# BWLM: A Balanced Weight Learning Mechanism for Long-Tailed Image Recognition
## 4 Experiments
### Ablation Study
Our method BFS balances out the accuracy of Many and Few of CB and BS, indicating that our idea is effective. This compensates for the lack of CB for Few classes and BS for Many classes. But when weight decay is used to further balance weights, the accuracy can be improved greatly. In particular, CEW reaches 46.4%. BWLM learns the weights of Few classes from BSW and Many classes from CBW, increasing the accuracy to 47.5%. **Classifier's weight norms. ** Figure 5a, using the classifier weight norms of the ImageNet-LT validation set, further proves the effectiveness of weight learning. The classifier weight norms of the naive model have a relatively large numerical span from Many classes to Few classes and show a \"top-heavy\" downward trend. The addition of weight decay to other models has greatly shortened the weight gap between the Many and Few classes. Especially for our proposed BWLM, the classifier weight norm shows a small upward trend, which gives the Medium and Few classes a \"fighting power\" in the image recognition. **Classifier's weight norms. ** Figure 5b, using the classifier weight norms of the ImageNet-LT validation set, when the classes are sorted in descending \(n_{j}\) order (black dashed line). Blue line: a single model to learn the classifier weights. There is a significant difference between Many and Few classes. Orange line: weights after using weight decay for \(L_{CB}\). Green line: weights after using weight decay for \(L_{BS}\). Red line: weights after using weight decay for \(L_{BFS}\). (**b**) Descending speed of All classes accuracy between compared methods in CIFAR100-LT different IFs. The dashed line represents the comparison method in [64]. \"Focal+CR\": focal loss with curvature regularization; \"CE+CR\": cross entropy with curvature regularization; \"CB+CR\": CB with curvature regularization. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**ImageNet-LT**} \\ \cline{2-5}  & **Many** & **Medium** & **Few** & **All** \\ \hline naive & 57.6 & 32.5 & 13.4 & 39.6 \\ weight transfer & & & & \\ +CE & 55.5 & 48.5 & 19.4 & 44.6 \\ +CB & 51.6 & 45.2 & 18.0 & 41.5 \\ +BS & 52.9 & 47.7 & 25.3 & 44.6 \\ +BFS & 52.8 & 47.7 & 24.3 & 44.5 \\ +CEW & **62.8** & **51.6** & 13.1 & 46.4 \\ +CBW & **61.7** & 50.2 & 26.3 & 47.0 \\ +BSW & 58.2 & 50.1 & **29.7** & **47.3** \\ +BWLM & 60.0 & **50.8** & **26.9** & **47.5** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ablation study on ImageNet-LT with respect to accuracy (%). “naive”: single model with cross-entropy loss; “+”: after weight transfer in the second stage; “CE”: cross-entropy; “CB”: Class-Balanced focal loss; “BS”: balanced softmax; “BFS”: Balanced focal and softmax; “CEW”: CE with weight decay; “CBW”: CB with weight decay; “BSW”: BS with weight decay. The best and the second-best results are shown in **underline**bold** and **bold**, respectively. Figure 5: (**a**) The classifier weight norms of the ImageNet-LT validation set, when the classes are sorted in descending \(n_{j}\) order (black dashed line). Blue line: a single model to learn the classifier weights. There is a significant difference between Many and Few classes. Orange line: weights after using weight decay for \(L_{CB}\). Green line: weights after using weight decay for \(L_{BS}\). Red line: weights after using weight decay for \(L_{BFS}\). (**b**) Descending speed of All classes accuracy between compared methods in CIFAR100-LT different IFs. The dashed line represents the comparison method in [64]. “Focal+CR”: focal loss with curvature regularization; “CE+CR”: cross entropy with curvature regularization; “CB+CR”: CB with curvature regularization.