TriadicFrameworks
Overview

vST for Multi‑Model Alignment#

Substrate Definition#

The substrate is architecture‑agnostic and applies to LLMs, PLMs, diffusion models, VAEs, flow models, simulators, robotics policies, embedding stores, and hybrid systems.

1. Purpose of the Multi‑Model Alignment Substrate#

The multi‑model substrate provides a structured, reproducible framework for:

  • aligning latent spaces across architectures and modalities
  • mapping regime behavior (R₁/R₂/R₃) across heterogeneous inference systems
  • comparing scaling behavior across model families
  • projecting high‑dimensional states into 3D–9D cores for cross‑model interpretability
  • detecting drift across architectures, checkpoints, or training runs
  • establishing a unified dimensional grammar for all model types

Multi‑model alignment requires a substrate that is neutral, invertible, and invariant‑preserving across all architectures.

2. Substrate Overview#

The multi‑model substrate models heterogeneous latent spaces using:

  • Dimensional Primitives (DP)
  • Triadic Dimensional Primitives (TDP)
  • Scaling Primitives (SP)
  • Coherence Primitives (CP)
  • Alignment Primitives (AP)

These primitives define the structure of cross‑model alignment, regime mapping, and projection behavior.

The substrate is anchored by the Triadic Dimensional Cores:

  • 3D Structural Core
  • 6D Interaction Core
  • 9D Coherence Core

and extended through the 1024D high‑dimensional substrate.

3. Alignment Primitives#

3.1 Alignment Primitive (AP)#

The AP is the minimal unit of cross‑model comparability.
It captures:

  • local geometric compatibility
  • variance‑aligned structure
  • regime‑consistent mapping
  • projection‑stable correspondence

APs allow two heterogeneous latent states to be compared without requiring architectural similarity.

3.2 Cross‑Architecture TDP (TDP‑X)#

A TDP‑X is a triad of APs that expresses full cross‑model regime behavior.

It captures:

  • stable alignment (R₁ ↔ R₁)
  • transitional alignment (R₂ ↔ R₂)
  • dispersed alignment (R₃ ↔ R₃)

TDP‑X is the backbone of multi‑model regime mapping.

3.3 Cross‑Model Scaling Primitive (SP‑X)#

SP‑X governs dimensional expansion across architectures.

It ensures:

  • invariant‑preserving scaling
  • compatibility between different latent dimensionalities
  • stable projection into triadic cores
  • consistent scaling‑law interpretation across models

SP‑X is essential for aligning models with different latent sizes (e.g., 4096D LLM ↔ 1024D diffusion ↔ 256D PLM).

3.4 Cross‑Modality Coherence Primitive (CP‑X)#

CP‑X identifies stable or unstable regions in cross‑model alignment.

It captures:

  • coherent alignment regions
  • transitional alignment regions
  • dispersed or incompatible regions
  • cross‑modality regime transitions

CP‑X is essential for drift detection and vST validation.

4. Triadic Dimensional Cores for Multi‑Model Alignment#

4.1 3D Structural Core#

Captures motif‑level geometry shared across models.

Used for:

  • cross‑modality motif comparison
  • alignment of stable regimes
  • low‑variance structural mapping

4.2 6D Interaction Core#

Captures relational structure across architectures.

Used for:

  • cross‑model interaction surfaces
  • alignment of transitional regimes
  • sampler‑ or decoder‑dependent reorientation

4.3 9D Coherence Core#

Captures pathway‑level coherence across heterogeneous inference systems.

Used for:

  • cross‑model coherence mapping
  • alignment of inference trajectories
  • invertible projection from higher dimensions

The 9D core is the anchor for all cross‑model alignment.

5. High‑Dimensional Substrate (64D–1024D)#

The multi‑model substrate spans the dimensional ladder:

  • 64D — minimal cross‑model substrate
  • 128D — expanded alignment surfaces
  • 256D — multi‑primitive interaction
  • 512D — high‑variance cross‑architecture regions
  • 1024D — full research‑grade alignment substrate

Each step preserves:

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

This ensures stable alignment across architectures and modalities.

6. Cross‑Model Alignment Structure#

Cross‑model alignment is modeled as:

  • sequences of APs
  • grouped into TDP‑X
  • expanded through SP‑X
  • classified using CP‑X

This structure enables:

  • regime‑aware alignment
  • cross‑modality comparison
  • cross‑architecture drift detection
  • unified scaling‑law interpretation

7. Projection into Triadic Cores#

High‑dimensional states from different models are projected into:

  • 9D for coherence alignment
  • 6D for interaction alignment
  • 3D for geometric alignment

Projection must remain:

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

Projection is essential for cross‑model interpretability.

8. Substrate Outputs#

The multi‑model substrate produces:

  • cross‑model regime maps
  • alignment surfaces
  • scaling‑law diagnostics
  • projection‑stability indicators
  • drift‑detection signals
  • vST validation outputs

These outputs support reproducible, substrate‑level alignment across architectures, modalities, and inference systems.

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