# Cras: Curriculum Regularization and Adaptive Semi-Supervised Learning with Noisy Labels
## 3 Proposed Method
In contrast with DivideMix, CRAS without CR consistently performed better than, or as well as, DivideMix, despite using the same hyperparameters for all of the noise patterns. In real environments, it is difficult to identify the proportion of noise in datasets. Therefore, these results demonstrate that AWL is robust to unknown noise rates. * To study the influence of AWL, we trained a network (without AWL) using CR as a warm-up for DivideMix. Although the performance degradation was relatively small, it was more pronounced for higher noise rates. These results suggest that CR has a more significant impact on performance than AWL and that the warm-up performance is crucial for the combined sample selection and SSL strategy. However, CR results in a significant decrease in accuracy without AWL for 90% label noise. These results are discussed in Section 4.4.2. * The effectiveness of CR compared with ELR+ was evaluated by comparing the results of CRAS without AWL to those of DivideMix and ELR+ combined. For noise rates other than 50%, CR performed notably better than ELR+, thereby demonstrating its superior effectiveness. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**WebVision**} & \multicolumn{2}{c}{**ILSVRC12**} \\  & **Top1** & **Top5** & **Top1** & **Top5** \\ \hline Decoupling (17\({}^{\prime}\)) [41] & 62.54 & 84.74 & 58.26 & 82.26 \\ MentorNet (18\({}^{\prime}\)) [21] & 63.00 & 81.40 & 57.80 & 79.92 \\ Co-teaching (18) [22] & 63.58 & 85.20 & 61.48 & 84.70 \\ F-correction (19\({}^{\prime}\)) [34] & 61.12 & 82.68 & 57.36 & 82.36 \\ Interactive-CV (19\({}^{\prime}\)) [20] & 65.24 & 85.34 & 61.60 & 84.98 \\ DivideMix (20\({}^{\prime}\)) [25] & 77.32 & 91.64 & 75.20 & 90.84 \\ ELR+ (20\({}^{\prime}\)) [24] & 77.78 & 91.68 & 70.29 & 89.76 \\ MOT (21\({}^{\prime}\)) [51] & 77.90 & 91.90 & 73.80 & 91.70 \\ LongReMix (23\({}^{\prime}\)) [38] & **78.92** & 92.32 & - & - \\ \hline CRAS & 78.60 & **93.00** & **76.72** & **92.88** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of CRAS with state-of-the-art methods with respect to test accuracy on the mini-WebVision dataset. These results represent the top1 (top5) accuracy (%) on the WebVision validation set and the ImageNet ILSVRC12 validation set. The results of the baseline methods were copied from the original papers. \begin{table}
\begin{tabular}{l c} \hline \hline
**Method** & **Test Accuracy (\%)** \\ \hline Cross-Entropy & 69.21 \\ Joint-Optim (18\({}^{\prime}\)) [33] & 72.16 \\ M\_correction (19\({}^{\prime}\)) [40] & 71.00 \\ DivideMix \({}^{\star}\) (20\({}^{\prime}\)) [25] & 74.11 \\ ELR+ (20\({}^{\prime}\))[24] & 74.45 \\ CORES (21\({}^{\prime}\)) [62] & 73.24 \\ LongReMix (23\({}^{\prime}\)) [38] & 74.38 \\ \hline CRAS & **74.54** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of CRAS with state-of-the-art methods with respect to test accuracy (%) on the Clothing1M dataset. The results of the baseline methods were copied from the original papers, but the results annotated with * were obtained from the experiments using the authors’ public code. #### 4.4.2 Analysis of the Numbers of Clean Labels and Labeled Samples

We now assess the effectiveness of each component, such as CR and AWL, with respect to label precision, area under the curve (AUC), and the rate of labeled samples. Label precision is defined as the proportion of labels classified as clean that are actually clean labels. When the precision is 1, all labels contained in the labeled sample set are clean labels, in which case the setup is similar to that of the standard SSL. AUC takes into account both the clean label proportion and how well the model fits to labels that are incorrectly classified as clean. In SSL-based LNL, the rate of labeled samples is defined as the ratio of the number of labeled samples to the total number of labeled and unlabeled samples. A higher rate corresponds to a smaller number of unlabeled samples.