---
title: "LIMEN Dynamics Series: Internal Stability of LLMs"
tags:
  - llm
  - interpretability
  - dynamics
  - qwen
  - hidden-states
  - limen
  - idchain
license: cc-by-nc-nd-4.0
---

# LIMEN Dynamics Series: Internal Stability of LLMs

**A Comprehensive Analysis of Trajectory Instability, Regime Taxonomy, and Methodological Robustness in Large Language Models.**

**Author:** Jean-Denis Bosange Batuli  
**Date:** May 2026  

---

## The Series

This dataset hosts the full technical reports and supporting data for the LIMEN Dynamics research series. We recommend reading them in order:

### 1. Four Dynamical Regimes in Large Language Models: An Empirical Phase Map
**[Download on Zenodo](https://doi.org/10.5281/zenodo.20348878)**  
*The Foundation.* Introduces the `ct_t` metric and identifies four consistent regimes: Underactive, Adaptive, Transition, Chaotic. Demonstrates why Qwen models exhibit unique structural stability across 158 runs and 10 models.

### 2. Conditional Dynamic Signatures in Large Language Models
**[Download on Zenodo](https://doi.org/10.5281/zenodo.20361289)**  
*The Rigor.* A large-scale audit across 17 open-source models (70M to 3B parameters, 1,224 runs) examining normalisation sensitivity, variance decomposition, documented falsifications, and non-stationarity profiles. Proves that dynamic stability is a conditional observable: architecture explains 7% of variance, prompt category 17%, residual variance 76%.

### 3. Dynamic-Layer Controllability without Universal Semantic Recovery
**[Download on Zenodo](https://doi.org/10.5281/zenodo.20400171)**  
*The Depth.* Explores how instability propagates across transformer layers and identifies specific "Dynamic Layer Signatures" that predict output regimes before generation completes. Presents the fragmented topology at panel scale and the COLLAPSE-RIVALRY cyclical structure with 84% reopening rate on 638 cycles.

---

## Key Findings

| Finding | Source | Details |
| :--- | :--- | :--- |
| **Four Dynamical Regimes** | Paper 1 | UNDERACTIVE (1.55-1.70), ADAPTIVE (2.27-2.92), TRANSITION (~2.97), CHAOTIC (4.42-35.55) |
| **Qwen is Structurally Stable** | Paper 1 | Qwen family is the only family observed in the ADAPTIVE zone across 10 models |
| **Stability is Conditional** | Paper 2 | 76% of variance is residual/prompt-dependent. Architecture alone explains only 7% |
| **80% Trajectories Non-Stationary** | Paper 2 | Only 13% of token-level trajectories remain in a single regime throughout generation |
| **Documented Falsifications** | Paper 2 | Six small-panel hypotheses did not survive scale-up to n=17 |
| **Layer Coordination Matters** | Paper 3 | Inter-layer phase synchronization predicts trajectory collapse before it happens |
| **COLLAPSE-RIVALRY Cycle** | Paper 3 | 84% reopening rate after collapse on 638 observed cycles |
| **Fragmented Topology** | Paper 3 | Fragmentation index 0.65, only two robust mutual pairs (opt-pythia, phi-qwen) |

---

## Repository Structure

- `Four_Dynamical_Regimes.pdf`: Paper 1.
- `Conditional_Dynamic_Signatures.pdf`: Paper 2.
- `Dynamic_Layer_Controllability.pdf`: Paper 3.


---

## 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](https://www.unbind.world)
- **LinkedIn:** [Jean-Denis Bosange Batuli](https://www.linkedin.com/in/jean-denis-bosange-b2b693326)
- **Contact:** jean.bosange@gmail.com

---

## Citation

If you use this work or dataset, please cite the relevant paper:

```bibtex
@misc{bosange_batuli_2026_limem_series,
  author = {Bosange Batuli, Jean-Denis},
  title = {LIMEN Dynamics Series: Internal Stability of LLMs},
  year = {2026},
  publisher = {Zenodo / Hugging Face},