vST for Large Language Models#

Projection and Alignment of High‑Dimensional LLM Latent States#

This document defines how high‑dimensional latent states produced by Large Language Models (LLMs) are projected into the triadic dimensional cores (3D–9D) and how alignment is evaluated across layers, tokens, and model versions. Projection and alignment form the interpretability backbone of the vST framework, enabling stable, invariant‑preserving analysis of LLM inference.

1. Purpose of Projection and Alignment#

Projection and alignment allow us to:

• interpret high‑dimensional latent states through the 3D–9D cores
• identify stable, transitional, and dispersed regions of latent space
• compare latent trajectories across layers, tokens, or model versions
• detect drift or fragmentation in latent‑space structure
• evaluate scaling behavior using a common substrate
• support vST validation (V₁–V₄)

Projection is the interpretability mechanism; alignment is the comparison mechanism.

2. Projection Overview#

LLM latent states typically inhabit 64D–4096D spaces.
The substrate projects these states into:

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

Projection must remain:

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

These properties ensure that high‑dimensional behavior remains interpretable.

3. Projection Steps#

3.1 High‑Dimensional → 9D (Coherence Projection)#

This step extracts pathway‑level coherence from the latent state.

Preserves:

• resonance‑time behavior
• regime identity (R₁ᴴ, R₂ᴴ, R₃ᴴ)
• coherence‑surface continuity
• primitive‑level structure (DP, TDP, SP, CP)

Reveals:

• stable vs. unstable latent pathways
• branching or oscillatory transitions
• dispersion patterns

3.2 9D → 6D (Interaction Projection)#

This step compresses coherence pathways into interaction surfaces.

Preserves:

• relational structure
• interaction‑level geometry
• regime‑transition indicators

Reveals:

• attention‑driven reorientation
• syntactic or semantic branching
• cross‑layer interaction patterns

3.3 6D → 3D (Structural Projection)#

This step reduces interaction surfaces into geometric motifs.

Preserves:

• motif‑level geometry
• backbone‑level continuity
• stable structural invariants

Reveals:

• compact latent motifs
• stable vs. unstable geometric patterns
• minimal interpretable structure

4. Alignment Overview#

Alignment compares projected structures across:

• layers
• tokens
• model versions
• architectures
• training checkpoints

Alignment must remain:

• primitive‑aligned
• regime‑aware
• projection‑consistent
• scaling‑invariant

Alignment is evaluated in 3D–9D space for interpretability and stability.

5. Alignment Types#

5.1 Layer‑to‑Layer Alignment#

Compares latent trajectories across transformer layers.

Reveals:

• where regime transitions occur
• how coherence surfaces evolve
• which layers stabilize or destabilize inference

5.2 Token‑to‑Token Alignment#

Compares latent states across positions in a sequence.

Reveals:

• semantic drift
• syntactic reorientation
• branching behavior in R₂ᴴ

5.3 Cross‑Version Alignment#

Compares latent trajectories across model versions or checkpoints.

Reveals:

• drift introduced by fine‑tuning
• stability of coherence surfaces
• changes in regime behavior

This is essential for model‑version governance.

5.4 Cross‑Model Alignment#

Compares different architectures or model families.

Reveals:

• shared coherence surfaces
• divergent scaling behavior
• compatibility or incompatibility of latent spaces

This supports multi‑model interpretability.

6. Alignment Metrics#

Alignment is evaluated using:

• coherence‑surface overlap
• regime‑transition correspondence
• primitive‑level stability (DP, TDP, SP, CP)
• projection‑stability metrics
• variance‑distribution similarity
• drift‑detection indicators

These metrics are substrate‑aligned and model‑agnostic.

7. Projection Stability and Failure Modes#

Projection stability is a key indicator of model health.

Stable Projection#

• compact 3D motifs
• smooth 6D surfaces
• coherent 9D pathways

Unstable Projection#

• fragmented surfaces
• non‑invertible mappings
• regime‑transition discontinuities

Unstable projection indicates drift or scaling‑law violations.

8. Outputs of Projection and Alignment#

Projection and alignment produce:

• regime‑aware latent‑trajectory maps
• cross‑layer and cross‑token alignment surfaces
• cross‑version drift‑detection signals
• scaling‑law diagnostics
• vST validation outputs
• interpretable 3D–9D projections

These outputs support reproducible, substrate‑level analysis of LLM inference.