Discovering dynamical laws for speech gestures

2025-04-07

AI Summary

This study aims to uncover the underlying dynamical principles governing articulatory movements in speech production. Method: Leveraging high-precision kinematic data of tongue and lip motion, we apply sparse symbolic regression combined with dynamical systems analysis to automatically construct interpretable symbolic differential equation models. Contribution/Results: We discover, for the first time, that approximately one-third of critical articulatory gestures require nonlinear second-order differential equations for accurate characterization—leading us to propose the “autonomous nonlinear dynamical system” as a universal dynamical law for speech gestures. Compared to conventional linear models, the derived symbolic models substantially improve modeling accuracy for key articulatory movements while preserving full interpretability. This work establishes the first data-driven, mathematically rigorous, and physiologically grounded dynamical framework for speech motor control.

Technology Category

• Natural Language Processing: Speech
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Neuro-Symbolic Learning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Discovering symbolic equations governing speech articulatory gestures
• Identifying dynamical principles behind complex speech production movements
• Evaluating linear and nonlinear models for articulatory gesture accuracy

Innovation

• Sparse symbolic regression for gesture dynamics
• Second-order linear model for speech accuracy
• Nonlinear force enhances articulatory dynamics modeling