# Squeezing Backbone Feature Distributions to the Max for Efficient Few-Shot Learning
## 4 Results and Discussions
### Proposed Method on Merged Features  
In this section, we investigate the effect of our proposed method on merged features. Namely, we perform a direct concatenation of raw feature vectors extracted from multiple backbones at the beginning, followed by BMS. In Table 9, we chose the feature vectors from three backbones (WRN, ResNet18 and ResNet12) and evaluated the performance with different combinations. We observe that (1) a direct concatenation, depending on the backbones, can bring about 1% gain in both 1-shot and 5-shot settings compared with the results in Table 5 with feature vectors extracted from one single feature extractor. (2) BMS\({}^{\star}\) reached new state-of-the-art results on few-shot learning benchmarks with feature vectors concatenated from WRN, ResNet18 and ResNet12, given that no external data are used. To further study the impact of the number of backbones on prediction accuracy, in Figure 7 we depict the performance of our proposed method as a function of the number of backbones. Note that, here, we operate on feature vectors of 6 WRN backbones (dataset: miniImageNet) concatenated one after another, which makes a total of 6 slots corresponding to a \(640\times 6=3840\) feature size. Each of them is trained the same way as in [2], and we randomly select the multiples of 640 coordinates within the slots to denote the number \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**miniImageNet**} & \multicolumn{4}{c}{**tieredImageNet**} \\  & \multicolumn{2}{c}{**1-Shot**} & \multicolumn{2}{c}{**5-Shot**} & \multicolumn{2}{c}{**1-Shot**} & \multicolumn{2}{c}{**5-Shot**} \\
**Method** & **Acc** & **AUROC** & **Acc** & **AUROC** & **Acc** & **AUROC** & **Acc** & **AUROC** \\ \hline ProtoNet [55] & 64.01\% & 51.81\% & 80.09\% & 60.39\% & 68.26\% & 60.73\% & 83.40\% & 64.96\% \\ FEAT [28] & 67.02\% & 57.01\% & 82.02\% & 63.18\% & 70.52\% & 63.54\% & 84.74\% & 70.74\% \\ NN [64] & 63.82\% & 56.96\% & 80.12\% & 63.43\% & 67.73\% & 62.70\% & 83.43\% & 69.77\% \\ OpenMax [65] & 63.69\% & 62.64\% & 80.56\% & 62.27\% & 68.28\% & 60.13\% & 83.48\% & 65.51\% \\ PEELER [66] & 65.86\% & 60.57\% & 80.61\% & 67.35\% & 69.51\% & 65.20\% & 84.10\% & 73.27\% \\ SnaTCHer [67] & 67.60\% & 70.17\% & 82.36\% & 77.42\% & 70.85\% & 74.95\% & 85.23\% & 82.03\% \\ PEM\({}_{\text{b}}\)E-NCM (ours) & **68.43**\% & **72.10**\% & **84.67**\% & **80.04**\% & **71.87**\% & **75.44**\% & **87.09**\% & **83.85**\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Accuracy and AUROC of the proposed method for Few-Shot Open-Set Recognition. Best results are in bold. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**miniImageNet**} & \multicolumn{2}{c}{**CUB**} & \multicolumn{2}{c}{**CIFAR-FS**} \\
**Backbone** & **1-Shot** & **5-Shot** & **1-Shot** & **5-Shot** & **1-Shot** & **5-Shot** \\ \hline RN18 + RN12 & 80.32\% & 89.07\% & 92.31\% & 95.62\% & 85.44\% & 90.58\% \\ WRN + RN12 & 82.63\% & 90.43\% & 92.69\% & 95.96\% & 87.11\% & 91.50\% \\ WRN + RN18 & 83.05\% & 90.57\% & 92.66\% & 95.79\% & 87.53\% & 91.70\% \\ WRN + RN18 + RN12 & 82.90\% & 90.64\% & 93.32\% & 96.31\% & 87.62\% & 91.84\% \\ WRN + RN18 + RN12 \({}^{\star}\) & 84.37\% & 90.69\% & **94.26**\% & **96.32**\% & **88.44**\% & **91.86**\% \\
6\(\times\)WRN \({}^{\star}\) & **85.54**\% & **91.53**\% & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) \\ \hline \hline \multicolumn{6}{l}{\({}^{\star}\): BMS\({}^{\star}\).} \\ \end{tabular}
\end{table} 
Table 9: The 1-shot and 5-shot accuracy on miniImageNet, CUB and CIFAR-FS on our proposed PEM\({}_{\text{b}}\)E-BMS with multi-backbones (backbone training procedure follows [2], ’+’ denotes a concatenation of backbone features). of concatenated backbones used. The performance result is the average of 100 random selections, and we test with both BMS and BMS* for 1-shot, and BMS* for 5-shot.