# Squeezing Backbone Feature Distributions to the Max for Efficient Few-Shot Learning
## 4 Results and Discussions
### Ablation Studies  
Ablation study on the proposed method: in this section, we have a closer look at the impact of our proposed methodology steps. The idea is to better understand the contribution of each step to the final performance. Namely, we conduct an ablation study on the prediction accuracy with or without (1) PEME, which is the proposed preprocessing steps on extracted raw features, and (2) proposed Boosted Min-sized Sinkhorn algorithm that integrates self-distillation for refined prototypes. Note that in the case of BMS*, the algorithm is equivalent to MAP presented in [1] without the newly proposed self-distillation method. In Table 4, we can see that both PEME and self-distillation play an important role in improving the prediction performance. As such, this experiment supports the interest of both steps to reach the best possible accuracy. \begin{table}
\begin{tabular}{c l l l l} \hline \hline \multicolumn{1}{c}{**Setting**} & \multicolumn{1}{c}{**Method**} & \multicolumn{1}{c}{**1-Shot**} & \multicolumn{1}{c}{**5-Shot**} \\ \hline \multirow{6}{*}{Inductive} & Baseline++ [18] & 40.44 \(\pm\) 0.75\% & 56.64 \(\pm\) 0.72\% \\  & Manifold Mixup [59] & 46.21 \(\pm\) 0.77\% & 66.03 \(\pm\) 0.71\% \\  & S2M2\_R [2] & 48.24 \(\pm\) 0.84\% & 70.44 \(\pm\) 0.75\% \\  & PT + NCM [1] & 48.37 \(\pm\) 0.19\% & 70.22 \(\pm\) 0.17\% \\  & PEM\_bE-NCM (ours) & \(\mathbf{50.71\pm 0.19\%}\) & \(\mathbf{73.15\pm 0.16\%}\) \\ \hline \multirow{6}{*}{Transductive} & LaplacianShot [51] & 55.46\% & 66.33\% \\  & Transfer + SGC [19] & 58.63 \(\pm\) 0.25\% & 73.46 \(\pm\) 0.17\% \\ \cline{1-1}  & PT + MAP [1] & 63.17 \(\pm\) 0.31\% & 76.43 \(\pm\) 0.19\% \\ \cline{1-1}  & PEM\_nE-BMS (ours) & 62.93 \(\pm\) 0.28\% & 79.10 \(\pm\) 0.18\% \\ \cline{1-1}  & PEM\_nE-BMS* (ours) & \(\mathbf{63.90\pm 0.31\%}\) & \(\mathbf{79.15\pm 0.18\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The 1-shot and 5-shot accuracy of state-of-the-art methods when performing cross-domain classification (backbone: WRN). Best results are in bold. \begin{table}
\begin{tabular}{c l l l l} \hline \hline \multicolumn{1}{c}{**Setting**} & \multicolumn{1}{c}{**Method**} & \multicolumn{1}{c}{**1-Shot**} & \multicolumn{1}{c}{**5-Shot**} \\ \hline \multirow{6}{*}{Transductive} & DSN-MR [58] & ResNet12 & 78.00 \(\pm\) 0.90\% & 87.30 \(\pm\) 0.60\% \\  & Transfer + SGC [19] & WRN & 83.90 \(\pm\) 0.22\% & 88.76 \(\pm\) 0.15\% \\  & MCT [53] & ResNet12 & 87.28 \(\pm\) 0.70\% & 90.50 \(\pm\) 0.43\% \\ \cline{1-1}  & PT + MAP [1] & WRN & 87.69 \(\pm\) 0.23\% & 90.68 \(\pm\) 0.15\% \\ \cline{1-1}  & LST + MAP [57] & WRN & 87.79 \(\pm\) 0.23\% & 90.73 \(\pm\) 0.15\% \\ \cline{1-1}  & PEM\_nE-BMS (ours) & WRN & 86.93 \(\pm\) 0.23\% & 91.18 \(\pm\) 0.15\% \\ \cline{1-1}  & PEM\_nE-BMS* (ours) & WRN & \(\mathbf{87.83\pm 0.22\%}\) & \(\mathbf{91.20\pm 0.15\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
**Generalization to backbone architectures. ** To further stress the interest of the ingredients inn the proposed method reaching top performance, in Table 5 we investigate the impact of our proposed method on different backbone architectures and benchmarks in the transductive setting. For comparison purposes, we also replace our proposed BMS algorithm with a standard K-Means algorithm where class prototypes are initialized with the available labeled samples for each class. We can observe that: (1) the proposed method consistently achieves the best results for any fixed backbone architecture, (2) the feature extractor trained on WRN outperforms the others with our proposed method on different benchmarks, (3) there are significant drops in accuracy with k-means, which stresses the interest of BMS, and (4) the prior on \(\mathbf{Q}\) (BMS vs. BMS*) is of major interest for 1-shot, boosting the performance by an approximation of 1% on all tested feature extractors. Overall, these experiments demonstrate the interest of the proposed methodology with respect to existing alternatives.