# Discovering dynamical laws for speech gestures

arXiv: https://arxiv.org/abs/2504.04849 · HTML: https://mlsanity.com/paper/2504.04849/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 96 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Neural inhibition during speech planning contributes to contrastive hyperarticulation](https://mlsanity.com/paper/2209.12278/) (2022)
- [Scaling laws for nonlinear dynamical models of articulatory control](https://mlsanity.com/paper/2411.12720/) (2024)

## Built on by (most cited first, 1 of 1)

- [Dynamical model parameters from ultrasound tongue kinematics](https://mlsanity.com/paper/2510.18629/) (2025)

## Abstract (arXiv)

A fundamental challenge in the cognitive sciences is discovering the dynamics that govern behaviour. Take the example of spoken language, which is characterised by a highly variable and complex set of physical movements that map onto the small set of cognitive units that comprise language. What are the fundamental dynamical principles behind the movements that structure speech production? In this study, we discover models in the form of symbolic equations that govern articulatory gestures during speech. A sparse symbolic regression algorithm is used to discover models from kinematic data on the tongue and lips. We explore these candidate models using analytical techniques and numerical simulations, and find that a second-order linear model achieves high levels of accuracy, but a nonlinear force is required to properly model articulatory dynamics in approximately one third of cases. This supports the proposal that an autonomous, nonlinear, second-order differential equation is a viable dynamical law for articulatory gestures in speech. We conclude by identifying future opportunities and obstacles in data-driven model discovery and outline prospects for discovering the dynamical principles that govern language, brain and behaviour.