vST for Multi‑Model Alignment#
Example: Cross‑Model Alignment Regime Map (LLM ↔ Diffusion ↔ PLM)#
This example demonstrates how to construct a cross‑model alignment regime map across three heterogeneous architectures:
- a 4096D Large Language Model (LLM)
- a 1024D diffusion model
- a 256D Protein Language Model (PLM)
The goal is to classify alignment behavior into the triadic alignment regimes:
- A₁ᴴ — stable alignment
- A₂ᴴ — transitional alignment
- A₃ᴴ — dispersed / incompatible alignment
and to visualize how these regimes manifest across dimensional scales.
1. Scenario Overview#
We assume:
- three models with different latent dimensionalities
- a shared semantic or structural anchor (e.g., “binding site description” ↔ “protein structure” ↔ “image prompt”)
- cross‑model latent states extracted from each system
- projection into the 9D coherence core
The example is architecture‑agnostic.
2. Step 1 — Extract Latent States#
Let:
- ( z_{\text{LLM}} \in \mathbb{R}^{4096} )
- ( z_{\text{Diff}} \in \mathbb{R}^{1024} )
- ( z_{\text{PLM}} \in \mathbb{R}^{256} )
represent latent states associated with the same conceptual anchor.
Observed Properties#
- LLM latent: high‑capacity, semantically rich
- Diffusion latent: geometry shaped by noise schedule
- PLM latent: compact, structurally constrained
3. Step 2 — Project All Latents into 9D#
Project each latent into the 9D coherence core.
Reveals#
- LLM: compact, stable geometry → A₁ᴴ
- Diffusion: branching, transitional geometry → A₂ᴴ
- PLM: partially compatible, partially dispersed → A₂ᴴ → A₃ᴴ boundary
Interpretation#
The 9D projection exposes cross‑model compatibility:
- LLM ↔ Diffusion: transitional alignment
- LLM ↔ PLM: stable → transitional
- Diffusion ↔ PLM: transitional → dispersed
4. Step 3 — Construct the Regime Map#
| Model Pair | Regime | Characteristics |
|---|---|---|
| LLM ↔ PLM | A₁ᴴ → A₂ᴴ | mostly stable, minor reorientation |
| LLM ↔ Diffusion | A₂ᴴ | branching, sampler‑dependent |
| Diffusion ↔ PLM | A₂ᴴ → A₃ᴴ | partial incompatibility |
5. Step 4 — Validate with vST Layers#
- V₁: structural coherence preserved for LLM ↔ PLM
- V₂: dimensional continuity intact across all pairs
- V₃: regime transitions substrate‑aligned
- V₄: core alignment stable for LLM ↔ PLM, transitional for others
6. Summary#
This example demonstrates:
- how to classify cross‑model alignment regimes
- how 9D projection reveals compatibility and divergence
- how vST layers validate cross‑architecture behavior
- how regime maps support multi‑model interpretability