TriadicFrameworks
Overview

vST for Large Language Models#

Latent‑Trajectory Regimes in LLM Inference#

This document defines the latent‑trajectory regimes that arise during inference in Large Language Models (LLMs). These regimes generalize the triadic resonance structure of the 3D–9D substrate and describe how stability, transition, and dispersion behaviors manifest in high‑dimensional latent spaces (64D–4096D).

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.

Powered by Docsbook