## 5 Results
### Out-Of-Domain Generalization  
We evaluate _out-of-domain generalization_ by applying parameters inference and re-synthesis on two sets of audio samples either produced by other synthesizers, or with vocal imitations. We rely on the same evaluation method as previously described and provide results for the audio similarity in Table 2 (Right). Here, the overall distribution of scores remains consistent with previous observations. However, it seems that the average error is quite high, indicating a potentially distant reconstruction of some examples. This might be explained by the limited number of parameters used for training our models. Therefore, they cannot account for complex sounds with various types of modulations. Interestingly, while the addition of more parameters to perform the optimization allows to reduce the global approximation error in AE models, it seems to worsen the feed-forward estimation. This seems to further confirm our original hypothesis that feed-forward approaches are not able to handle advanced interactions in the parameters.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Out-of-Domain (32 p.)**} & \multicolumn{2}{c}{**Out-of-Domain (64 p.)**} \\ \cline{2-5}  & **SC** & **MSE** & **SC** & **MSE** \\ \hline \(MLP\) & \(2.348\pm 2.1\) & \(37.99\pm 7.8\) & \(4.534\pm 5.1\) & \(40.42\pm 3.7\) \\ \(CNN\) & \(2.311\pm 2.2\) & \(29.22\pm 8.2\) & \(6.329\pm 1.9\) & \(36.93\pm 2.3\) \\ \(ResNet\) & \(2.322\pm 1.6\) & \(31.07\pm 9.5\) & \(4.645\pm 3.1\) & \(27.46\pm 2.3\) \\ \hline \(AE\) & \(1.225\pm 2.2\) & \(27.37\pm 7.2\) & \(2.557\pm 1.7\) & \(27.16\pm 1.4\) \\ \(VAE\) & \(1.237\pm 1.3\) & \(27.06\pm 7.1\) & \(1.141\pm 1.2\) & \(27.15\pm 1.3\) \\ \(VAE\) & \(\mathbf{1.194\pm 1.5}\) & \(26.10\pm 6.4\) & \(\mathbf{0.999\pm 0.9}\) & \(25.13\pm 1.3\) \\ \(VAE_{flow}\) & \(1.193\pm 1.8\) & \(27.03\pm 6.4\) & \(1.022\pm 1.7\) & \(26.49\pm 1.3\) \\ \hline \(Flow_{reg}\) & \(1.201\pm 1.2\) & \(\mathbf{26.07\pm 7.7}\) & \(1.132\pm 1.6\) & \(\mathbf{24.74\pm 1.3}\) \\ \hline \(Flow_{dis.}\) & \(1.209\pm 1.4\) & \(26.77\pm 7.3\) & \(1.532\pm 1.8\) & \(27.89\pm 1.7\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison between baselines, *AEs, and our _flows_ on the out-of-domain parameters inference task. We report across-folds mean and variance for parameters (MSE) and audio (SC and MSE) errors.  
Figure 4: _Latent neighborhoods_. We select two examples from the test set that map to distant locations in the latent space \(\mathbf{z}\) and perform random sampling in their local neighborhood to observe the parameters and audio. We also display the latent interpolation between those points.  
In order to better understand the results and limits of our proposal, we display in Figure 3 the resynthesis of random examples taken from the synthesizer (left) and vocal imitations (right) datasets. As we can see, in all cases, our proposal accurately reproduces the temporal spectral shape of target sounds, even if the timbre is somewhat distant. Upon closer listening, it seems that the models fail to reproduce the local timbre of voices but performs quite well with sounds from other synthesizers. However, the evolution of the spectral shape is still reproduced. Interestingly, this provides a form of _vocal sketching control_ where the user inputs vocal imitations of the sound that he is looking for. This allows to quickly produce an approximation of the intended sound and, then, exploring the audio neighborhood of the sketch for intuitive refinement.