The relation between the continuous and the discrete: A note on the first principles of speech dynamics

- The principles of a dynamical framework of speech production are identified.
- A theory of contrast relying on dynamical systems is reviewed and discussed.
- A theory of word serialization using recurrent neural networks is reviewed and discussed.
- Autoregressive techniques are proposed for learning dynamical parameters are proposed.

The goal of this paper is to show how dynamical theories of phonetics and phonology bridge the dualistic gap between discrete phonological descriptions and continuous phonetic descriptions. By delving into the first principles of dynamics, it is shown that dynamical theories do not assume separate sets of principles to describe discrete and continuous aspects of a system. Rather, the discrete description is shown to predict the continuous one, using the concept of a differential equation, which is thoroughly explained. Linear and nonlinear differential equations are introduced using a discrete approximation, and then used to show how phonological contrast has been accounted for using dynamical systems analysis. A dynamical recurrent neural network model of word formation is then discussed to show how linguistic plans for words are serialized and coordinated into motoric word plans for different articulatory systems in the vocal tract. Furthermore, it is shown that many aspects of the discrete, time-invariant phonological description can be predicted from observed variable continuous phonetic functions, using the principle of least squares and recurrent neural networks.