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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
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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
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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
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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
- LinkedIn: Jean-Denis Bosange Batuli
- Contact: jean.bosange@gmail.com
Citation
If you use this work or dataset, please cite the relevant paper:
@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},
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