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vST for Protein Language Models#

Sequence‑Embedding Regimes in PLM Inference#

Sequence‑embedding regimes provide a reproducible, invariant‑preserving framework for interpreting PLM behavior across residues, layers, and model sizes.

1. Purpose of Sequence‑Embedding Regimes#

Sequence‑embedding regimes allow us to:

  • classify residue‑level embedding behavior into stable, transitional, and dispersed phases
  • identify coherence surfaces along the protein sequence
  • detect instability or drift across checkpoints or versions
  • analyze scaling‑law behavior across PLM sizes
  • project high‑dimensional embeddings into 3D–9D cores
  • support vST validation (V₁–V₄)

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

2. Regime Overview#

PLM embeddings 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:

  • residue embeddings
  • attention outputs
  • MLP activations
  • cross‑layer embedding pathways

3. Stable Regime (R₁ᴴ)#

Definition#

A region of embedding space where residue embeddings converge consistently and maintain coherence across layers.

Characteristics#

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

Interpretation#

R₁ᴴ corresponds to stable biochemical or structural signals, often associated with:

  • conserved motifs
  • secondary‑structure anchors
  • stable residue environments

4. Transition Regime (R₂ᴴ)#

Definition#

A region where embedding trajectories undergo reorientation, branching, or oscillatory behavior across residues.

Characteristics#

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

Interpretation#

R₂ᴴ captures dynamic behavior such as:

  • boundary regions between structural elements
  • ambiguous or flexible residues
  • context‑dependent biochemical signals

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

5. Dispersion Regime (R₃ᴴ)#

Definition#

A region where embedding 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 embedding behavior, often associated with:

  • low‑confidence predictions
  • disordered regions
  • rare or poorly represented sequence patterns

6. Regime Transitions Along the Sequence#

Residue‑level embedding trajectories move through regimes as the model processes the sequence:

  • R₁ᴴ → R₂ᴴ
    onset of structural or biochemical ambiguity
  • R₂ᴴ → R₁ᴴ
    return to stable structural context
  • R₂ᴴ → R₃ᴴ
    breakdown of coherence
  • R₃ᴴ → R₂ᴴ
    partial recovery

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

7. Regime Detection Signals#

Regime identity is detected using:

  • variance distribution across dimensions
  • coherence‑surface continuity along the sequence
  • 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 residue 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 Sequence‑Embedding Regime Analysis#

Sequence‑embedding regime analysis produces:

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

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

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