# Deep Learning for Neuromuscular Control of Vocal Source for Voice Production
## 3 Results
### Control System  
Figure 8 shows how the cost function given in Equation (13) was reduced as a function of the epoch (sample) number for the training data. The cost reduced to 0.0032 in normalized units at the end of the 8820 epochs. The error did not distribute equally across the three types of features/parameters. The individual cost values in normalized units for control, somatosensory, and acoustic targets were obtained as 0.0067, 0.0019, and 0.0011, respectively, at the end of the training. The error was highest for predicting muscle activations. Physiologically, a set of somatosensory and acoustic features could be achieved by many combinations of muscle activations, described as motor equivalence. Therefore, higher errors in muscle states does not necessarily imply error in reaching the targets but the presence of alternate activations that result in the same somatosensory and acoustic targets. A combined cost value of 0.0041 was obtained for the test data in normalized units at the end of 0.2 s of simulation. The individual cost values in normalized units for muscle, somatosensory, and acoustic features from the test data were obtained as 0.0076, 0.0021, and 0.0027, respectively, at the end of the 0.2 s of simulation. This indicates that the performance decreased on the test data, but only slightly. Here, as well, the major error occurred in reaching the muscle targets. Figure 9 shows the example target and predicted radiated pressure (sound) signals generated by _LeTalker_ for some of the test data cases. The first row shows the pressure signal with an f\({}_{\text{o}}\) in the speech range, the second row shows a signal with a higher f\({}_{\text{o}}\), the third row shows the waveforms with higher SPL, the fourth row shows the waveforms with a lower  
Figure 7: Difference between targets and predictions for the four acoustic features from PtoA NN test data in actual units. spectral centroid, and the fifth row shows the waveforms with more noise in the signal. From the waveforms, it can be observed that the predicted signals reached the steady state between 40 and 80 ms, typically seen in _LeTalker_. The predicted radiated pressure signals obtained by the control of neural architecture were very similar to the targeted signals. However, there were slight differences between the targets and the predicted signals. The difference is apparent in the pitch and amplitude of the signals. For example, the f\({}_{0}\) is lower in the predicted signal compared to the targeted signal (second row), and the amplitude is lower in the predicted signal compared to the targeted signal (fourth row). The differences in other two features cannot be observed easily from the waveforms. Therefore, the targeted features and their corresponding predictions for these five examples are given in Table 2.  
From Table 2, it can be observed that for the muscle parameters, a significant difference occurred in reaching LCA activation (\(a_{LC}\)). There were slight differences in the prediction of \(a_{CT}\) and \(a_{TA}\) as well (first and fifth row). Lung pressure was predicted accurately for all five examples. With regard to somatosensory features, the differences are small for all the four features. For the acoustic features, there are significant differences in some cases for all the features. These results indicate that across all the test cases, the error would be higher in the prediction of \(a_{LC}\), and moderately high in the prediction of \(a_{CT}\), \(a_{TA}\) and the four acoustic features. Figure 8: Cost value used to train the control system as a function of sample (epoch) number. Figure 10 shows the error in % for all the twelve features/parameters from the controller test data. Like the boxplots for PtoA NN results, the \(y\)-axis was limited to exclude the outliers for better visibility. As observed from the individual cost values, the error in % is higher in predicting muscle targets (\(\pm\)80%) than somatosensory and acoustic targets (\(\pm\)30%), excluding outliers.