A low-dimensional dynamical basis for tongue shape control

Sam Kirkham; Patrycja Strycharczuk

cs.CLOct 16, 2026

A low-dimensional dynamical basis for tongue shape control

Authors: Sam Kirkham, Patrycja Strycharczuk

Organizations: Phonetics Laboratory, Lancaster University, United Kingdom · Linguistics and English Language, University of Manchester, United Kingdom

Abstract

Speech production involves the control of a high-dimensional articulatory system with many degrees-of-freedom, but a widespread hypothesis is that speakers navigate this complexity using a set of lower-dimensional control variables. Common candidates for these control variables include individual articulators (e.g. tongue body) and abstract tract variables (e.g. tongue body constriction location), but identifying the most appropriate coordinate system for articulatory control remains an open question. In this study, we advance a model in which holistic tongue shape modes represent a potential low-dimensional control basis for a simple dynamical law. We first discover empirical tongue shape modes in a cross-speaker coordinate space and then fit the model to ultrasound data on monophthongal vowels from 36 speakers of British English. A three-dimensional linear point attractor fitted to these time-varying modes recovers the dynamics of tongue shape with a high degree of accuracy. This suggests that complex tongue movement can arise from independent modes that linearly combine under simple dynamical laws, thereby relocating some complexity from the control signal to the coordinate system. We show that this framing explains why one-dimensional articulatory measures can exhibit observable nonlinearities, and hypothesize that shape modes are a plausible kinematic expression of underlying muscle synergies.

Figures & tables

Figure 1: The proposed model architecture, where tongue shape modes are the control basis that drive tongue shape dynamics. One-dimensional measurements therefore represent a projection from tongue shape space into a new coordinate system.

Figure 2: Mode mixing can manufacture apparent nonlinearity. Top left: two independent linear modes

x_{1},x_{2}

. Top right: the acceleration of

x_{1}

is captured essentially perfectly by a linear law (

x_{2}

likewise, not shown). Bottom left: their linear superposition

y=x_{1}+x_{2}

. Bottom right: the acceleration of

y

is poorly fit by a linear model and can be fitted using a cubic term even though the underlying system is linear.

Figure 3: Left: Principal component loadings, with the mean midsagittal tongue shape and

\pm 1

SD perturbation. Right: Time-varying principal components in bad , with midsagittal tongue contours at evenly spaced times across the [C 1 VC 2 ] window.

Figure 4: Tongue contour reconstruction for bod . Each panel is a selected frame across the [C- 1 V-C 2 ] window, with raw contour (grey), 3-PC reduction (black), model prediction (red). RMSE is the difference between model prediction and 3-PC input.

Figure 5: Parameter-recovery error as a function of window duration across damping ratio (rows) and parameter (columns).

Model	$\text{RMSE}_{\text{clo}}$	$\text{RMSE}_{\text{rel}}$	$\text{sep}_{V}$	$\text{sep}_{D}$	$V>D$
unconstrained	0.177 [0.157, 0.221]	0.286 [0.248, 0.327]	0.57 [0.47, 0.88]	0.51 [0.46, 0.68]	23/36
+ $\mathrm{PC}_{1}$ $\zeta_{\mathrm{critical}}$	0.220 [0.182, 0.263]	0.384 [0.303, 0.452]	0.52 [0.48, 0.63]	0.52 [0.43, 0.63]	19/36
+ $\mathrm{PC}_{1-3}$ $\zeta_{\mathrm{critical}}$	0.263 [0.218, 0.322]	0.472 [0.372, 0.592]	0.50 [0.45, 0.65]	0.52 [0.44, 0.60]	18/36
+ pin $x^{*}$	0.230 [0.191, 0.296]	0.407 [0.338, 0.505]	5.14 [4.00, 6.29]	0.52 [0.31, 0.73]	36/36
+ pin $x^{*}$ + $\mathrm{PC}_{1}$ $\zeta_{\mathrm{critical}}$	0.303 [0.250, 0.379]	0.531 [0.433, 0.707]	5.14 [4.00, 6.29]	0.52 [0.31, 0.73]	36/36
+ pin $x^{*}$ + $\mathrm{PC}_{1-3}$ $\zeta_{\mathrm{critical}}$	0.357 [0.325, 0.462]	0.647 [0.539, 0.869]	5.14 [4.00, 6.29]	0.52 [0.31, 0.73]	36/36

Table 1: Model comparison for a damped harmonic oscillator fitted to

\mathrm{PC}_{1-3}

tongue contours. Unconstrained represents a model with free parameters for

x^{*},\zeta,\omega

. Each cell is the sample median with the interquartile range in brackets; RMSE in millimetres, clo/rel = closure/release.

V>D

counts speakers with

\text{sep}_{V}>\text{sep}_{D}

Figure 6: Distributions of the target

\mathbf{x}^{*}

for PC 1 –PC3 across vowel closure (colours) and release (grey).

Figure 7: Target values in {PC 1 , PC 2 } space for speaker MCR14. Crosses represent by-vowel medians and points represent individual tokens. Axes have been oriented to align with conventions for representing vowels in

\{F\textsubscript{1}F\textsubscript{2}\}

space.

