vST for Generative Models#
Example: 1024D Latent Projection and Cross‑Checkpoint Alignment#
This example demonstrates how a 1024D latent state from a generative model is projected into the triadic cores (9D → 6D → 3D), and how two checkpoints are aligned using vST.
It illustrates projection stability, primitive‑aligned mapping, and drift detection.
1. Scenario Overview#
We assume:
- a 1024D latent diffusion model
- two checkpoints: C₁ (earlier) and C₂ (later)
- a single latent state ( z ) sampled at a mid‑trajectory step
- a need to compare latent geometry across checkpoints
2. Step 1 — Extract Latent States#
Let:
[ z_{C_1}, z_{C_2} \in \mathbb{R}^{1024} ]
represent the latent state under each checkpoint.
Observed Properties#
- ( z_{C_1} ): slightly higher variance
- ( z_{C_2} ): more compact, refined structure
3. Step 2 — Project 1024D → 9D#
Project both latent states into the 9D coherence core.
Reveals#
- ( z_{C_1} ): branching, transitional geometry (R₂ᴴ)
- ( z_{C_2} ): compact, stable geometry (R₁ᴴ)
Interpretation#
The later checkpoint exhibits improved coherence.
4. Step 3 — Project 9D → 6D#
The 6D interaction projection shows:
- smoother surfaces for ( z_{C_2} )
- cross‑step coupling more stable
- fewer oscillatory transitions
5. Step 4 — Project 6D → 3D#
The 3D structural projection shows:
- ( z_{C_1} ): oscillatory motifs
- ( z_{C_2} ): compact, low‑variance motifs
Interpretation#
The 3D projection reveals motif‑level refinement across checkpoints.
6. Step 5 — Cross‑Checkpoint Alignment#
Alignment in 9D and 6D shows:
- consistent structural backbone
- improved coherence surfaces in C₂
- reduced fragmentation
- stable primitive‑aligned mapping
7. Step 6 — Drift Detection#
Using vST drift categories:
- D₁ Structural Drift: low
- D₂ Dimensional Drift: none
- D₃ Regime Drift: moderate (R₂ᴴ → R₁ᴴ shift)
- D₄ Projection Drift: none
Interpretation#
The drift is positive — a refinement, not a degradation.
8. Summary#
This example demonstrates:
- how 1024D latent states are projected into triadic cores
- how cross‑checkpoint alignment reveals structural improvement
- how drift detection isolates transitional changes
- how vST ensures invariant‑preserving comparison