Bridging Experiment: Embedding Geometry → Attention Head Behavior

Motivation

Two prior studies established independent evidence that MESN™ produces measurably different internal representations in transformer models:

• Study A — Embedding Geometry(Qwen3-Embedding-8B, 4096-dim): MESN™ operators produce embeddings with 0.866 average cosine similarity to equivalent prose. Prose paraphrases cluster at 0.935 internal similarity — MESN™ sits 4.4% further out, occupying its own region of embedding space.
• Study B — 43-Model DLA Study (including Qwen3-8B): +17.1% DLA advantage across 72 matched stimulus pairs, 70/72 pair wins, 8/8 specialization families positive.

The gap between these studies: Embeddings measure what the representation is (a single vector capturing meaning). DLA measureshow the model processes the input (which attention heads activate to predict what comes next). Are these the same phenomenon measured differently, or independent effects?

This experiment bridges the two.

Experiment 1: MESN™ Position Relative to the NL Cloud

For each of 20 concept pairs spanning 5 domains (science, social/economic, technical, abstract, causal), we generate 1 MESN™ variant, 7 NL paraphrases, and 1 reversed MESN™ variant. We measure where the MESN™ DLA profile sits relative to the NL paraphrase cluster.

MESN™ sits outside the NL paraphrase cloud in every single pair. Twenty for twenty. The NL variants cluster tightly at 0.979 — essentially interchangeable to the model's attention system. MESN™ is consistently 3.8% outside that cluster.

Comparison to Embedding Study

The gap magnitudes are strikingly similar (4.4% embedding vs 3.8% DLA) despite measuring fundamentally different things.

Directionality

Applying MESN™ operators between two concepts such as A and B produces DLA profiles with mean cosine similarity of 0.969. While this is only 0.01 below the 0.979 NL internal similarity in absolute terms, it falls roughly 2 standard deviations outside the tightly-clustered NL paraphrase distribution — a consistent displacement, not a borderline one. The key contrast: NL paraphrases that reverse argument order (“B follows from A”) still cluster at 0.979 with forward-order variants. MESN™ operators create a measurably different activation geometry that word reordering alone does not.

MESN™ operators reshape attention patterns at a level that natural language word order alone cannot reach. The positional and relational signals encoded by structured operators produce measurably different head activation geometries — differences that persist even when prose paraphrases reverse word order to express the same directionality.

Per-Family DLA Advantage

8/8 specialization families show positive MESN™ advantage:

Experiment 2: Operator Divergence — Two Spaces, Two Stories

5 concept pairs × 11 MESN™ operators + prose baseline. We rank operators by how far each diverges from the prose baseline in both embedding space and DLA space.

Spearman ρ = −0.345 (p = 0.328)— weak negative correlation. The rankings don't just fail to correlate — they tell opposite stories:

• Embedding space favors negation/contrast operators — the negation and contrastive operators most change what something means
• DLA space favors transformation/metaphor operators — the transformation and metaphor operators most change how the model processes it

The operators that most change what something means (embedding) are different from the operators that most change how the model processes it (DLA). Negation changes where you end up; transformation changes how you get there.

Experiment 3: The Token Efficiency Champion

Three versions of a system prompt — prose, full MESN™ (with metadata scaffolding), and condensed MESN™ (operators and content only):

MESN™ achieves high cosine similarity to prose DLA profiles with dramatically fewer tokens — and the advantage compounds with scale. As context grows, the savings are more exponential than linear: the geometric efficiency gap widens precisely where token budgets matter most.

Full MESN™ is lesstoken-efficient than prose (−31.6%) because its metadata headers and scaffolding dilute the per-token DLA without contributing to the attention profile. The efficiency gain comes from the operator notation itself. The 514 tokens removed between full and condensed are structurally decorative — the attention heads respond to operators and concept bindings, not documentation wrapping. For production contexts where token budget matters: strip to condensed.

Cross-Experiment Synthesis

The Three-Layer Picture

What Transfers Across Spaces

• The gap magnitude transfers — 4.4% embedding vs 3.8% DLA, remarkably consistent across measurement spaces
• The cloud exclusion transfers — 0 of 20 pairs inside the cloud in DLA space, confirming the embedding-space finding
• MESN™-to-MESN™ clustering transfers — full and condensed versions are much more similar to each other than either is to prose
• 8/8 family direction transfers — all families positive in both this experiment and the 43-model study

What Does NOT Transfer

• Operator divergence rankings do not transfer (ρ = −0.345) — embedding geometry and DLA behavior measure orthogonal properties
• Family advantage rankings partially reshuffle — the directional operator disproportionately engages constraint and hierarchy tracking

MESN™ operators have two independent axes of effect. Negation operators maximally change meaning. Transformation operators maximally change processing. These are orthogonal — a richer story than “one effect, measurable two ways.”

Limitations

Single model (Qwen3-8B base). Single operator in Experiment 1 (only the MESN™ directional operator). 5 concept pairs in Experiment 2. MPS fp16 vs CUDA bf16 (0.993 baseline match confirms equivalence). No causal interventions — all measurements are observational.