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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

TL;DR

This work treats speech production as a high-dimensional dynamical process and uses Lyapunov-spectrum analysis of hierarchical embeddings to distinguish psychotic from healthy discourse. By analyzing word- and sentence-level trajectories generated from two transformer models, the study finds uniformly contracting micro-dynamics at the word level but evolving, higher-dimensional, and partially expanding macro-dynamics at the discourse level, with robust separation between groups. The key finding is that discourse-level dynamics (captured by $LE_{max}$, $N_{LE}$, and $D_{KY}$) differentiate psychosis from health, while symptom severity does not map monotonically onto these dynamical measures. This physics-inspired framework provides a robust, model-agnostic biomarker of discourse organization in psychosis and paves the way for larger, cross-linguistic dynamical analyses of thought disorder.

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.

Lyapunov Spectral Analysis of Speech Embedding Trajectories in Psychosis

TL;DR

This work treats speech production as a high-dimensional dynamical process and uses Lyapunov-spectrum analysis of hierarchical embeddings to distinguish psychotic from healthy discourse. By analyzing word- and sentence-level trajectories generated from two transformer models, the study finds uniformly contracting micro-dynamics at the word level but evolving, higher-dimensional, and partially expanding macro-dynamics at the discourse level, with robust separation between groups. The key finding is that discourse-level dynamics (captured by , , and ) differentiate psychosis from health, while symptom severity does not map monotonically onto these dynamical measures. This physics-inspired framework provides a robust, model-agnostic biomarker of discourse organization in psychosis and paves the way for larger, cross-linguistic dynamical analyses of thought disorder.

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.
Paper Structure (22 sections, 4 equations, 3 figures, 10 tables)

This paper contains 22 sections, 4 equations, 3 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Multilevel embedding and dynamical analysis of structured psychiatric interviews
  3. Clinical Study Protocol for Psychosis
  4. Clinical characteristics of the psychotic cohort and implications for dynamical analysis
  5. Speech parameters as reference indicators of psychosis
  6. Hierarchical embedding representation
  7. Dynamical analysis of embedding vectors via Lyapunov spectra
  8. Dynamical interpretation of speech embeddings
  9. Lyapunov spectrum and stability analysis
  10. Results and Discussion
  11. Micro--macro transition in speech dynamics: word versus answer embeddings
  12. Answer-level dynamics distinguish psychotic and healthy speech
  13. Inter-subject variability and outlier behavior.
  14. Robustness across language models
  15. Summary
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Schematic overview of the analysis procedure.
  • 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.