Abstract
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.
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Notes
Muscle force F generated by the biomechanical model is specified as
$$\begin{aligned} F=\rho [\exp (cA)-1], \end{aligned}$$(1)where c is a form parameter accounting for the gain of the feedback from the muscle to the motoneurons pool and \(\rho \) a magnitude parameter directly related to force-generating capability. A is the muscle activation corresponding to
$$\begin{aligned} A=l-\lambda +\mu \dot{l}, \end{aligned}$$(2)where l is the actual muscle length, \(\dot{l}\) the muscle shortening or lengthening velocity and \(\mu \) a damping coefficient due to proprioceptive feedback (Payan and Perrier 1997).
For simplicity, the main text presents the case of sequences of 3 phonemes, without loss of generality. For a general n-phoneme sequence, the proposed cost function would correspond to the perimeter of the corresponding \((n-1)\)-simplex defined by the n control variables in the six-dimensional control space. For the present three-phoneme case, the 2-simplex corresponds to the triangle introduced in the text. Rigorously, influence of every phoneme of the sequence on every other one would be rather modeled by a cost function involving distances between every pair of phonemes. In order to avoid the corresponding quadratic combinatorial growth of the number of terms in the cost function, its definition has been simplified into the one presented here.
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Acknowledgments
Authors wish to thank Pierre Bessière and Jean-Luc Schwartz for guidance and inspiring conversations.
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The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 339152, “Speech Unit(e)s,” PI: Jean-Luc-Schwartz).
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Patri, JF., Diard, J. & Perrier, P. Optimal speech motor control and token-to-token variability: a Bayesian modeling approach. Biol Cybern 109, 611–626 (2015). https://doi.org/10.1007/s00422-015-0664-4
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DOI: https://doi.org/10.1007/s00422-015-0664-4