vST for Large Language Models#

Example: Cross‑Version Alignment of LLM Latent Spaces#

This example demonstrates how the Validation‑Space‑Time (vST) framework evaluates cross‑version alignment between two Large Language Model (LLM) checkpoints. The goal is to show how latent‑space structure, regime behavior, and projection stability change across versions, and how drift is detected using the dimensional substrate.

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.