vST for Large Language Models#

Latent‑Trajectory Regimes in LLM Inference#

Latent‑trajectory regimes provide a reproducible, invariant‑preserving framework for interpreting LLM behavior across tokens, layers, and model sizes.

1. Purpose of Latent‑Trajectory Regimes#

Latent‑trajectory regimes allow us to:

• classify LLM inference behavior into stable, transitional, and dispersed phases
• identify coherence surfaces in embedding and hidden‑state space
• detect instability or drift across checkpoints or versions
• analyze scaling‑law behavior across model sizes
• project high‑dimensional trajectories into 3D–9D cores
• support vST validation (V₁–V₄)

These regimes form the backbone of substrate‑level LLM analysis.

2. Regime Overview#

LLM latent trajectories follow the same triadic structure as the dimensional substrate:

1. Stable Regime (R₁ᴴ)
2. Transition Regime (R₂ᴴ)
3. Dispersion Regime (R₃ᴴ)

The superscript H indicates high‑dimensional behavior.

These regimes appear in:

• token embeddings
• attention outputs
• MLP activations
• residual streams
• cross‑layer latent pathways

3. Stable Regime (R₁ᴴ)#

Definition#

A region of latent space where trajectories converge consistently and maintain coherence across layers and tokens.

Characteristics#

• compact, low‑variance latent vectors
• stable coherence surfaces
• predictable projection into 3D–9D cores
• primitive‑level integrity (DP, TDP, SP)
• minimal sensitivity to perturbations

Interpretation#

R₁ᴴ corresponds to stable inference behavior, often associated with:

• predictable next‑token distributions
• well‑formed syntactic or semantic structure
• high‑confidence model states

4. Transition Regime (R₂ᴴ)#

Definition#

A region where latent trajectories undergo reorientation, branching, or oscillatory behavior.

Characteristics#

• moderate variance across dimensions
• branching or oscillatory latent patterns
• partial coherence‑surface stability
• increased sensitivity to context or perturbation
• regime‑transition indicators in resonance‑time space

Interpretation#

R₂ᴴ captures dynamic behavior such as:

• topic shifts
• syntactic reconfiguration
• semantic branching
• uncertainty resolution

It is the “decision‑making” region of LLM inference.

5. Dispersion Regime (R₃ᴴ)#

Definition#

A region where latent trajectories lose coherence and disperse across high‑dimensional space.

Characteristics#

• high variance across dimensions
• fragmented or diffuse coherence surfaces
• unstable primitive‑level structure
• non‑compact projections into 3D–9D cores
• susceptibility to drift or hallucination

Interpretation#

R₃ᴴ corresponds to unstable or divergent inference behavior, often associated with:

• hallucination
• incoherent continuation
• semantic drift
• over‑generalization

6. Regime Transitions in LLMs#

Latent trajectories move through regimes as inference progresses:

• R₁ᴴ → R₂ᴴ
  onset of branching or reorientation
• R₂ᴴ → R₁ᴴ
  return to stable structure
• R₂ᴴ → R₃ᴴ
  breakdown of coherence
• R₃ᴴ → R₂ᴴ
  partial recovery

Transitions must remain continuous and invariant‑preserving across layers and tokens.

7. Regime Detection Signals#

Regime identity is detected using:

• variance distribution across dimensions
• coherence‑surface continuity
• primitive‑level stability (DP, TDP, SP, CP)
• resonance‑time behavior
• vST validation layers (V₁–V₄)

These signals collectively determine regime classification.

8. Regime Behavior Across the Dimensional Ladder#

Regime behavior must remain consistent across:

• 64D latent embeddings
• 128D–512D hidden states
• 1024D+ attention and MLP activations

The substrate ensures:

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

Regime identity must be preserved under projection into 3D–9D cores.

9. Outputs of Latent‑Trajectory Regime Analysis#

Latent‑trajectory regime analysis produces:

• regime‑aware token‑level diagnostics
• cross‑layer coherence maps
• scaling‑law indicators
• drift‑detection signals
• vST validation outputs
• projection‑stability metrics

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