Lyapunov Spectral Analysis of Speech Embedding Trajectories in Psychosis

Jelena Vasic; Branislav Andjelic; Ana Mancic; Dusica Filipovic Djurdjevic; Ljiljana Mihic; Aleksandar Kovacevic; Nadja P. Maric; Aleksandra Maluckov

nlin.AOFeb 18, 2026

Lyapunov Spectral Analysis of Speech Embedding Trajectories in Psychosis

Authors: Jelena Vasic, Branislav Andjelic, Ana Mancic, Dusica Filipovic Djurdjevic, Ljiljana Mihic, Aleksandar Kovacevic, Nadja P. Maric, Aleksandra Maluckov

Organizations: Institute of Mental Health, Milana Kašanina 3, Belgrade, Serbia · Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovica 6, Novi Sad, Serbia · Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, Serbia · Faculty of Philosophy, University of Belgrade, 18-20 ˇCika Ljubina street, Belgrade, Serbia ·

Abstract

We analyze speech embeddings from structured clinical interviews of psychotic patients and healthy controls by treating language production as a high-dimensional dynamical process. Lyapunov exponent (LE) spectra are computed from word-level and answer-level embeddings generated by two distinct large language models, allowing us to assess the stability of the conclusions with respect to different embedding presentations. Word-level embeddings exhibit uniformly contracting dynamics with no positive LE, while answer-level embeddings, in spite of the overall contraction, display a number of positive LEs and higher-dimensional attractors. The resulting LE spectra robustly separate psychotic from healthy speech, while differentiation within the psychotic group is not statistically significant overall, despite a tendency of the most severe cases to occupy distinct dynamical regimes. These findings indicate that nonlinear dynamical invariants of speech embeddings provide a physics-inspired probe of disordered cognition whose conclusions remain stable across embedding models.

Figures & tables

Panel of Figure 1 — Figure 1: Schematic overview of the analysis procedure.

Group	$\langle LE_{\max}\rangle\pm\sigma$	$<\Sigma>\pm\sigma(\Sigma)$	$N_{LE}$
Severe	$-0.190\pm 0.031$	$-269.13\pm 13.80$	$0$
Moderate	$-0.226\pm 0.047$	$-295.29\pm 41.31$	$0$
Mild	$-0.256\pm 0.052$	$-319.58\pm 41.37$	$0$
Healthy	$-0.199\pm 0.028$	$-264.53\pm 17.35$	$0$

Table 1: Lyapunov spectrum statistics for word-level sentence embeddings.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Severe	$0.189\pm 0.053$	$-260.27\pm 29.41$	$25.86\pm 15.60$	$66.92\pm 38.46$
Moderate	$0.238\pm 0.070$	$-284.99\pm 49.14$	$34.30\pm 26.31$	$83.54\pm 63.75$
Mild	$0.144\pm 0.084$	$-314.00\pm 63.26$	$26.11\pm 28.55$	$63.14\pm 68.41$
Healthy	$0.341\pm 0.080$	$-292.94\pm 42.00$	$63.00\pm 31.97$	$146.15\pm 71.42$

Table 2: Group-averaged Lyapunov spectrum characteristics for BERTić answer embeddings under four-group clinical classification

<...>

. All quantities are reported as mean

\pm

standard deviation across subjects within each group.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Psychosis	$0.192\pm 0.080$	$-288.38\pm 54.69$	$29.19\pm 24.20$	$72.00\pm 58.35$
Healthy	$0.341\pm 0.080$	$-292.94\pm 42.00$	$63.00\pm 31.97$	$146.15\pm 71.42$

Table 3: LE spectrum statistics for BERTić answer embeddings under two-group classification (Healthy vs. Psychosis). Values are given as mean

\pm

standard deviation.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Severe	$0.189\pm 0.053$	$-260.27\pm 29.41$	$25.86\pm 15.60$	$66.92\pm 38.46$
Mild+Moderate	$0.193\pm 0.089$	$-298.73\pm 58.11$	$30.42\pm 26.95$	$73.87\pm 64.97$
Healthy	$0.341\pm 0.080$	$-292.94\pm 42.00$	$63.00\pm 31.97$	$146.15\pm 71.42$

Table 4: LE spectrum statistics for BERTić answer embeddings under three-group classification. Values are given as mean

\pm

standard deviation.

