vST for Multi‑Model Alignment#
Projection of Heterogeneous Latent Spaces and Construction of Cross‑Model Alignment Surfaces#
1. Purpose of Projection in Multi‑Model Alignment#
Projection enables us to:
- interpret heterogeneous latent spaces through a shared 3D–9D substrate
- identify stable, transitional, and dispersed cross‑model alignment regimes
- map coherence surfaces across architectures and modalities
- compare inference pathways across model families
- detect drift or incompatibility in cross‑model structure
- support vST validation (V₁–V₄)
Cross‑model projection must be architecture‑neutral, invertible, and invariant‑preserving.
2. Projection Overview#
Models may inhabit radically different latent spaces:
- LLMs: 1024D–8192D
- PLMs: 256D–2048D
- Diffusion models: 64D–4096D
- Simulators: structured state‑spaces
- Robotics policies: control‑trajectory manifolds
- Embedding stores: 64D–4096D
The substrate projects all of these into:
- 9D Coherence Core
- 6D Interaction Core
- 3D Structural Core
Projection must remain:
- invertible
- primitive‑aligned (DP, TDP‑X, SP‑X, CP‑X)
- regime‑aware (A₁ᴴ, A₂ᴴ, A₃ᴴ)
- scaling‑invariant
- architecture‑neutral
3. Projection Steps#
3.1 High‑Dimensional → 9D (Cross‑Model Coherence Projection)#
This step extracts cross‑model coherence pathways.
Preserves
- alignment regime identity (A₁ᴴ, A₂ᴴ, A₃ᴴ)
- resonance‑time behavior
- primitive‑level structure (DP, TDP‑X, SP‑X, CP‑X)
- cross‑model coherence surfaces
Reveals
- stable cross‑model compatibility
- transitional reorientation
- dispersed or incompatible regions
3.2 9D → 6D (Cross‑Model Interaction Projection)#
This step compresses coherence pathways into interaction surfaces.
Preserves
- relational geometry across architectures
- cross‑modality coupling
- regime‑transition indicators
Reveals
- architecture‑dependent reorientation
- modality‑driven divergence
- early incompatibility signatures
3.3 6D → 3D (Cross‑Model Structural Projection)#
This step reduces interaction surfaces into geometric motifs.
Preserves
- motif‑level alignment geometry
- stable structural invariants
- cross‑model continuity
Reveals
- compact motifs in A₁ᴴ
- oscillatory geometry in A₂ᴴ
- diffuse patterns in A₃ᴴ
4. Alignment Surfaces Overview#
Alignment surfaces are geometric manifolds that represent how two or more models relate across:
- latent spaces
- inference pathways
- modalities
- architectures
- dimensional scales
They are constructed in 9D, refined in 6D, and visualized in 3D.
Alignment surfaces must remain:
- primitive‑aligned
- regime‑aware
- projection‑consistent
- scaling‑invariant
- architecture‑neutral
5. Types of Alignment Surfaces#
5.1 Latent‑Space Alignment Surfaces#
Compare latent geometries across models.
Used for:
- LLM ↔ PLM
- diffusion ↔ autoregressive
- VAE ↔ flow models
5.2 Inference‑Trajectory Alignment Surfaces#
Compare inference pathways across architectures.
Used for:
- diffusion trajectories ↔ autoregressive decoding
- simulator rollouts ↔ robotics control trajectories
5.3 Cross‑Modality Alignment Surfaces#
Compare embeddings across modalities.
Used for:
- text ↔ image
- protein ↔ structure
- control ↔ simulation
5.4 Cross‑Architecture Alignment Surfaces#
Compare models with different inductive biases.
Used for:
- transformer ↔ convolutional
- diffusion ↔ autoregressive
- graph neural network ↔ sequence model
6. Alignment Surface Stability and Failure Modes#
Stable Alignment Surfaces#
- smooth geometry
- compact motifs
- coherent 9D pathways
- consistent cross‑model mapping
Unstable Alignment Surfaces#
- fragmented surfaces
- non‑invertible projections
- regime‑transition discontinuities
- architecture‑dependent divergence
Unstable surfaces indicate drift, incompatibility, or scaling‑law violations.
7. Alignment Failure Modes#
Alignment failures include:
- cross‑modality incompatibility
- architecture‑driven divergence
- scaling discontinuities
- loss of primitive‑aligned projection
- inconsistent 3D–9D mapping
These failures signal structural misalignment.
8. Outputs of Projection and Alignment Surfaces#
Projection and alignment analysis produces:
- cross‑model coherence maps
- alignment surfaces in 9D, 6D, and 3D
- cross‑architecture drift‑detection signals
- scaling‑law diagnostics
- vST validation outputs
- interpretable cross‑model projections
These outputs support reproducible, substrate‑level alignment across architectures, modalities, and inference systems.