# Deep Learning for Neuromuscular Control of Vocal Source for Voice Production
## 4 Discussion  
The current study focused on developing a neural-network-based control system for the vocal source. One acoustics feedforward controller (afdc) and two feedback controllers (sfbc and afbc) were used to generate muscle activations and lung pressure to control the vocal source. A three-mass-model-based vocal system called _LeTalker_ was used as the physical plant. The _LeTalker_ generates somatosensory features as output, but the acoustic features should be computed from the oral pressure signal. Therefore, in the current study, a neural network (PtoA NN) was trained to compute the four acoustic features using 25 ms of the oral pressure signal. The results indicated that the PtoA NN was able to predict the four acoustic features very accurately. The error was less than \(\pm\)6% for all the four acoustic features, excluding the outliers. The number of outliers ranged between 2.7% and 8.6% for the four acoustic features. A significant number of outliers in the data is expected because the lung pressure and the three muscle activations were varied randomly to generate the data. Unusual input combinations would result in several configurations that does not result in natural phonation, making the predictions extremely difficult. However, varying the input parameters randomly was necessary to explore the entire territory and make the controllers robust. The results from the controller testing suggested that, for a given target, the control system produces parameters that result in sustained phonation that is within \(\pm\)15 Hz of the targeted f\({}_{\text{o}}\) and \(\pm\)2 dB of the targeted SPL, highlighting the stability of the control system. Previous studies found that accurate voice imitators also made errors as high as \(\pm\)15 Hz during pitch imitation tasks [38], indicating excellent performance by the developed control system. In the current study, the weights of the three controllers were updated simultaneously using a single cost function without providing any a priori knowledge about the role to each controller. Such an approach facilitated the testing of the hypothesis that the feedforward controller dominates the control after training compared to the feedback controllers. The results obtained in the current study supported the hypothesis that the range of afdc outputs is higher than the range of sfbc and afbc outputs. This finding was observed in other studies as well [3; 39]. Due to the inherent delays in the feedback, after training, the feedforward controller dominates, and the contribution of the feedback controllers will be minimal unless there is external disturbance [40]. This also confirms the previous observations where adults could produce speech intelligibly even after hearing loss [41]. The variation in the outputs of the feedforward controller was significantly higher than the variation in the outputs of the feedback controllers except for the TA muscle activation. This is understandable because TA muscle control is more complex compared to the other control  
Figure 12: Boxplots of each controller outputs across all the test data. Here, affc—acoustic feedforward controller, sfbc—somatosensory feedback controller, and afbc—acoustic feedback controller. parameters. The TA muscle changes both adduction (thyromuscularis portion of TA muscle) as well as tension (thyrovocalis portion of TA muscle) in the vocal folds. The example waveforms indicated that the controllers could generate lung pressure and muscle activations that produced a wide variety of phonations. However, there were some differences between the targeted and predicted waveforms in terms of pitch and amplitude. It could be because of the representation of the speech signal with only four acoustic features which may not be adequate. We will address this limitation in future studies by exploring muti-parameter representation of the timbre. Across all the test cases, the error in % was highest in reaching muscle targets (\(\pm 80\%\)). Major contributions came from \(a_{LC}\) and \(a_{TA}\).