Figure 2: Box plots and corresponding mean values of the maximal Lyapunov exponent and the Kaplan–Yorke dimension for answer embeddings in healthy controls and subjects with psychosis.

Figure 3: Box plots and corresponding mean values of the maximal Lyapunov exponent and the Kaplan–Yorke dimension for answer embeddings for subjects stratified in 3 groups: healthy, mild+moderate and severe psychosis.

ID	ICD-10 diag.	PANSS P	PANSS N	PANSS G	PANSS Total	Severity
P1	F20.0	23	31	45	99	Severe
P2	F23	15	24	45	84	Moderate
P16	F20.9	31	26	54	111	Severe
P20	F20.0	29	27	54	110	Severe
P21	F20.1	18	44	49	111	Severe
P24	F29	21	26	51	98	Severe

Table 5: Clinical characteristics of the psychotic cohort. Diagnoses are reported according to ICD-10. Severity groups are assigned based on PANSS total score and are used for stratification in the dynamical analysis.

Group	$<LE_{max}>$	$<\Sigma>$
Moderate	$-0.4698\pm 0.0488$	$-925.41\pm 39.72$
Mild	$-0.4826\pm 0.0529$	$-935.69\pm 31.41$
Healthy	$-0.5154\pm 0.0577$	$-952.09\pm 27.52$
Severe	$-0.4342\pm 0.0432$	$-929.14\pm 33.30$

Table 6: Lyapunov statistics for word embeddings using four-group classification.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Psychosis	$0.241\pm 0.078$	$-337.827\pm 30.824$	$51.38\pm 35.74$	$126.90\pm 85.10$
Healthy	$0.353\pm 0.096$	$-318.811\pm 39.555$	$120.78\pm 58.37$	$280.28\pm 125.46$

Table 7: Lyapunov spectrum statistics for alternative LLM answer embeddings under two-group classification (Healthy vs. Psychosis). Values are given as mean

\pm

standard deviation.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Severe	$0.214\pm 0.065$	$-317.023\pm 22.146$	$55.17\pm 37.23$	$133.70\pm 86.59$
Mild+Moderate	$0.250\pm 0.082$	$-346.393\pm 29.796$	$50.11\pm 36.25$	$124.64\pm 97.64$
Healthy	$0.353\pm 0.096$	$-318.811\pm 39.555$	$120.78\pm 58.37$	$280.28\pm 125.46$

Table 8: Lyapunov spectrum statistics for alternative LLM answer embeddings under three-group classification.

Group	$<LE_{max}>$	$<\Sigma>$	$<N_{LE}>$	$<D_{KY}>$
Severe	$0.214\pm 0.065$	$-317.023\pm 22.146$	$55.17\pm 37.23$	$133.69\pm 86.59$
Moderate	$0.250\pm 0.099$	$-349.820\pm 20.819$	$45.67\pm 30.31$	$132.82\pm 101.23$
Mild	$0.251\pm 0.067$	$-343.346\pm 35.663$	$54.55\pm 42.77$	$116.45\pm 75.43$
Healthy	$0.353\pm 0.096$	$-318.811\pm 39.555$	$120.78\pm 58.37$	$280.28\pm 125.46$

Table 9: Lyapunov spectrum statistics for alternative LLM answer embeddings under four-group clinical classification.

Group	Cosine	Euclidean	KL	Hellinger	Bhattacharyya	JS
Severe Psychosis	0.0557 $\pm$ 0.0083	4.482 $\pm$ 0.343	0.165 $\pm$ 0.090	0.200 $\pm$ 0.057	0.0616 $\pm$ 0.0337	0.0503 $\pm$ 0.0263
Moderate Psychosis	0.0508 $\pm$ 0.0054	4.276 $\pm$ 0.353	0.137 $\pm$ 0.079	0.178 $\pm$ 0.057	0.0507 $\pm$ 0.0320	0.0412 $\pm$ 0.0245
Mild Psychosis	0.0537 $\pm$ 0.0067	4.432 $\pm$ 0.330	0.167 $\pm$ 0.075	0.205 $\pm$ 0.056	0.0622 $\pm$ 0.0281	0.0514 $\pm$ 0.0225
Healthy	0.0506 $\pm$ 0.0052	4.110 $\pm$ 0.228	0.133 $\pm$ 0.042	0.184 $\pm$ 0.036	0.0480 $\pm$ 0.0171	0.0407 $\pm$ 0.0135

Table 10: Group-level statistics of QA semantic distances (mean

\pm

SD across subjects).