		$\omega$ (rad/s)		$\zeta$		$\omega_{\zeta_{\text{critical}}}$ (rad/s)
Model	PC	closure	release	closure	release	closure	release
unconstrained	1	22.5 [18.3, 24.7]	25.1 [21.9, 28.6]	0.64 [0.50, 0.77]	0.38 [0.28, 0.53]	23.2 [17.1, 25.6]	32.1 [26.1, 39.0]
	2	24.1 [20.1, 29.4]	20.5 [17.2, 24.8]	0.55 [0.37, 0.90]	0.16 [0.11, 0.26]	25.6 [19.1, 30.4]	12.8 [8.6, 35.3]
	3	28.5 [25.0, 34.0]	23.5 [20.7, 27.3]	0.66 [0.55, 0.98]	0.24 [0.17, 0.31]	32.5 [24.9, 38.7]	23.2 [16.5, 37.0]
+ pin $x^{*}$	1	23.0 [18.8, 24.0]	22.7 [19.5, 26.1]	0.70 [0.65, 0.78]	0.57 [0.39, 0.69]	25.0 [20.3, 28.1]	29.2 [22.4, 37.0]
	2	22.7 [19.4, 26.6]	15.4 [12.6, 16.9]	0.68 [0.58, 0.78]	0.27 [0.19, 0.37]	25.6 [21.7, 30.3]	14.0 [11.7, 18.8]

Table 2: Estimated

\omega

(rad/s) and

\zeta

for the unconstrained and pinned-target (+ pin

x^{*}

) models, as well as estimates for

\omega

when damping is fixed to critical (

\omega_{\zeta_{\text{critical}}}

) for all PCs. Each cell is the median with interquartile range in brackets.

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May 22, 2026

Articulatory strategy as a source of variation in acoustic vowel dynamics

Acoustic vowel dynamics have some speaker-identifying characteristics, which have been ascribed to individual properties of articulatory strategies: formant transitions have a particular shape because speakers move their articulators, using specific and practised movements. However, there is little existing evidence that different articulatory strategies systematically affect formant dynamics. The present study corroborates the link between the two. Ultrasound tongue imaging data from 36 speakers of Northern-Anglo English are used to identify distinct articulatory strategies for the production of palatal vowel /i/. Tongue shape in /i/ is found to be a significant predictor of formant dynamics in diphthongs with a palatal offglide. The observed relationships can be explained by the characteristics of articulatory movement conditioned by vocal tract shape. Greater articulatory displacement of tongue root and/or dorsum produces greater distortion from the mean tongue shape in palatal vowels, and it also requires higher articulatory velocities, resulting in relatively earlier and steeper formant transitions. The results contribute to the conceptual understanding of individuality in speech, by illuminating the regularising and individual aspects of articulatory compensation.

Patrycja Strycharczuk, Justin J. H. Lo, Sam Kirkham

Linguistics and English Language, University of Manchester, United Kingdom · Linguistics and English Language, Lancaster University, United Kingdom

Speech Production

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Oct 17, 2026

Vocal-Tract Acoustics, Aerodynamics, and Overlap-and-Add Synthesis in DYNARTmo

This paper presents the acoustic and aerodynamic extension of DYNARTmo, a dynamic articulatory model for visualizing and synthesizing speech production. Gestural control trajectories determine vocal-tract geometry, which is converted into an acoustic tube with nasal branching and effective lateral passages. A lumped aerodynamic network relates prescribed glottal motion and pulmonary pressure to airflow and supraglottal pressure storage. Phonatory excitation, oral friction, and glottal aspiration are synthesized as separate contributions. Frame-specific acoustic responses are combined by overlap-and-add, preserving response tails beyond individual control frames. Three German words, Tasse'', Muse'', and ``Lade'', illustrate the coordination of articulation, pressure, flow, and acoustic sources across vowels, nasals, laterals, fricatives, and plosives. The implementation has been optimized by the author primarily for sound recognizability; independent perceptual evaluation remains outstanding, and fricative-noise naturalness requires further refinement. The model provides an inspectable, articulatorily controlled production plant for future neural simulations of babbling, imitation, and early word acquisition. Further work will improve acoustic realism, reduce empirical source corrections, and extend the sensory information available to developmental learning models.

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Medical School, RWTH Aachen University, Aachen, Germany · Kröger Lab, Belgium, www.speechtrainer.eu

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Mar 18, 2026

AURORA Model of Formant-to-Tongue Inversion for Didactic and Clinical Applications

This paper outlines the conceptual and computational foundations of the AURORA (Acoustic Understanding and Real-time Observation of Resonant Articulations) model. AURORA predicts tongue displacement and shape in vowel sounds based on the first two formant values. It is intended as a didactic aid helping to explain the relationship between formants and the underlying articulation, as well as a foundation for biofeedback applications. The model is informed by ultrasound tongue imaging and acoustic data from 40 native speakers of English. In this paper we discuss the motivation for the model, the modelling objectives as well as the model architecture. We provide a qualitative evaluation of the model, focusing on selected tongue features. We then present two tools developed to make the model more accessible to a wider audience, a Shiny app and a prototype software for real-time tongue biofeedback. Potential users include students of phonetics, linguists in fields adjacent to phonetics, as well as speech and language therapy practitioners and clients.

Patrycja Strycharczuk, Sam Kirkham

University of Manchester · Lancaster University

Speech Processing Clinical Speech Processing

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Abstract

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