## 3 Learned Separation
### Training
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Instrument** & **SDR** & **SIR** & **SAR** \\ \hline \multirow{6}{*}{Ours} & Oboe (a.) & 9.6 & 47.2 & 9.6 \\  & Epubonium (a.) & 8.7 & 33.7 & 8.7 \\ \cline{2-5}  & Piccolo (s.) & 17.2 & 36.5 & 17.2 \\  & Organ (s.) & 14.3 & 50.3 & 14.3 \\ \cline{2-5}  & Piccolo (s.) & 6.8 & 22.1 & 6.9 \\  & Organ (s.) & 7.3 & 19.2 & 7.7 \\  & Oboe (s.) & 8.3 & 46.3 & 8.3 \\ \hline \multirow{6}{*}{[20]} & Oboe (a.) & 18.6 & 33.6 & 18.8 \\  & Epubonium (a.) & 14.7 & 31.5 & 14.7 \\ \cline{2-5}  & Piccolo (s.) & 11.2 & 25.9 & 11.3 \\ \cline{2-5}  & Organ (s.) & 10.1 & 20.7 & 10.5 \\ \cline{2-5}  & Piccolo (s.) & 4.2 & 24.8 & 4.3 \\ \cline{2-5}  & Organ (s.) & 6.0 & 20.0 & 6.3 \\ \cline{2-5}  & Oboe (s.) & 5.3 & 12.4 & 6.4 \\ \hline \multirow{6}{*}{[18]} & Oboe (a.) & 8.7 & 25.8 & 8.8 \\  & Epubonium (a.) & 4.6 & 14.5 & 5.3 \\ \cline{1-1} \cline{2-5}  & Piccolo (s.) & 14.2 & 27.9 & 14.4 \\ \cline{1-1}  & Organ (s.) & 11.8 & 25.1 & 12.1 \\ \cline{1-1} \cline{2-5}  & Piccolo (s.) & 6.5 & 20.0 & 6.7 \\ \cline{1-1}  & Organ (s.) & 6.6 & 17.3 & 7.1 \\ \cline{1-1}  & Oboe (s.) & 9.0 & 21.9 & 9.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the separation algorithms on the data by [18]. Instruments labeled as “s.” are synthetic, those labeled as “a.” are acoustic. Best numbers are highlighted. separation can be achieved, these dictionaries are not attained as the result of training, even when they are supplied as the initial value. Due to the use of neural networks, our approach is very flexible with respect to the choice of the loss function. In the spirit of blind separation, we chose the weights for the respective distances such that they constitute a reasonable comprise for all the samples on which we tested them, but this choice is not necessarily optimal for the individual samples. While a linear combination is the most straight-forward way to account for all the considered distances, a non-linear mapping could potentially be better. Moreover, even though we have not found any distance functions yielding better performance than the ones we use, more experiments could be conducted. With our approach, we hope to provide a blueprint for the combined use of backpropagation gradients and policy gradients in the application of neural networks on non-convex parameter identification problems. [PERSON] devised, implemented, and tested the algorithm. [PERSON] and [PERSON] wrote the manuscript and conceived additional experiments. [PERSON] supervised the research and revised the manuscript. All authors have read and agreed to the published version of the manuscript

[PERSON] and [PERSON] acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-project number 281474342/GRK2224/1. Not applicable. The functioning source code for the algorithm is available on GitHub ([[https://github.com/rgcda/Musiep](https://github.com/rgcda/Musiep)]([https://github.com/rgcda/Musiep](https://github.com/rgcda/Musiep)), accessed on 6 September 2021) under the GNU General Public License (version 3). The input data from [18] can be downloaded from the respective website ([[https://sites.google.com/site/mperesult/musicSeparationresults](https://sites.google.com/site/mperesult/musicSeparationresults)]([https://sites.google.com/site/mperesult/musicSeparationresults](https://sites.google.com/site/mperesult/musicSeparationresults)), accessed on 6 September 2021). For all the other samples, we provide the input data along with the best-case separation results on the institute website ([[https://www.math.colostate.edu/~king/software.html#Musiep](https://www.math.colostate.edu/~king/software.html#Musiep)]([https://www.math.colostate.edu/~king/software.html#Musiep](https://www.math.colostate.edu/~king/software.html#Musiep)), accessed on 6 September 2021). Due to the stochastic nature of parallel computing, training results are not exactly reproducible.