vST for Generative Models#

Terminology#

1. Substrate Terms#

Generative‑Model Substrate#

A structured, invariant‑preserving framework for representing and interpreting latent‑space behavior across 64D–1024D.

Latent Space#

The high‑dimensional vector space in which generative models perform sampling, denoising, decoding, or transformation.

Coherence Surface#

A stable region in latent space where generative states maintain structural continuity across sampling steps or checkpoints.

2. Primitive Terms#

Dimensional Primitive (DP)#

The minimal unit of latent‑space structure, capturing local coherence, variance behavior, and projection stability.

Triadic Dimensional Primitive (TDP)#

A triad of DPs forming the smallest unit capable of expressing full generative‑regime behavior (R₁, R₂, R₃).

Scaling Primitive (SP)#

A rule‑based expansion unit that preserves invariants during dimensional scaling (e.g., model size, latent dimensionality, sampler complexity).

Coherence Primitive (CP)#

A minimal unit identifying stable, transitional, or dispersed regions in latent space.

3. Core Terms#

Triadic Dimensional Core (TDC)#

The 3D–9D substrate composed of one or more TDPs, used for interpretable projection of latent states.

3D Structural Core#

Captures motif‑level geometry in stable generative phases.

6D Interaction Core#

Captures relational structure across sampling steps or decoding transitions.

9D Coherence Core#

Captures pathway‑level coherence across generative trajectories.

4. Regime Terms#

High‑Dimensional Regimes (R₁ᴴ, R₂ᴴ, R₃ᴴ)#

The triadic regime structure expressed in 64D–1024D latent spaces.

Stable Regime (R₁ / R₁ᴴ)#

Compact, coherent, low‑variance generative behavior.

Transitional Regime (R₂ / R₂ᴴ)#

Branching, oscillatory, or reorientation behavior across sampling or decoding phases.

Dispersed Regime (R₃ / R₃ᴴ)#

Diffuse, noisy, or unstable latent behavior.

5. Scaling Terms#

Scaling Behavior#

The structured expansion of latent‑space capacity as model size, sampler complexity, or latent dimensionality increases.

Scaling Regimes (S₁, S₂, S₃)#

Triadic scaling behavior describing stable, transitional, and dispersion‑prone scaling phases.

Dimensional Continuity#

The requirement that latent‑space expansion remains smooth and invariant‑preserving across the dimensional ladder.

6. Projection Terms#

Invertible Projection#

A projection from high‑dimensional latent space into 3D–9D that preserves primitive‑level structure and regime identity.

Regime‑Aware Projection#

A projection that maintains correct mapping of R₁, R₂, and R₃ behaviors.

Primitive‑Aligned Projection#

A projection that preserves DP, TDP, SP, and CP structure.

7. Alignment Terms#

Cross‑Checkpoint Alignment#

Comparison of latent‑space structure across training checkpoints.

Cross‑Sampler Alignment#

Comparison of latent trajectories across different sampling algorithms or noise schedules.

Cross‑Architecture Alignment#

Comparison of latent‑space behavior across generative architectures.

8. Validation Terms#

vST (Validation‑Space‑Time)#

A substrate‑level validation framework evaluating structural coherence, dimensional continuity, regime behavior, and core alignment.

Validation Layers (V₁–V₄)#

Four structured evaluation layers ensuring invariant‑preserving behavior across the dimensional ladder.

9. Drift Terms#

Drift#

A deviation from expected substrate behavior, indicating instability or invariant failure.

Drift Categories (D₁–D₄)#

Classification of drift into structural, dimensional, regime, or projection drift.

Drift Severity#

A measure of drift magnitude (low, moderate, high).