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.