vST for Multi‑Model Alignment#

Cross‑Architecture Scaling Behavior Across the Dimensional Ladder#

This document defines how multi‑model alignment behaves as dimensionality, model size, modality complexity, and architectural diversity increase. It maps cross‑model scaling laws onto the 3D–1024D dimensional ladder, providing a reproducible, invariant‑preserving framework for understanding how alignment capacity grows, stabilizes, or fragments across heterogeneous systems.

Scaling in multi‑model alignment is not about increasing parameters — it is about increasing compatibility, coherence, and alignment bandwidth across models.

1. Purpose of Multi‑Model Scaling Analysis#

Cross‑model scaling analysis enables us to:

• interpret how alignment capacity expands with model size and modality diversity
• identify stable, transitional, and dispersed scaling regimes
• detect scaling discontinuities across architectures
• evaluate cross‑model compatibility at different dimensional levels
• support vST validation (V₁–V₄)
• project alignment surfaces into 3D–9D cores for interpretability

Scaling is the backbone of cross‑model comparability.

2. Dimensional Ladder for Multi‑Model Alignment#

Cross‑model alignment naturally aligns with the substrate’s dimensional ladder:

• 3D — geometric alignment motifs
• 6D — interaction‑surface alignment
• 9D — coherence‑pathway alignment
• 64D — minimal cross‑model substrate
• 128D — expanded alignment surfaces
• 256D — multi‑primitive cross‑architecture interaction
• 512D — high‑variance cross‑modality regions
• 1024D — full research‑grade alignment substrate

Each step increases alignment bandwidth and structural compatibility.

3. Scaling Primitives for Multi‑Model Alignment#

Scaling behavior is governed by Cross‑Model Scaling Primitives (SP‑X), which ensure:

• invariant‑preserving dimensional expansion
• compatibility between heterogeneous latent spaces
• stable projection into triadic cores
• consistent scaling‑law interpretation across architectures

SP‑X is essential for aligning models with different latent sizes, modalities, or inference dynamics.

4. Scaling Regimes in Multi‑Model Alignment#

4.1 Stable Scaling Regime (S₁ᴹ)#

Characteristics:

• smooth increase in alignment capacity
• stable cross‑model coherence surfaces
• predictable improvements in compatibility
• consistent regime behavior (A₁ᴴ ↔ A₁ᴴ transitions remain bounded)

Occurs in:

• small → medium model comparisons
• similar modalities (e.g., LLM ↔ PLM)
• well‑conditioned cross‑model projections

4.2 Transitional Scaling Regime (S₂ᴹ)#

Characteristics:

• rapid expansion of alignment surfaces
• increased variance across architectures
• branching or oscillatory cross‑model behavior
• sensitivity to modality or architecture differences

Occurs in:

• medium → large model comparisons
• cross‑modality alignment (e.g., text ↔ image)
• cross‑architecture transitions (e.g., diffusion ↔ autoregressive)

4.3 Dispersion Scaling Regime (S₃ᴹ)#

Characteristics:

• fragmentation of alignment surfaces
• unstable or divergent cross‑model mappings
• increased risk of alignment collapse
• non‑invertible projections into 3D–9D cores

Occurs in:

• extremely heterogeneous model pairs
• poorly conditioned cross‑modality mappings
• aggressive scaling or architecture changes

5. Scaling Behavior Across Model Families#

5.1 LLM ↔ PLM#

• high compatibility
• scaling mostly in S₁ᴹ
• stable alignment surfaces

5.2 LLM ↔ Diffusion#

• modality mismatch introduces S₂ᴹ
• alignment depends on projection stability

5.3 Diffusion ↔ Autoregressive Generators#

• different inference dynamics
• transitional scaling dominates (S₂ᴹ)

5.4 Simulators ↔ Robotics Policies#

• strong structural invariants
• scaling often stable (S₁ᴹ → S₂ᴹ)

5.5 Embedding Stores ↔ Generative Models#

• alignment depends on latent‑space conditioning
• scaling oscillates between S₂ᴹ and S₃ᴹ

6. Scaling‑Law Alignment Across Architectures#

Cross‑model scaling follows predictable patterns:

• alignment bandwidth increases with latent dimensionality
• variance increases with modality diversity
• coherence surfaces expand smoothly in S₁ᴹ, sharply in S₂ᴹ, and fragment in S₃ᴹ
• projection stability decreases as architectural heterogeneity increases

The substrate provides a structured way to interpret these patterns.

7. Projection Behavior Under Cross‑Model Scaling#

Projection into triadic cores must remain:

• invertible
• primitive‑aligned
• regime‑aware
• architecture‑neutral
• invariant‑preserving

Scaling affects projection as follows:

• 64D → 9D: stable
• 128D–256D → 9D: transitional
• 512D–1024D → 9D: sensitive, drift‑prone

Projection stability is a key indicator of cross‑model scaling health.

8. Scaling‑Driven Drift in Multi‑Model Alignment#

Scaling can introduce drift through:

• discontinuities in cross‑model latent‑space expansion
• unstable regime transitions
• fragmentation of alignment surfaces
• loss of primitive‑level compatibility

vST validation layers (V₁–V₄) detect these failures.

9. Outputs of Multi‑Model Scaling Analysis#

Scaling analysis produces:

• scaling‑regime classification (S₁ᴹ, S₂ᴹ, S₃ᴹ)
• cross‑model expansion diagnostics
• projection‑stability indicators
• alignment‑regime maps
• drift‑detection signals
• cross‑architecture comparison metrics

These outputs support reproducible, substrate‑aligned evaluation of multi‑model alignment.