## 5 Results
### Increasing Parameters Complexity  
We evaluate the robustness of different models by increasing the number of parameters from 16 to 32 and finally 64 (Table 1). As we can see, the accuracy of baseline models is highly degraded, notably on audio reconstruction. Interestingly, the gap between parameter and audio accuracies is strongly increased. This seems logical as the relative importance of parameters in larger sets provoke stronger  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Test Set–16 Parameters**} & \multicolumn{3}{c}{**Test Set–32 Parameters**} & \multicolumn{3}{c}{**Test Set–64 Parameters**} \\ \cline{2-10} \multicolumn{1}{c}{} & **Params** & \multicolumn{2}{c}{**Audio**} & **Params** & \multicolumn{2}{c}{**Audio**} & **Params** & \multicolumn{2}{c}{**Audio**} \\ \cline{2-10} \multicolumn{1}{c}{} & \(MSE_{n}\) & \(SC\) & \(MSE_{n}\) & \(MSE_{n}\) & \(SC\) & \(MSE_{n}\) & \(MSE_{n}\) & \(SC\) & \(MSE_{n}\) \\ \hline \(MLP\) & \(0.236\pm 0.44\) & \(6.226\pm 0.13\) & \(9.548\pm 3.1\) & \(0.218\pm 0.46\) & \(13.51\pm 3.1\) & \(36.48\pm 11.9\) & \(0.185\pm 0.41\) & \(39.59\pm 6.7\) & \(49.58\pm 2.7\) \\ \(CNN\) & \(0.171\pm 0.45\) & \(1.372\pm 0.29\) & \(6.329\pm 1.9\) & \(0.159\pm 0.46\) & \(19.18\pm 4.7\) & \(33.40\pm 9.4\) & \(0.202\pm 0.37\) & \(52.48\pm 7.2\) & \(76.13\pm 8.9\) \\ \(ResNet\) & \(0.191\pm 0.43\) & \(1.004\pm 0.35\) & \(6.422\pm 1.9\) & \(0.196\pm 0.49\) & \(10.37\pm 1.8\) & \(31.13\pm 9.8\) & \(0.248\pm 0.43\) & \(29.18\pm 3.8\) & \(78.15\pm 9.8\) \\ \hline \(AE\) & \(0.181\pm 0.40\) & \(0.893\pm 0.13\) & \(5.557\pm 1.7\) & \(0.169\pm 0.40\) & \(5.566\pm 12.1\) & \(17.71\pm 6.9\) & \(0.198\pm 0.37\) & \(81.23\pm 2.4\) & \(34.07\pm 2.4\) \\ \(VAE\) & \(0.182\pm 0.32\) & \(0.810\pm 0.03\) & \(4.901\pm 1.053\) & \(0.549\pm 1.4\) & \(16.85\pm 6.1\) & \(0.171\pm 0.37\) & \(5.125\pm 1.1\) & \(33.10\pm 2.4\) \\ \(WAE\) & \(\mathbf{0.159\pm 0.37}\) & \(0.787\pm 0.05\) & \(4.979\pm 1.5\) & \(\mathbf{0.147\pm 0.33}\) & \(3.967\pm 0.88\) & \(16.64\pm 6.2\) & \(\mathbf{0.167\pm 0.36}\) & \(8.960\pm 1.8\) & \(\mathbf{32.59\pm 2.1}\) \\ \(VAE_{flow}\) & \(0.199\pm 0.32\) & \(0.838\pm 0.02\) & \(4.975\pm 1.4\) & \(0.164\pm 0.34\) & \(1.418\pm 0.23\) & \(17.74\pm 6.8\) & \(0.174\pm 0.36\) & \(6.721\pm 1.4\) & \(38.81\pm 2.3\) \\ \hline \(Flow_{reg}\) & \(0.197\pm 0.31\) & \(\mathbf{0.752\pm 0.05}\) & \(\mathbf{4.409\pm 1.6}\) & \(0.193\pm 0.32\) & \(\mathbf{0.911\pm 1.4}\) & \(\mathbf{16.61\pm 7.4}\) & \(0.178\pm 0.37\) & \(\mathbf{4.794\pm 1.8}\) & \(\mathbf{34.49\pm 2.2}\) \\ \hline \(Flow_{dis}\) & \(0.199\pm 0.31\) & \(0.831\pm 0.04\) & \(5.103\pm 2.1\) & \(0.197\pm 0.42\) & \(1.481\pm 1.8\) & \(17.12\pm 7.9\) & \(0.182\pm 0.38\) & \(8.122\pm 1.8\) & \(34.97\pm 2.3\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison between baselines, * AEs, and our _flows_ on the test set with 16, 32, and 64 parameters. We report across-folds mean and variance for parameters (Mean-Squared Error [\(MSE_{n}\)]) and audio (Spectral Convergence [\(SC\)] and \(MSE_{n}\)) errors. The best results are indicated in bold.  
impacts on the resulting audio. Also, it should be noted that \(VAE*\) models now outperform baselines even on parameters accuracy. Although our proposal also suffers from larger sets of parameters, it appears as the most resilient and can still cope with this higher complexity. While the gap between AE variants is more pronounced, the _flows_ strongly outperform all methods (\(F=8.13\), \(p<0.001\)).