NDARTS has better performance than GDAS on CIFAR-10 and CIFAR-100 datasets, but slightly worse performance on ImageNet datasets. The model cell structure searched by the NDARTS algorithm is shown in Figure 20. As we can see, there is just one kind of cell in the NAS-Bench-201 search space. And there are just three intermediate nodes between the input and output. Finally, we can obtain the network by stacking the searched cell.