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Dynamical Systems Analysis Reveals Functional Regimes in Large Language Models

Hassan Ugail, Newton Howard

TL;DR

The paper tackles how temporal dynamics organize computations in large language models and introduces a neuroscience-inspired composite metric, $Ψ'$, that combines hierarchical temporal integration (via DFA/Hurst) with metastability (phase synchronisation). Using GPT-2-medium across five conditions, the authors show that $Ψ'$ discriminates structured reasoning from repetitive/noisy generation and from architectural perturbations, with integration and metastability behaving as dissociable components. The findings demonstrate that formal dynamical properties can characterize computational regimes in transformers, offering a principled, generalizable approach to interpretability that remains distinct from notions of machine consciousness. The work lays groundwork for cross-domain dynamical analyses in artificial systems and points to further methodological extensions and broader validations across models and tasks.

Abstract

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where temporal integration and metastability are core markers of neural organisation, we adapt these concepts to transformer models and discuss a composite dynamical metric, computed from activation time-series during autoregressive generation. We evaluate this metric in GPT-2-medium across five conditions: structured reasoning, forced repetition, high-temperature noisy sampling, attention-head pruning, and weight-noise injection. Structured reasoning consistently exhibits elevated metric relative to repetitive, noisy, and perturbed regimes, with statistically significant differences confirmed by one-way ANOVA and large effect sizes in key comparisons. These results are robust to layer selection, channel subsampling, and random seeds. Our findings demonstrate that neuroscience-inspired dynamical metrics can reliably characterise differences in computational organisation across functional regimes in large language models. We stress that the proposed metric captures formal dynamical properties and does not imply subjective experience.

Dynamical Systems Analysis Reveals Functional Regimes in Large Language Models

TL;DR

The paper tackles how temporal dynamics organize computations in large language models and introduces a neuroscience-inspired composite metric, , that combines hierarchical temporal integration (via DFA/Hurst) with metastability (phase synchronisation). Using GPT-2-medium across five conditions, the authors show that discriminates structured reasoning from repetitive/noisy generation and from architectural perturbations, with integration and metastability behaving as dissociable components. The findings demonstrate that formal dynamical properties can characterize computational regimes in transformers, offering a principled, generalizable approach to interpretability that remains distinct from notions of machine consciousness. The work lays groundwork for cross-domain dynamical analyses in artificial systems and points to further methodological extensions and broader validations across models and tasks.

Abstract

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where temporal integration and metastability are core markers of neural organisation, we adapt these concepts to transformer models and discuss a composite dynamical metric, computed from activation time-series during autoregressive generation. We evaluate this metric in GPT-2-medium across five conditions: structured reasoning, forced repetition, high-temperature noisy sampling, attention-head pruning, and weight-noise injection. Structured reasoning consistently exhibits elevated metric relative to repetitive, noisy, and perturbed regimes, with statistically significant differences confirmed by one-way ANOVA and large effect sizes in key comparisons. These results are robust to layer selection, channel subsampling, and random seeds. Our findings demonstrate that neuroscience-inspired dynamical metrics can reliably characterise differences in computational organisation across functional regimes in large language models. We stress that the proposed metric captures formal dynamical properties and does not imply subjective experience.
Paper Structure (25 sections, 6 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 25 sections, 6 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Dynamical organisation in neural systems
  4. Interpretability in language models
  5. Bridging neuroscience and artificial systems
  6. Methods
  7. Model and experimental conditions
  8. Activation recording and preprocessing
  9. Hierarchical integration via detrended fluctuation analysis
  10. Metastability via phase synchronisation variability
  11. Composite index $\Psi'$
  12. Statistical analysis
  13. Robustness analyses
  14. Results
  15. Component metrics across conditions
  16. ...and 10 more sections

Figures (3)

  • Figure 1: Mean $\Psi'$ across experimental conditions with standard error bars. Structured reasoning (intact-complex) exhibits the highest composite index, indicating elevated dynamical organisation. Repetitive output shows the lowest values, while noisy sampling yields intermediate but negative values. Both architectural perturbations (head pruning and weight noise) produce positive but reduced $\Psi'$ relative to intact-complex, suggesting partial maintenance of dynamical organisation despite structural degradation. Error bars represent standard error of the mean across 15 trials per condition.
  • Figure 2: Trial-level $\Psi'$ distributions across experimental conditions. Box plots show medians (horizontal lines), interquartile ranges (boxes), whiskers extending to 1.5$\times$IQR, and individual outliers (circles). Intact-complex exhibits a tight, elevated distribution indicating stable high dynamical organisation. Intact-repetition shows the lowest median with greatest dispersion, suggesting high sensitivity to specific repetition patterns. Intact-noisy demonstrates consistently low values with moderate spread. Both damaged conditions display intermediate distributions with increased variability, consistent with partial disruption of internal coordination where some trials maintain relatively high organisation while others show greater degradation. The overlapping distributions indicate continuous variation rather than discrete state transitions.
  • Figure 3: Robustness analyses demonstrating system-level properties of $\Psi'$. (a) Layer-subset analysis: $\Psi'$ computed from early layers only (blocks 1, 4), late layers only (blocks 7, 10), or all layers combined. Qualitative ordering of conditions remains stable across subsets, with late-layer recordings showing the clearest separation for structured reasoning. (b) Channel-subsampling analysis: $\Psi'$ computed from randomly sampled channel subsets at 25% (32 channels) and 50% (64 channels) of the total 128 channels, across three independent random seeds. Mean values and error bars (standard deviation across seeds) demonstrate stability under random channel reduction. (c) Multi-seed consistency: $\Psi'$ from 50% channel subsamples across five independent random seeds. Individual seed results shown as light gray points, means as dark bars. Consistent separation between intact-complex and other conditions is maintained across all seeds, with comparable variability across functional regimes. These analyses collectively demonstrate that $\Psi'$ captures distributed dynamical properties rather than depending on specific channels, layers, or measurement configurations.