jeanbatuli/LLM-Interne-Dynamic

🌌 Four Dynamical Regimes in Large Language Models

An Empirical Phase Map of Internal Trajectory Stability

📄 Full Working Paper: Download PDF on Zenodo
🏢 Author: Jean-Denis Bosange Batuli, CEO – IDChain SRL (Unbind)
📅 Date: May 2026

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🚀 Overview

Standard LLM evaluation focuses on output metrics (Perplexity, Benchmarks). This project introduces LIMEN (Liminal Internal Metric for Emergent Navigation), a framework that measures the internal geometric dynamics of Large Language Models during generation.

We demonstrate that LLMs do not generate text uniformly but traverse distinct Dynamical Regimes based on the stability of their hidden state trajectories.

🔑 Key Contributions

1. The ct_t Metric: A novel token-level instability metric computed from L2-normalized hidden states.
2. Four Regime Taxonomy: Identification of Underactive, Adaptive, Transition, and Chaotic regimes across 10 open-source models.
3. Qwen's Adaptive Stability: Empirical evidence that the Qwen family maintains a uniquely stable "Adaptive" regime compared to Llama or Gemma counterparts.
4. Collapse Prediction: A preliminary classifier capable of predicting "silent collapse" (output extinction) with high accuracy.

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📊 Main Findings

Regime	Ratio Range	Characteristics	Example Models
UNDERACTIVE	1.55 - 1.70	Low variance, rigid, limited adaptability	TinyLlama, Llama 3.2 3B
ADAPTIVE	2.27 - 2.92	Balanced flux/stability, controlled debt	Qwen 0.5B/1.5B/3B
TRANSITION	~2.97	Boundary zone, increasing variance	Qwen (specific conditions)
CHAOTIC	4.42 - 35.55	Violent spikes, high instability debt	Gemma 2B, GPT-2, DistilGPT-2

Key Insight: Model size does not predict stability. A smaller Qwen-1.5B is dynamically more stable than larger instruction-tuned models like Llama 3.2 3B.

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🧠 Methodology Snapshot

The core instability metric is defined as: $$c{t}_t={\delta }_t\times {\kappa }_{t}ct\_t\; =\; \backslash delta\_t\; \backslash times\; \backslash kappa\_t$$ Where:

• $\delta_t$: Displacement magnitude of L2-normalized hidden states.
• $\kappa_t$: Curvature (directional change) of the trajectory.

The Regime Indicator is derived from: $$\text{ratio\_norm}=\frac{\max (c{t}_t)}{\text{mean}(c{t}_t)}\backslash text\{ratio\backslash \_norm\}\; =\; \backslash frac\{\backslash max(ct\_t)\}\{\backslash mean(ct\_t)\}$$

(See the full paper for detailed mathematical definitions and normalization protocols.)

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🤝 Collaboration & Contact

This research is conducted by IDChain SRL (operating under the Unbind brand), focusing on real-time trajectory coherence detection for BCI and AI systems.

• 🌐 Website: unbind.world
• 💼 LinkedIn: Jean-Denis Bosange Batuli
• 📧 Contact: jean.bosange@gmail.com

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📜 Citation

If you use this work or dataset, please cite: jean denis bosange batuli. (2026). Four Dynamical Regimes in large Language Models : An Empirical Phase Map. Zenodo. https://doi.org/10.5281/zenodo.20348878

@misc{bosange_batuli_2026_limem,
  author = {Bosange Batuli, Jean-Denis},
  title = {Four Dynamical Regimes in Large Language Models: An Empirical Phase Map},
  year = {2026},
  publisher = {Zenodo},
  doi = (https://doi.org/10.5281/zenodo.20348878)},
  url = https://zenodo.org/records/20348878
}