vST for Multi‑Model Alignment#

Cross‑Model Alignment Regimes Across Architectures, Modalities, and Dimensional Scales#

This document defines the alignment‑regime structure that emerges when comparing heterogeneous models using the Validation‑Space‑Time (vST) framework and the 1024D dimensional substrate. These regimes generalize the triadic resonance structure (R₁/R₂/R₃) to the setting of cross‑model alignment, where latent geometries, inference pathways, and scaling behaviors differ across architectures and modalities.

Cross‑model regimes provide a reproducible, invariant‑preserving framework for interpreting alignment behavior across any pair (or set) of models.

1. Purpose of Cross‑Model Regime Analysis#

Cross‑model regime analysis enables us to:

• classify alignment behavior across heterogeneous architectures
• identify stable, transitional, and dispersed alignment regions
• detect incompatibilities or drift across models
• map coherence surfaces across modalities
• evaluate scaling‑law continuity across model families
• support vST validation (V₁–V₄)
• project alignment surfaces into 3D–9D cores for interpretability

Cross‑model alignment is structured, regime‑rich, and sensitive to scaling, modality, and architecture.

2. Regime Overview#

Cross‑model alignment follows the same triadic structure as the dimensional substrate:

1. Stable Alignment Regime (A₁ᴴ)
2. Transitional Alignment Regime (A₂ᴴ)
3. Dispersed / Incompatible Alignment Regime (A₃ᴴ)

The superscript H indicates high‑dimensional behavior (64D–1024D).

These regimes appear when aligning:

• LLMs ↔ PLMs
• diffusion ↔ autoregressive models
• simulators ↔ robotics policies
• embedding stores ↔ generative models
• any architecture ↔ any other architecture

3. Stable Alignment Regime (A₁ᴴ)#

Definition#

A region where two models exhibit coherent, low‑variance, structurally compatible latent behavior.

Characteristics#

• compact cross‑model motifs
• smooth alignment surfaces
• stable projection into 3D–9D cores
• primitive‑level compatibility (DP, TDP‑X, SP‑X, CP‑X)
• predictable cross‑model mapping

Interpretation#

A₁ᴴ corresponds to:

• shared semantic structure
• shared physical or biological invariants
• aligned inference pathways
• compatible scaling behavior

This is the “easy alignment” region.

4. Transitional Alignment Regime (A₂ᴴ)#

Definition#

A region where cross‑model alignment undergoes reorientation, branching, or partial fragmentation.

Characteristics#

• moderate variance across models
• oscillatory or branching alignment surfaces
• architecture‑dependent behavior
• increased sensitivity to scaling or modality differences
• regime‑transition indicators in resonance‑time space

Interpretation#

A₂ᴴ captures:

• alignment between models with different inductive biases
• cross‑modality transitions (e.g., text ↔ image)
• cross‑architecture transitions (e.g., diffusion ↔ autoregressive)
• mid‑trajectory alignment in simulators or robotics

It is the “structural hinge” of multi‑model alignment.

5. Dispersed / Incompatible Alignment Regime (A₃ᴴ)#

Definition#

A region where cross‑model alignment breaks down, producing diffuse, unstable, or incompatible mappings.

Characteristics#

• high variance across models
• fragmented or incoherent alignment surfaces
• unstable primitive‑level structure
• non‑compact projections into 3D–9D cores
• susceptibility to drift or scaling discontinuities

Interpretation#

A₃ᴴ corresponds to:

• modality mismatch
• architecture‑driven incompatibility
• scaling‑law divergence
• drift‑prone or chaotic behavior

This is the “alignment failure” region.

6. Cross‑Model Regime Transitions#

Cross‑model alignment moves through regimes as dimensionality, architecture, or modality changes:

• A₃ᴴ → A₂ᴴ
  partial compatibility emerges
• A₂ᴴ → A₁ᴴ
  stable alignment forms
• A₁ᴴ → A₂ᴴ
  architecture‑ or modality‑driven reorientation
• A₂ᴴ → A₃ᴴ
  incompatibility or drift emerges

Transitions must remain continuous and invariant‑preserving across dimensionality.

7. Regime Detection Signals#

Cross‑model regime identity is detected using:

• variance distribution across models
• coherence‑surface continuity
• primitive‑level stability (DP, TDP‑X, SP‑X, CP‑X)
• resonance‑time behavior
• cross‑model projection geometry
• vST validation layers (V₁–V₄)

These signals collectively determine regime classification.

8. Regime Behavior Across the Dimensional Ladder#

Regime behavior must remain consistent across:

• 64D minimal alignment substrate
• 128D–256D cross‑modality alignment
• 512D–1024D high‑capacity cross‑architecture alignment

The substrate ensures:

• structural invariants
• resonance‑time invariants
• projection invariants
• alignment invariants
• scaling invariants

Regime identity must be preserved under projection into 3D–9D cores.

9. Outputs of Cross‑Model Regime Analysis#

Cross‑model regime analysis produces:

• alignment‑regime maps
• cross‑architecture compatibility diagnostics
• scaling‑law indicators
• drift‑detection signals
• vST validation outputs
• projection‑stability metrics

These outputs support reproducible, substrate‑level interpretation of multi‑model alignment.