# Cras: Curriculum Regularization and Adaptive Semi-Supervised Learning with Noisy Labels
## 3 Proposed Method
\begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline \hline
**Dataset** & & & \multicolumn{4}{c}{**CIFAR-10**} & \multicolumn{4}{c}{**CIFAR-100**} & \multirow{4}{*}{**Asym.**} \\
**Noise Type** & & & \multicolumn{2}{c}{**Sym.**} & & \multicolumn{2}{c}{**Asym.**} & & \multicolumn{2}{c}{**Sym.**} & & \multicolumn{2}{c}{**Asym.**} \\
**Method/Noise Ratio** & & **20\%** & **50\%** & **80\%** & **90\%** & **40\%** & **20\%** & **50\%** & **80\%** & **90\%** & **40\%** \\ \hline \multirow{2}{*}{Cross-Entropy} & Best & 86.8 & 79.4 & 62.9 & 42.7 & 85.0 & 62.0 & 46.7 & 19.9 & 10.1 & - \\  & Last & 82.7 & 57.9 & 26.1 & 16.8 & 72.3 & 61.8 & 37.3 & 8.8 & 3.5 & - \\ \hline \multirow{2}{*}{Mixup (12\({}^{\prime}\)) [45]} & Best & 95.6 & 87.1 & 71.6 & 52.2 & - & 67.8 & 57.3 & 30.8 & 14.6 & - \\  & Last & 92.3 & 77.6 & 46.7 & 43.9 & - & 66.0 & 46.6 & 17.6 & 8.1 & - \\ \hline \multirow{2}{*}{Co-teaching+(18\({}^{\prime}\)) [23]} & Best & 89.5 & 85.7 & 67.4 & 47.9 & - & 65.6 & 51.8 & 27.9 & 13.7 & - \\  & Last & 88.2 & 77.6 & 45.5 & 30.1 & - & 64.1 & 45.3 & 15.5 & 8.8 & - \\ \hline \multirow{2}{*}{PENCIL (19\({}^{\prime}\)) [34]} & Best & 92.4 & 89.1 & 77.5 & 58.9 & 88.5 & 69.4 & 57.5 & 31.1 & 15.3 & - \\  & Last & 92.0 & 88.7 & 76.5 & 58.2 & 88.1 & 68.1 & 56.4 & 20.7 & 8.8 & - \\ \hline \multirow{2}{*}{DivideMix (20\({}^{\prime}\)) [25]} & Best & 96.1 & 94.6 & 93.2 & 76.0 & 93.4 & 77.3 & 74.6 & 60.2 & 31.5 & 60.8 \\  & Last & 95.7 & 94.4 & 92.9 & 75.4 & 92.1 & 76.9 & 74.2 & 59.6 & 31.0 & 55.5 \\ \hline \multirow{2}{*}{MOIT (21\({}^{\prime}\)) [51]} & Best & - & - & - & - & - & - & - & - & - \\  & Last & 93.1 & 90.0 & 79.0 & 69.6 & 92.0 & 73.0 & 64.6 & 46.6 & 36.0 & 55.0 \\ \hline \multirow{2}{*}{LongReMix (23\({}^{\prime}\)) [38]} & Best & \(\mathbf{96.3\pm}\) & 95.1 \(\pm\) & \(\mathbf{93.8\pm}\) & 79.9 \(\pm\) & \(\mathbf{94.7\pm}\) & \(\mathbf{77.9\pm}\) & \(\mathbf{75.5\pm}\) & \(\mathbf{62.3\pm}\) & \(\mathbf{34.7\pm}\) & \(\mathbf{59.8\pm}\) \\  & Last & 0.1 & 0.1 & 0.2 & 2.7 & 0.1 & 0.2 & 0.2 & 0.5 & 0.3 & 0.1 \\ \hline \multirow{2}{*}{CRAS} & Best & \(\mathbf{96.0\pm}\) & 94.8 \(\pm\) & 93.3 \(\pm\) & \(\mathbf{79.1\pm}\) & \(\mathbf{94.3\pm}\) & \(\mathbf{77.5\pm}\) & \(\mathbf{74.9\pm}\) & \(\mathbf{61.7\pm}\) & \(\mathbf{30.7\pm}\) & \(\mathbf{54.9\pm}\) \\  & Last & 0.1 & 0.1 & 0.2 & 3.1 & 0.1 & 0.2 & 0.2 & 0.5 & 5.9 & 0.4 \\ \hline \multirow{2}{*}{CRAS} & Best & \(\mathbf{95.7\pm}\) & \(\mathbf{95.4\pm}\) & \(\mathbf{93.8\pm}\) & \(\mathbf{80.0\pm}\) & 93.1 \(\pm\) & \(\mathbf{79.5\pm}\) & \(\mathbf{77.0\pm}\) & \(\mathbf{65.0\pm}\) & \(\mathbf{34.5\pm}\) & \(\mathbf{78.0\pm}\) \\  & Last & 0.1 & 0.0 & 0.0 & 0.7 & 0.0 & 0.0 & 0.1 & 0.0 & 0.5 & 0.1 \\ \hline \multirow{2}{*}{CRAS} & Best & \(\mathbf{95.5\pm}\) & \(\mathbf{95.1\pm}\) & \(\mathbf{93.5\pm}\) & \(\mathbf{78.9\pm}\) & 91.9 \(\pm\) & \(\mathbf{79.0\pm}\) & \(\mathbf{76.5\pm}\) & \(\mathbf{64.7\pm}\) & \(\mathbf{34.1\pm}\) & \(\mathbf{77.6\pm}\) \\  & Last & 0.1 & 0.1 & 0.0 & 0.8 & 0.1 & 0.0 & 0.1 & 0.0 & 0.6 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test accuracy (%) on CIFAR-10 and CIFAR-100 datasets with symmetric and asymmetric noise. Results of baseline methods are copied from the original papers and [PERSON] et al. [25]. The maximum accuracy is expressed as Best, and the average accuracy of the last ten epochs is expressed as Last. The standard deviations are also reported for three different randomly generated types of noise. ### Ablation Study

#### 4.4.1 Influence of Each Component

We conducted an ablation study of the CRAS method on CIFAR-100 to investigate the influence of each of its components. We analyzed the results presented in Table 5 as follows:

* To study the influence of CR, we trained two networks (with and without CR) using a standard warm-up. CRAS without CR demonstrated a degraded performance for all of the noise rates. As the noise rate increased, CRAS without CR outperformed DivideMix, suggesting that AWL helps prevent overfitting to a small number of labels.