Direct Logit Attribution Studies

The most counterintuitive finding. MESN™ produces high perplexity on input — the model finds it surprising, harder to parse than natural language. Yet it produces low perplexity on output — more fluent, more coherent generation than equivalent prose prompts. Generation PPL ratio falls below 1.0 in 28 of 43 models.

This is an anti-pattern. The universal assumption in prompt engineering is “make input easy for the model.” Our data shows the opposite: harder initial processing produces deeper encoding and better transfer.

This mirrors Robert Bjork's desirable difficultyframework from cognitive neuroscience — effortful encoding leads to stronger memory and better generalization. MESN™ works not despite being hard for the model to process, but because it forces multi-family attention head recruitment rather than falling into what we call the “prose groove” — lazy, diffuse attention patterns that natural language enables.

A single MESN™ expression activates heads across 4 or more specialization families simultaneously — symbolic, relational, hierarchical, and meta-routing heads all fire together. This is a form of attention convergence that natural language rarely achieves. All 43 models show 8/8 specialization family activation under structured input.

69.7% of model completions spontaneously generate structured operators in their output — despite zero MESN™ in any model's training data. This isn't learned behavior. The architecture is expressing a preference.

When given structured input, the notation enters the KV cache and shapes subsequent token generation. The model doesn't just process Structured Notation — it continues in it, suggesting the notation aligns with something fundamental in how transformer attention self-organizes.

The DLA advantage is not constant — it increases monotonically with input complexity in 38 of 43 models. Short stimuli show +8.9% mean DLA advantage; extended stimuli show +14.7% — a 65% amplification. MESN™ becomes more valuable precisely where it matters most: in complex, information-dense contexts.

Base models consistently show ~2x stronger DLA signal than their instruction-tuned counterparts across all 10 matched pairs. Instruction tuning — RLHF in particular — optimizes the model for the comfortable prose groove, reducing its ability to benefit from structured input.

This creates a practical tension: base models have stronger DLA advantage but instruction-tuned models follow task instructions better. The implication is that current alignment techniques inadvertently narrow the model's cognitive repertoire.

The structured advantage is not model-specific. It appears across GQA, MHA, and MLA attention mechanisms. It appears in dense and mixture-of-experts architectures. It appears from 3.8B to 141B parameters. Models with zero exposure to MESN™ in training — including Kimi-K2, trained entirely outside our ecosystem — interpret it natively, connecting its patterns to attention topology and equilibrium dynamics.

This suggests MESN™ is not a learned convention but a resonant frequency of transformer attention — the format these architectures were always capable of processing most effectively.