# Squeezing Backbone Feature Distributions to the Max for Efficient Few-Shot Learning
## 4 Results and Discussions
### Ablation Studies
We note that, interestingly, the performance of the method appears quite robust to a non-optimal choice of these parameters. Figure 4: Accuracy of 5-way, 1-shot classification setting on minilmageNet, CUB and CIFAR-FS as a function of \(q\). Figure 5: _Cont._  
Figure 3: Plot of feature vectors (extracted from WRN) from 3 randomly selected classes (each with its own color). (**left**) Naive features. (**right**) Preprocessed features using power transform. Convergence analysis: in this section, we discuss the convergence of the proposed method in Algorithm 2, namely the convergence of **P** as a function of the number of iteration step noted \(n_{step}\). We conduct this experiment in a 5-way, 1-shot setting on miniImageNet (backbone: WRN). In Figure 6 (left), we depict \(\|\Delta\textbf{P}\|_{2}\) as a function of \(n_{step}\), with \(\|\Delta\textbf{P}\|_{2}\) being defined as \(\|\textbf{P}(t+1)-\textbf{P}(t)\|^{2},1\leq t\leq n_{step}\), namely the Euclidean difference between the current **P** and the one computed in the previous step. Furthermore, we remind the reader that the goal of the proposed algorithm is to minimize the energy computed in Equation (5). Therefore, in Figure 6 (right), we depict the energy (value of Equation (5)) as a function of \(n_{step}\). We can see that both \(\|\Delta\textbf{P}\|_{2}\) and energy tend to stabilize with more iteration steps. Proposed method on backbones pre-trained with external data: in this experiment, we compare our proposed method BMS* with the work in [63] that pre-trains the backbone with the help of external illumination data for augmentation, followed by PT + MAP in [1] for class center estimation. Here, we use the same backbones as [63] and replace PT + MAP with our proposed BMS* under the same conditions. Results are presented in Table 7. Note that we also show the re-implemented results of [63], and our method reaches superior performance on all tested benchmarks using external data in [63]. \begin{table}
\begin{tabular}{c l l l} \hline \hline
**Benchmark** & **Method** & **1-Shot** & **5-Shot** \\ \hline \multirow{3}{*}{miniImageNet} & Illu-Aug [63] & \(82.99\pm 0.23\%\) & \(89.14\pm 0.12\%\) \\  & Illu-Aug-_re_ & \(83.53\pm 0.25\%\) & \(89.38\pm 0.12\%\) \\  & \(\text{PEM}_{\text{n}}\text{E-BMS*}\) (ours) & \(\mathbf{83.85\pm 0.25\%}\) & \(\mathbf{90.07\pm 0.12\%}\) \\ \hline \multirow{3}{*}{CUB} & Illu-Aug [63] & \(94.73\pm 0.14\%\) & \(96.28\pm 0.08\%\) \\  & Illu-Aug-_re_ & \(94.63\pm 0.15\%\) & \(96.06\pm 0.08\%\) \\  & \(\text{PEM}_{\text{n}}\text{E-BMS*}\) (ours) & \(\mathbf{94.78\pm 0.15\%}\) & \(\mathbf{96.43\pm 0.07\%}\) \\ \hline \multirow{3}{*}{CIFAR-FS} & Illu-Aug [63] & \(87.73\pm 0.22\%\) & \(91.09\pm 0.15\%\) \\  & Illu-Aug-_re_ & \(87.76\pm 0.23\%\) & \(91.04\pm 0.15\%\) \\ \cline{1-1}  & \(\text{PEM}_{\text{n}}\text{E-BMS*}\) (ours) & \(\mathbf{87.83\pm 0.23\%}\) & \(\mathbf{91.49\pm 0.15\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The proposed method on backbones pre-trained with external data. Note that _-re_ denotes the re-implementation of an existing method. Best results are in bold. Figure 5: Accuracy of the proposed method on miniImageNet (backbone: WRN) as a function of training epoch \(e\) (**top**) and regulation parameter \(\lambda\) (**bottom**). Figure 6: Convergence of BMS (1-shot on miniImagenet). (**left**) \(\|\Delta\textbf{P}\|_{2}\) as a function of \(n_{step}\). (**right**) Energy (1-shot on miniImagenet) as a function of \(n_{step}\). Proposed method on Few-Shot Open-Set Recognition: Few-Shot Open-Set Recognition (FSOR) as a new trending topic deals with the fact that there are open data mixed in query set \(\mathbf{Q}\) that do not belong to any of the supposed classes used for label predictions. Therefore, this often requires a robust classifier that is able to correctly classify the non-open data as well as rejecting the open ones. In Table 8, we apply our proposed PEME for feature preprocessing, followed by an NCM classifier and compare the results with other state-of-the-art alternatives.