# Cras: Curriculum Regularization and Adaptive Semi-Supervised Learning with Noisy Labels
## 3 Proposed Method
By comparing this rate with the label precision, we can determine how effectively our proposed method can select accurately labeled samples. Figure 2 visualizes the label precision, AUC, and rate of labeled samples for each component throughout the training process. For 20% and 50% label noise, the precision remained very close to 1, even with DivideMix. However, the use of CR helped prevent correct labels from being incorrectly identified as noise, thereby increasing the number of labeled samples. CR significantly enhanced precision and AUC under conditions with high label noise (over 80%) and proved to be more robust than the standard warm-up methods. In particular, although precision improved substantially, a severely reduced number of labels destabilized the training in scenarios with 90% label noise. Under conditions with high label noise and a limited number of correct labels, AWL effectively prevented overfitting to labels and maintained the precision of noise detection. \begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Method/Noise Ratio** & & **20\%** & **50\%** & **80\%** & **90\%** \\ \hline \multirow{2}{*}{CRAS} & Best & **79.5** & **76.9** & **65.0** & **33.8** \\  & Last & **79.0** & **76.4** & **64.7** & **33.3** \\  & Best & 77.0 & 74.8 & 60.6 & 32.8 \\  & Last & 76.5 & 74.3 & 60.3 & 32.1 \\  & Best & **79.5** & 75.8 & 64.5 & 29.2 \\  & Last & 78.9 & 75.3 & 64.2 & 28.6 \\  & Best & 78.1 & 75.8 & 60.2 & 28.0 \\  & Last & 77.8 & 75.3 & 59.9 & 27.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of ablation studies with respect to test accuracy (%) on CIFAR-100 datasets with symmetric noise. Figure 2: _Cont._

#### 4.4.3 Comparison of Training Time

Table 6 presents a comparison of the overall training times of DivideMix and CRAS. In this experiment, we used a single NVIDIA A6000 GPU. CRAS took 30 min less than DivideMix. The most time-consuming phase in DivideMix is the phase of dividing the training data. CRAS allows for a longer warm-up period by introducing CR, and the reduction in the division phases decreases the total training time. Specifically, the warm-up phase in CRAS extends to 60 epochs, whereas DivideMix has a warm-up of only 30 epochs. Therefore, the inclusion of the process outlined in Algorithm 1 has a relatively small effect on the computation time of CRAS. ### Sensitivity to Hyperparameters

We evaluated the effect of the settings of two hyperparameters: \(m\) for AWL and the threshold \(\tau\) for CR. Figure 3 shows the adaptive weights for different values of \(m\). The hyperparameter \(m\) is highly sensitive in situations where the labeled sample ratio \(r\) is extremely low, for example, when the noise rate is high. However, its sensitivity can be captured at the stage of designing the scaling function, so that the range of hyperparameters to be explored can be limited. Therefore, \(m\) is not determined experimentally by preparing several patterns; instead, it is determined to some extent at the design stage of the scaling function. In the case of Figure 3, \(m=0.6\), for which the weight value increases smoothly as \(r\) decreases, is the optimal parameter. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **DivideMix**[25] & **CRAS** \\ \hline Time (hours) & 3.5 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the total training times of DivideMix and CRAS on CIFAR-100 dataset with 90% symmetric noise. Figure 3: Adaptive weight distributions of (13) for various values of hyperparameter \(m\) when the number of classes is 100. Figure 2: Precision of noisy label detection, AUC, and rate of labeled samples (%) on CIFAR-100 dataset with symmetric noise. Figure 4 illustrates the sensitivity of CRAS to different target thresholds \(\tau\). CRAS is robust to the hyperparameter \(\tau\) because its accuracy varies by no more than 2% for various values of \(\tau\). Therefore, if we set \(\tau\) to a small value, there are no targets below the threshold for most classes, and CR learns in a similar manner to ELR+.