# Squeezing Backbone Feature Distributions to the Max for Efficient Few-Shot Learning
## 4 Results and Discussions
### Ablation Studies
Preprocessing impact: in Table 6, we compare our proposed feature preprocessing PEME with other preprocessing techniques such as batch normalization, which standardizes extracted feature values into \([0,1]\) for a considered task, along with other ones being used in [35]. The experiment is conducted on miniImageNet (backbone: WRN). For all that is put into comparison, we run either an NCM classifier or BMS after preprocessing, depending on the settings. The obtained results clearly show the interest of PEME compared with existing alternatives, and we also observe that the power transform helps increase the accuracy on both inductive and transductive settings. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**BMS*} & \multicolumn{2}{c}{**Accuracy**} \\
**w/PEME** & **w/Self-Distillation** & **1-Shot** & **5-Shot** \\ \hline  & & 75.60 \(\pm\) 0.29\% & 84.13 \(\pm\) 0.16\% \\ \hline ✓ & & 82.92 \(\pm\) 0.26\% & 88.82 \(\pm\) 0.13\% \\ \hline  & ✓ & 80.19 \(\pm\) 0.27\% & 87.40 \(\pm\) 0.13\% \\ \hline ✓ & ✓ & **83.35 \(\pm\) 0.25**\% & **89.53 \(\pm\) 0.13**\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ablation study on our proposed PEME and BMS* with self-distillation on miniImageNet (backbone: WRN). Best results are in bold. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**miniImageNet**} & \multicolumn{2}{c}{**CUB**} & \multicolumn{2}{c}{**CIFAR-FS**} \\
**Method** & **Backbone** & **1-Shot** & **5-Shot** & **1-Shot** & **5-Shot** & **1-Shot** & **5-Shot** \\ \hline \multirow{3}{*}{K-MEANS} & ResNet12 & 72.73 \(\pm\) 0.23\% & 84.05 \(\pm\) 0.14\% & 87.35 \(\pm\) 0.19\% & 92.31 \(\pm\) 0.10\% & 78.39 \(\pm\) 0.24\% & 85.73 \(\pm\) 0.16\% \\  & ResNet18 & 73.08 \(\pm\) 0.22\% & 84.67 \(\pm\) 0.14\% & 87.16 \(\pm\) 0.19\% & 91.97 \(\pm\) 0.09\% & 79.95 \(\pm\) 0.23\% & 86.74 \(\pm\) 0.16\% \\  & WRN & 76.67 \(\pm\) 0.22\% & 86.73 \(\pm\) 0.13\% & 88.28 \(\pm\) 0.19\% & 92.37 \(\pm\) 0.10\% & 83.69 \(\pm\) 0.22\% & 89.19 \(\pm\) 0.15\% \\ \hline \multirow{3}{*}{BMS (ours)} & ResNet12 & 77.62 \(\pm\) 0.28\% & 86.95 \(\pm\) 0.15\% & 90.14 \(\pm\) 0.19\% & 94.30 \(\pm\) 0.10\% & 81.65 \(\pm\) 0.25\% & 88.38 \(\pm\) 0.16\% \\  & ResNet18 & 79.30 \(\pm\) 0.27\% & 87.94 \(\pm\) 0.14\% & 90.50 \(\pm\) 0.19\% & 94.29 \(\pm\) 0.09\% & 84.16 \(\pm\) 0.24\% & 89.39 \(\pm\) 0.15\% \\  & WRN & 82.07 \(\pm\) 0.25\% & 89.51 \(\pm\) 0.13\% & 91.01 \(\pm\) 0.18\% & 94.60 \(\pm\) 0.09\% & 86.93 \(\pm\) 0.23\% & 91.18 \(\pm\) 0.15\% \\ \hline \multirow{3}{*}{BMS* (ours)} & ResNet12 & 79.03 \(\pm\) 0.28\% & 87.01 \(\pm\) 0.15\% & 91.34 \(\pm\) 0.19\% & 94.32 \(\pm\) 0.09\% & 82.87 \(\pm\) 0.27\% & 88.43 \(\pm\) 0.16\% \\  & ResNet18 & 80.56 \(\pm\) 0.27\% & 87.98 \(\pm\) 0.14\% & 91.39 \(\pm\) 0.19\% & 94.31 \(\pm\) 0.09\% & 85.17 \(\pm\) 0.25\% & 89.42 \(\pm\) 0.16\% \\ \cline{1-1}  & WRN & **83.35 \(\pm\) 0.25**\% & **89.53 \(\pm\) 0.13**\% & **91.91 \(\pm\) 0.18**\% & **94.62 \(\pm\) 0.09**\% & **87.83 \(\pm\) 0.22**\% & **91.20 \(\pm\) 0.15**\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The 1-shot and 5-shot accuracy of the proposed method on different backbones and benchmarks. Comparison with the k-means algorithm. Best results are in bold. Effect of power transform: we firstly conduct a Gaussian hypothesis test on each of the 640 coordinates of raw extracted features (backbone: WRN) for each of the 20 novel classes (dataset: miniImageNet). Following [PERSON] and [PERSON]'s methodology [61; 62] and \(p=1e-3\), only one of the \(640\times 20=12800\) tests return positive, suggesting a very low pass rate for raw features. However, after applying the power transform, we record a pass rate that surpasses 50%, suggesting a considerably increased number of positive results for Gaussian tests. This experiment shows the effect of power transform being able to adjust feature distributions into more Gaussian-like ones.