vST for Large Language Models#
Projection and Alignment of High‑Dimensional LLM Latent States#
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.