# DYMatch: Semi-Supervised Learning with Dynamic Pseudo Labeling and Feature Consistency
## 4 Experiments
### Ablation Study  
Since DYMatch combines two effective methods, i.e., the dynamic pseudo-label estimation method based on the Gaussian mixture model and the consistency regularization method based on feature correlation, the ablation studies were conducted to provide a deeper understanding of the factors contributing to DYMatch's good performance. In this subsection, the results are presented only for the experiments involving 40 and 4000 labeled data on CIFAR-10. As shown in Table 6, the error rates of DYMatch_PL (i.e., DYMatch with only dynamic pseudo-label estimation method based on the Gaussian mixture model) were lower than those of DYMatch_CR (i.e., DYMatch with only consistency regularization method based on feature correlation), but the combination of these two methods led to the better performance of DYMatch than DYMatch_PL and DYMatch_CR. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Office31 (31)** & \multicolumn{2}{c}{**Office-Home (65)**} & \multicolumn{2}{c}{**DomainNet (345)**} \\ \hline \multirow{2}{*}{**Model**} & **10 Labels** & **10 Labels** & **50 Labels** & **50 Labels** & **500 Labels** \\  & **per Class** & **per Class** & **per Class** & **per Class** \\ \hline ReMixMatch [8] & 30.12 \(\pm\) 0.33 & 68.69 \(\pm\) 0.07 & 46.42 \(\pm\) 0.36 & 82.54 \(\pm\) 0.11 & 76.23 \(\pm\) 0.23 \\ FixMatch [9] & 28.36 \(\pm\) 0.20 & 55.73 \(\pm\) 0.23 & 46.27 \(\pm\) 0.23 & 79.12 \(\pm\) 0.03 & 73.79 \(\pm\) 0.15 \\ FlexMatch [10] & 25.13 \(\pm\) 0.33 & 54.56 \(\pm\) 0.30 & 43.99 \(\pm\) 0.03 & 66.12 \(\pm\) 0.15 & 53.45 \(\pm\) 0.23 \\ DoubleMatch [23] & 26.30 \(\pm\) 0.30 & 56.45 \(\pm\) 0.13 & 45.25 \(\pm\) 0.13 & 70.32 \(\pm\) 0.32 & 55.43 \(\pm\) 0.12 \\ SimMatch [47] & 26.09 \(\pm\) 0.12 & 53.65 \(\pm\) 0.09 & 45.01 \(\pm\) 0.04 & 65.95 \(\pm\) 0.20 & 51.33 \(\pm\) 0.04 \\ SoftMatch [11] & 22.50 \(\pm\) 0.32 & 52.66 \(\pm\) 0.14 & 40.91 \(\pm\) 0.12 & 64.24 \(\pm\) 0.18 & **50.13 \(\pm\) 0.05** \\ \hline DYMatch (ours) & **20.31 \(\pm\) 0.26** & **52.29 \(\pm\) 0.26** & **40.42 \(\pm\) 0.10** & **63.81 \(\pm\) 0.10** & 50.93 \(\pm\) 0.07 \\ \hline Fully-Supervised & 13.54 & 32.48 & & 43.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The Error Rates for Other Object Recognition Datasets with Different Numbers of Labelled Images. (The numbers of data for each category contained in each domain adaptation dataset are given). The best result is in bold. The comparison between DYMatch_CR and DYMatch_PL highlights their differences in utilizing the unlabeled data. In DYMatch_CR, the feature maps were used after the backbone \(f(\cdot)\) for feature-correlation consistency regularization. However, the lack of selection on unlabeled data, a large amount of data that cannot be accurately identified by the model may greatly hinder the convergence of the model. On the contrary, DYMatch_PL employed the dynamic pseudo-label estimation method, which effectively filter the unlabeled data during the training process. Consequently, compared to DYMatch_CR, DYMatch_PL proved to be more effective in utilizing the unlabeled data. Moreover, the superior performance of DYMatch indicated that the combination of these two methods resulted in a more efficient utilization of unlabeled data. We also compared the performance of DYMatch when applying feature-correlation consistency regularization method at different layers, i.e., after the backbone \(f(\cdot)\) or after the classification module \(g(\cdot)\). DYMatch_F denotes DYMatch using the feature representation after the backbone \(f(\cdot)\), and DYMatch_G denotes DYMatch employing the feature representation after the classification module \(g(\cdot)\). Table 7 obviously shows that the error rates of DYMatch_G is significantly higher than that of DYMatch_F. This result also demonstrated that performing consistency regularization after the classification module \(g(\cdot)\) limited the performance of the model due to the coupling with the dynamic pseudo-label estimation method.