# BWLM: A Balanced Weight Learning Mechanism for Long-Tailed Image Recognition
## 4 Experiments
### Ablation Study  
**Choose \(\alpha\) of BWLM. ** In Formula (17), we set the hyperparameter \(\alpha\) to adjust the usage weights of CB and BS. \(\alpha\) represents the usage weight of CB, and \(1-\alpha\) represents the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **IF** & **Training Samples** & **Testing Samples** & **Classes** & **Max Class Size** & **Min Class Size** \\ \hline ImageNet-LT [34] & 256 & 115,846 & 50,000 & 1000 & 1280 & 5 \\ \hline  & 200 & 9502 & 10,000 & 100 & 500 & 2 \\ CIFAR100-LT [59] & 100 & 10,847 & 10,000 & 100 & 500 & 5 \\  & 50 & 12,608 & 10,000 & 100 & 500 & 10 \\  & 10 & 19,573 & 10,000 & 100 & 500 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specific information of five long-tailed image recognition datasets. Figure 3: The class frequency distributions of five datasets. (**Left**): it indicates that as IF increases, the larger the class index, the less the class sample. (**Right**): we use the large-scale dataset ImageNet-LT, which has IF = 256.  
usage weight of BS. Figure 4 shows the accuracy of various classes on the five datasets, and analyzes the impact of \(\alpha\) on All, Many, Medium, and Few classes of five datasets with different IFs. From the impact of \(\alpha\) on the accuracy of Many classes in Figure 4b, it can be seen that almost all datasets can achieve the optimal results when \(\alpha\) reaches its maximum value. It can be proven that CB reduces the redundancy of Many classes and focuses more on the accuracy of Many classes. In Figure 4c,d, Medium and Few classes can achieve optimal results when the value of \(\alpha\) is small. Therefore, BS focuses more on classes with less data volume, which can also be proven. For All classes in Figure 4a, as \(\alpha\) changes, the accuracy of all classes shows a slow downward trend in five datasets with different IFs. Since the number of Few classes is much more than that of Many classes, the overall performance of All classes is aligned with Few classes, that is, the optimal performance can be reached when \(\alpha\) is set to be small. Although the optimal value of IF = 100 is obtained when \(\alpha=0.7\), the accuracy difference is only 0.01 when \(\alpha=0.1\) and \(\alpha=0.7\). Therefore, we suggest using BWLM by first setting \(\alpha=0.1\) by default. In the comparison experiments, we select \(\alpha\) based on the optimal value of BWLM on the different datasets in Figure 4a. **The effect of each component. ** To make our proposed balancing technique more suitable for application in the second stage, we also include weight decay in the first stage. This effective non-learning technique can perform post hoc scales on the classifier learned in the first stage. Our results are based on the ImageNet LT results in Table 2, where the accuracy of different classes is listed for all algorithms. We divide it into two categories for comparison: CE, CB, BS, and BFS is the reweighting loss function; CEW, CBW, BSW, and BWLM is the method after adding weight decay to the reweighting loss function. Firstly, as the weight transfer CE for the first stage increases from 39.6% of the naive model to 44.6%, it indicates the importance of weight transfer. Secondly, it is also very important  
Figure 4: The impact of parameter \(\alpha\) on the accuracy of classes for datasets with different IFs. The blue star denotes the highest accuracy. (**a**) The impact of \(\alpha\) on the accuracy of All classes. (**b**) The impact of \(\alpha\) on the accuracy of Many classes. (**c**) The impact of \(\alpha\) on the accuracy of Medium classes. (**d**) When IF = 10, all classes are with more than 20 samples so Few classes do not exist and the accuracy of other IFs shows an irregular downward trend. to use the balance loss function to learn classifiers based on weight transfer. Then we find that using only the equilibrium loss function without weight decay slightly improves the accuracy for only Few classes.