vST for Large Language Models#

Example: Cross‑Version Alignment of LLM Latent Spaces#

The example is model‑agnostic and applies to any transformer‑based LLM.

1. Scenario Overview#

We compare two versions of the same LLM:

• Model A (v1.0) — baseline checkpoint
• Model B (v1.1) — fine‑tuned or updated checkpoint

We analyze:

• latent‑trajectory alignment
• regime‑transition correspondence
• coherence‑surface stability
• projection behavior (1024D → 9D → 6D → 3D)
• drift category and severity

The comparison uses a single token’s latent pathway across all layers.

2. Step 1 — Extract Latent Pathways#

For each model, extract the 1024D hidden‑state vectors:

[ h^{A}_1,\ h^{A}_2,\ \dots,\ h^{A}_L ] [ h^{B}_1,\ h^{B}_2,\ \dots,\ h^{B}_L ]

Observed Properties#

Model A (v1.0)

• smooth variance distribution
• stable DP/TDP structure
• predictable regime transitions

Model B (v1.1)

• increased variance in mid‑layers
• sharper regime transitions
• mild fragmentation in late layers

Interpretation#

Model B exhibits structural changes introduced by fine‑tuning or training updates.

3. Step 2 — Classify Regime Behavior#

Using substrate‑aligned regime detection:

Model A (v1.0)#

• Layers 1–10: R₁ᴴ
• Layers 11–20: R₂ᴴ
• Layers 21–24: R₁ᴴ
• Layers 25–32: mild R₂ᴴ

Model B (v1.1)#

• Layers 1–8: R₁ᴴ
• Layers 9–18: strong R₂ᴴ
• Layers 19–22: R₁ᴴ
• Layers 23–32: R₂ᴴ → R₃ᴴ onset

Interpretation#

Model B shows:

• earlier entry into R₂ᴴ
• stronger oscillatory behavior
• partial dispersion in late layers

This indicates potential drift.

4. Step 3 — Project 1024D → 9D#

Project both models’ latent pathways into the 9D coherence core.

Model A (v1.0)#

• smooth coherence surfaces
• stable curvature
• consistent primitive alignment

Model B (v1.1)#

• sharper curvature changes
• partial fragmentation in late layers
• reduced projection stability

Interpretation#

Model B’s coherence surfaces show signs of structural drift.

5. Step 4 — Project 9D → 6D → 3D#

Evaluate projection stability across dimensional reductions.

Model A (v1.0)#

• compact 3D motifs
• smooth 6D interaction surfaces
• stable mapping across layers

Model B (v1.1)#

• oscillatory 6D surfaces
• diffuse 3D motifs in late layers
• partial loss of primitive alignment

Interpretation#

Model B exhibits projection drift, especially near the output layers.

6. Step 5 — Alignment Analysis#

Compare the two models’ projected trajectories.

Alignment Results#

• Early layers: high alignment (stable R₁ᴴ)
• Mid layers: moderate divergence (stronger R₂ᴴ in Model B)
• Late layers: significant divergence (R₃ᴴ onset in Model B)

Coherence‑Surface Overlap#

• 82% overlap in early layers
• 61% overlap in mid layers
• 34% overlap in late layers

Interpretation#

The models share early‑layer structure but diverge significantly in deeper layers.

7. Step 6 — vST Validation#

Apply vST layers (V₁–V₄) to both models.

Model A (v1.0)#

• V₁: pass
• V₂: pass
• V₃: pass
• V₄: pass

Model B (v1.1)#

• V₁: minor warnings (structural coherence)
• V₂: warning (dimensional continuity)
• V₃: warning (regime instability)
• V₄: warning (core alignment)

Interpretation#

Model B remains functional but exhibits measurable structural instability.

8. Step 7 — Drift Detection#

Assign drift categories (D₁–D₄) and severity.

Model B (v1.1)#

• D₁ Structural Drift: low
• D₂ Dimensional Drift: moderate
• D₃ Regime Drift: moderate
• D₄ Projection Drift: moderate

Severity: Moderate Drift#

Interpretation#

Model B introduces meaningful structural changes that may affect reliability or alignment.

9. Summary#

This example demonstrates:

• how to compare latent pathways across model versions
• how regime behavior reveals structural changes
• how projection exposes coherence‑surface divergence
• how vST layers quantify stability
• how drift detection identifies meaningful differences

Cross‑version alignment is essential for evaluating model updates, fine‑tuning, and long‑term model governance.