📌 CIv6 Hypothesis for Structural Break Detection

LLM as a geometric-algebraic engines of concept formation

Hypothesis:

Structural breaks in univariate time series can be detected by observing qualitative shifts in the internal state dynamics of a pretrained Large Language Model (LLM), when presented with Cellular Automata (ECA)-encoded representations of the time series. When ECA evolution is tuned to the edge of chaos, it amplifies underlying dynamical patterns and transitions, which are then reflected as phase-shifts or topological discontinuities in the LLM’s latent state geometry (e.g., activation trajectories, attention flux, curvature, and Fisher Information Metric). These internal state changes can serve as indicators of regime shifts, enabling a cybernetic, model-agnostic detection framework.

🧠 Theoretical Foundations

Component Explanation
ECA at Edge of Chaos ECAs such as Rule 110 exhibit sensitivity to initial conditions and can produce complex structures that reflect temporal dependencies. When applied to time series, they serve as a preprocessing lens to amplify subtle dynamical features.
LLM Internal States Pretrained LLMs process symbolic sequences via high-dimensional embeddings. Their internal states (activations, attention maps, and derivatives) encode rich information about structure, syntax, and anomaly.
Structural Breaks Regime shifts (e.g., changes in volatility or drift) result in distinct symbolic and dynamical signatures which—after ECA transformation—can be detected as internal shifts in the LLM’s latent space.
Cybernetic Lens (CIv6) The system is viable if it can internally track perturbations, reconfigure interpretive dynamics, and signal change without retraining. The LLM serves as a frozen model with dynamic internal state responses—key to the viable system model.

🛠️ Solution Proposal

1. Input Encoding Pipeline

  • Data: Univariate time series $X = {x_1, x_2, …, x_T}$

  • Transformation:

    • Convert $X$ to binary symbolic representation via quantile or delta encoding.
    • Apply ECA evolution (Rule 110, 54, etc.) over a fixed window length to generate 2D bitmaps.
    • Flatten or serialize 2D ECA outputs as token sequences compatible with LLM input (e.g., “000111010…”).

2. LLM State Probing

  • Model: Use a frozen pretrained transformer (e.g., GPT-2, Mistral, or Phi-2).

  • Probing Strategy:

    • Record hidden states $h_t^{(l)}$ across layers $l$ and tokens $t$ for each input window.

    • Optionally extract:

      • Fisher Information Metric (FIM): Measures sensitivity of internal states.
      • Loop Energy / Wilson loop analogy: Track persistent activation cycles.
      • Activation Geometry: Compute curvature, dimensionality, or cluster separation.
    • Encode internal trajectories over time for comparative analysis.

3. Structural Break Signal Extraction

  • Define change metrics on internal state manifolds:

    • Embedding distance between consecutive ECA input windows.
    • KL divergence or Mahalanobis distance on FIMs.
    • Topological indicators (e.g., Betti numbers, persistent homology).

  • Thresholding:

    • Use MDL-based or BDM-based complexity thresholds to detect when a meaningful break occurs.
    • Incorporate prior information or allow self-adaptation via cybernetic feedback (loop-based validation).

4. Output

  • Annotated timeline of likely structural break points.
  • Optionally provide saliency maps (which token/bit caused the internal change).
  • Confidence levels based on internal variability and entropy across multiple layers.

🔁 System Architecture

Raw Time Series → Symbolic Encoding → ECA Evolution →
→ Tokenization → LLM Internal Probing →
→ State Trajectory Analysis → Structural Break Inference →
→ Feedback to User/System for Interpretability & Adaptation

🧪 Test Plan

Goal Metric Baseline Experimental
Structural Break Detection Accuracy Precision/Recall, F1 Bai & Perron (OLS breaks), BIC methods LLM State Shift + ECA
Sensitivity to Minor Shifts ROC-AUC, Detection Delay Change Point Detection Libraries LLM FIM / Loop tracking
Generalization Dataset Transferability Train on Simulated Data Evaluate on Market Data
Interpretability Visual & Textual Trace None FIM curvature, loop path visualizations

🧭 Next Steps Before Implementation

  1. Finalize Choice of ECA Rules:

    • Prioritize those at the edge of chaos (e.g., 54, 110, 30 variants).

  2. Select LLM Probing Interface:

    • Use HuggingFace models for ease of introspection.

  3. Define Internal State Metrics:

    • Fisher Information Matrix, Attention Flow, Activation Drift.

  4. Build Lightweight Prototyping Environment:

    • Google Colab / local inference using quantized models.

  5. Simulate Breaks & Validate Internal Reactions:

    • Create controlled datasets with known breaks (e.g., AR(1) regime shift).