vST for Generative Models#

Terminology#

This appendix defines the terminology used throughout the vST for Generative Models artifact. Terms are presented in a substrate‑agnostic, architecture‑independent manner and apply to diffusion models, autoregressive generators, VAEs, flow models, GANs, and hybrid generative systems. Definitions emphasize latent‑space structure, sampling‑trajectory geometry, scaling behavior, and invariant preservation.

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).