# Deep Learning for Neuromuscular Control of Vocal Source for Voice Production
## 4 Discussion
The error in % for the other two control parameters was less than \(\pm 40\%\). The error in % was less than \(\pm 30\%\) for both somatosensory and acoustic features, excluding the outliers. The higher error in the prediction of control targets could be due to the nonlinearity and motor equivalence present in _LeTalker_. The _LeTalker_ includes non-linear source-filter interaction phenomenon [33] described in Equation (1), which can lead to the generation of same output for multiple combinations of muscle activations. The somatosensory and acoustic features were reached with little variation in \(a_{LC}\) activation around 0.5. This could be due to the minimal dependence of the chosen acoustic and somatosensory features in the current study on \(a_{LC}\). The \(a_{LC}\) is primarily an adductor muscle, and glottal width was not considered as one of the somatosensory features in the current study. The glottal width is two-dimensional [42] and varies along the length and thickness of the vocal fold surface. It is typically measured at the level of the vocal processes (posterior end of the vocal folds). In the _LeTalker_, the steady-state glottal width was zero at the vocal processes for most of the control parameter combinations, resulting in no pattern to learn with a change in control parameters. As noticed with individual waveforms, the difference in targeted and predicted acoustic and somatosensory features could be due to the use of only four acoustic and four somatosensory features. We will explore more accurate representation of the speech waveform using acoustic features, especially for timbre, and include more somatosensory and proprioceptive features for better representation of the vocal fold posturing. Neural networks train well on normally distributed data [43; 44]. However, varying all the control parameters with normal distributions in the current study eliminated data at extreme values (i.e., values closer to 0 and closer to 1) of the muscle activations. Randomly varying all the control parameters using uniform distribution produced data even at the extremes of muscle activations. However, in the current study, the neural networks performed poorly on uniformly distributed control parameters. Therefore, the data to train and test the control system were generated by varying \(\mathrm{P_{L}}\) and \(a_{LC}\) using normal distribution, and \(a_{TA}\) and \(a_{CT}\) using uniform distribution as a compromise. In the future, we will build the control system to overcome this limitation. Some of the somatosensory and acoustic features generated using the above-mentioned control parameters have a non-Gaussian distribution. Therefore, the acoustic features were transformed into normal distribution using a quantile transformer and the three fiber stresses were converted into logarithmic scale before training the networks. Such a transformation enhanced the performance of the neural networks. Since the targets were constant across time in the current setup, we used feedforward artificial neural networks to represent the controllers. However, we will use recurrent neural networks in the future to accommodate time-varying targets. Since the focus of the current study was the control of vocal source, we kept the airway constant. In the future, we will include the control of the vocal tract as well for more realistic applications. Also, in the current study, we used only the acoustic and somatosensory features as targets. In the future, we will include reflex proprioceptive loops as well for more accurate representation of the control system. We believe that this work is a steppingstone to simulate and study various motor disorders related to voice. In disorders such as Parkinson's disease, ataxia, and flaccid paralysis, the feedforward motor program is disrupted due to damage to downstream motor control processes. It alters the established relationships between the motor commands, sensory sequences, and movement outcomes [45].