CEML
🧠 CEML: Cognitive Entropy Minimization Law
A Unified Framework for Information Selection
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“Intelligence is the efficient compression of reality.”
The Cognitive Entropy Minimization Law (CEML) postulates that intelligent agents (biological or artificial) optimize their internal models by maximizing Contextual Coherence while simultaneously minimizing Internal Entropy (Thermodynamic & Computational Cost).
It unifies Friston’s Free Energy Principle, Occam’s Razor, and Landauer’s Limit into a single computable metric used to detect hallucination and validate truth-claims.
📐 The Master Equation
The fitness $J(s)$ of any information structure $s$ within a context $\Omega$ is defined as:
\[J(s) = \frac{\mathcal{C}(s \mid \Omega)}{\mathcal{H}(s) + \epsilon}\]| Variable | Component | Definition |
|---|---|---|
| $\mathcal{C}$ | Contextual Coherence | Semantic alignment (Cosine Similarity) |
| $\mathcal{H}$ | Entropic Cost | Description length / Complexity (Shannon Entropy) |
| $\epsilon$ | Epsilon | Regularization constant ($10^{-9}$) |
🌀 The Golden Threshold ($\phi$)
The system uses the Golden Ratio as the boundary for “Resonance”. A signal is considered fully integrated (True/Valid) only if its efficiency score exceeds $\phi$.
\[\text{Resonance State} \iff J(s) \ge 1.618...\]Regime Classification
Based on the demo logic (core/demo.py):
- 🟢 RESONANCE ($J \ge \phi$): High Coherence, Optimal Entropy. (Signal Accepted)
- 🔵 HALLUCINATION ($C \uparrow, H \downarrow_{fake}$): High Coherence but artificially low entropy (Overfitting).
- 🔴 DISSONANCE: Low Coherence or High Entropy (Noise/Chaos).
🚀 Usage
1. Python Engine (Proof of Concept)
Test the selection logic on text vectors or probability distributions.
```bash
Clone and enter
git clone https://github.com/Lichen-Universe/CEML.git cd CEML/core
Run the cognitive selector demo
python demo.py
Run the distribution entropy test
python distributions_test.py