---
language:
- en
tags:
- state-space
- physical-simulation
- quantum-mechanics
- differential-equations
- g-code
- edge-llm
- sovereign-ai
- muon-optimizer
license: mit
metrics:
- causal-entropy-loss
---

# 📐 SAGE-Lumen-3M: Sovereign State-Space Transition Engine
**SAGE-Lumen-3M** is an ultra-compact, parameter-disciplined 3 million parameter language model optimized for offline edge execution on homelab nodes (e.g., AMD Ryzen APUs).

Unlike general-purpose chatbots, SAGE-Lumen-3M is built strictly as a **Symbolic Physical Reasoning and State-Space Transition Simulator**. It models trajectories across three primary domains:
1. **Discrete-Time Quantum Walks (DTQW):** Simulating 1-D position states under Hadamard-coin operations.
2. **Biophysical ODE Trajectories:** Homeostatic insulin-glucose couplings and islet cell neovascularization.
3. **Non-Planar G-code Toolpaths:** Predicting Z-axis warp corrections dynamically against mechanical thermals.

## 🧠 Architectural Specifications
- **Parameters:** 2,754,816 active parameters (Tied Embeddings)
- **Vocabulary Size:** 2,048 (Capped BPE)
- **Decoder Layers:** 4 layers
- **Attention Heads:** 4 query heads, 1 Key-Value head (**Multi-Query Attention**)
- **Position Embeddings:** Rotary Positional Embeddings (**RoPE**)
- **Feed-Forward Blocks:** SwiGLU MLP (SiLU-gated, intermediate dimension 512)
- **Normalization:** RMSNorm (Root Mean Square Layer Normalization)
- **Training Optimization:** Matrix-preconditioned momentum (**Muon Optimizer** on 2D projections, AdamW on 1D variables).

## 🚀 Quickstart Usage (PyTorch)
```python
import torch
# Place the model on your local target device
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
```

For full details on SAGE (Sovereign Agentic Governance & Epistemic Protocol) or Logos OS, check our Github repository.