vST for Protein Language Models#

Terminology#

This appendix defines the terminology used throughout the vST for Protein Language Models artifact. Terms are presented in a substrate‑agnostic, model‑independent manner and apply to any transformer‑based PLM operating across the full dimensional ladder (3D → 1024D). Definitions emphasize primitive‑level structure, regime behavior, scaling continuity, and invariant preservation.

1. Substrate Terms#

PLM Substrate#

A structured, invariant‑preserving framework for representing and interpreting protein‑sequence embeddings across 64D–4096D.

Dimensional Ladder#

The ordered sequence of dimensional regimes used for projection and scaling analysis:
3D → 6D → 9D → 64D → 128D → 256D → 512D → 1024D.

Coherence Surface#

A stable region in embedding space where residue‑level trajectories converge and maintain structural continuity.

2. Primitive Terms#

Dimensional Primitive (DP)#

The minimal unit of embedding‑space structure, capturing local coherence and variance behavior across residues.

Triadic Dimensional Primitive (TDP)#

A triad of DPs forming the smallest unit capable of expressing full regime behavior (R₁, R₂, R₃).

Scaling Primitive (SP)#

A rule‑based expansion unit that preserves invariants during dimensional scaling.

Coherence Primitive (CP)#

A minimal unit identifying stable, transitional, or dispersed regions in high‑dimensional embedding space.

3. Core Terms#

Triadic Dimensional Core (TDC)#

The 3D–9D substrate composed of one or more TDPs, used for interpretable projection of residue embeddings.

3D Structural Core#

Captures motif‑level geometry and compact residue‑level structure.

6D Interaction Core#

Captures relational and attention‑driven structure across residues.

9D Coherence Core#

Captures pathway‑level coherence and resonance‑time behavior across the sequence.

4. Regime Terms#

High‑Dimensional Regimes (R₁ᴴ, R₂ᴴ, R₃ᴴ)#

The triadic regime structure expressed in 64D–1024D embedding space.

Stable Regime (R₁ / R₁ᴴ)#

Compact, coherent, low‑variance embedding behavior.

Transition Regime (R₂ / R₂ᴴ)#

Branching, oscillatory, or reorientation behavior across residues.

Dispersion Regime (R₃ / R₃ᴴ)#

Diffuse, fragmented, or unstable embedding behavior.

5. Scaling Terms#

Scaling Behavior#

The structured expansion of embedding‑space capacity as PLM size increases.

Scaling Regimes (S₁, S₂, S₃)#

Triadic scaling behavior describing stable, transitional, and dispersion‑prone scaling phases.

Dimensional Continuity#

The requirement that embedding‑space expansion remains smooth and invariant‑preserving.

6. Projection Terms#

Invertible Projection#

A projection from high‑dimensional embedding space into 3D–9D that preserves primitive‑level structure and regime identity.

Regime‑Aware Projection#

A projection that maintains correct mapping of R₁, R₂, and R₃ behaviors.

Primitive‑Aligned Projection#

A projection that preserves DP, TDP, SP, and CP structure.

7. Alignment Terms#

Layer‑to‑Layer Alignment#

Comparison of residue‑level embedding trajectories across transformer layers.

Residue‑to‑Residue Alignment#

Comparison of embeddings across positions in a protein sequence.

Cross‑Version Alignment#

Comparison of embedding‑space structure across model versions or checkpoints.

Cross‑Model Alignment#

Comparison of embedding‑space geometry across different PLM architectures.

8. Validation Terms#

vST (Validation‑Space‑Time)#

A substrate‑level validation framework evaluating structural coherence, dimensional continuity, regime behavior, and core alignment.

Validation Layers (V₁–V₄)#

Four structured evaluation layers ensuring invariant‑preserving behavior across the dimensional ladder.

9. Drift Terms#

Drift#

A deviation from expected substrate behavior, indicating instability or invariant failure.

Drift Categories (D₁–D₄)#

Classification of drift into structural, dimensional, regime, or projection drift.

Drift Severity#

A measure of drift magnitude (low, moderate, high).