Lyapunov Exponent Estimation

See all 8 papers

Psychosis involves a deficit of information compression in connected speech
Sep 14, 2026Samuele Vallisa, Claudio Palominos, Rui He +6Computational Psycholinguistics Representation Geometry in Language Models
Grammar and Cognition Lab, Department of Translation & Language Sciences, Universitat Pompeu Fabra, Barcelona, Spain · Department of Neurosciences, Health Sciences Institute, Dokuz Eylul University, Izmir, Turkey. · Department of Psychiatry, Dokuz Eylul University, Izmir, Turkey. +4
Depression Markers in Speech: An Approach based on Tract Variables Dynamics
Jul 28, 2026Sahar Altalhi, Tanaya Guha, Alessandro VinciarelliDepression Detection Speech Processing
University of Glasgow (United Kingdom) and Taif University (Saudi Arabia) · University of Glasgow (United Kingdom)
Word-Aligned Prosody Reflects Speaker Differences More Than Depression or PTSD Severity
Oct 10, 2026Hsiang-Chen Yeh, Aurosweta Mahapatra, Shreeram Suresh Chandra +2Speech Prosody Clinical Speech Processing
Clinical Mental Health Counseling, Johns Hopkins University, Baltimore, MD, USA · Center for Language and Speech Processing (CLSP), Johns Hopkins University, Baltimore, MD, USA · College of Connected Computing, Vanderbilt University, Nashville, TN, USA

Sep 14, 2026J/K move · Enter open · S save

Psychosis involves a deficit of information compression in connected speech

Samuele Vallisa, Claudio Palominos, Rui He, Emre Bora+5

Grammar and Cognition Lab, Department of Translation & Language Sciences, Universitat Pompeu Fabra, Barcelona, Spain · Department of Neurosciences, Health Sciences Institute, Dokuz Eylul University, Izmir, Turkey. · Department of Psychiatry, Dokuz Eylul University, Izmir, Turkey.+4

Computational Psycholinguistics Representation Geometry in Language Models

Open paper AskPDF arXiv

Large language models (LLMs) with human-like performance on linguistic tasks have transformed the study of language in neurodiverse conditions. LLMs provide representations of linguistic input in the form of high-dimensional vectors (embeddings), and next-token predictions computed from these embeddings. Previous crosslinguistic evidence suggests a complexity reduction in the form of both lower intrinsic dimensionality (ID) of LLM representations and higher mean surprisal (prediction error) in psychosis. We hypothesized that these metrics reflect a general deficit of information compression in psychosis, linked to grammatical organization as what enables predictions in language.We operationalized surprisal difference as the difference between surprisal as estimated from word frequency and surprisal as based on a contextual LM, which is sensitive to grammatical organization over and above lexical concepts. Using a dataset of 144 Turkish speakers, including 106 patients with schizophrenia-spectrum disorders (SSD) - 56 with chronic schizophrenia (SZH), 33 with first-episode psychosis (FEP), and 17 with schizoaffective disorder (SZA) - and 38 healthy controls. We report: (1) Surprisal difference is attenuated in all clinical groups relative to controls, independently of word count; (2) Compressibility (intrinsic dimension) is reduced in SZH and FEP; (3) Syntactic complexity and compressibility both predict surprisal difference. These results, further refining an alteration in the geometry of the semantic space in psychosis as previously attested, suggest a broader deficit in information compression in this disorder, with a mechanistic underpinning in the operations of grammar.

Abstract

Lyapunov Exponent Estimation

Explore similar work

Psychosis involves a deficit of information compression in connected speech

Depression Markers in Speech: An Approach based on Tract Variables Dynamics

Word-Aligned Prosody Reflects Speaker Differences More Than Depression or PTSD Severity