This paper has been superseded
This paper has been consolidated into The Geometry of Failure (DOI: 10.5281/zenodo.19432168). The content below is retained for reference.
Executive Summary
Paper VIII established the terminal measurement limit: shaped noise injected at the final transformer layers cannot achieve domain-selective entropy effects because nonlinear mixing at intermediate layers scrambles the signal. This paper asks a natural follow-up: where in the forward pass does domain selectivity actually live?
We map the full selectivity profile at nine sampled transformer layers in Qwen-2.5 7B (28 layers total), measuring where domain selectivity peaks and where it vanishes. The answer is a weak Outcome A: mean selectivity peaks at intermediate layers 7-10 (mean selectivity approximately 0.5) and declines toward both input and output layers. Absolute selectivity is modest at all layers.
Key Findings
- Selectivity peaks at intermediate layers: Layers 7-10 show the highest domain selectivity (mean ~0.5), declining toward both input and output
- Domain asymmetry: Code (7 of 9 layers) and science (6 of 9) mostly exhibit positive selectivity; medical and legal are positive at only one layer each and anti-selective at most layers
- Modest absolute values: No layer achieves mean selectivity above 1.0 or diagonal dominance in the 4 x 4 response matrix; no layer exceeds the concentration barrier bound of k/d_eff ~ 1.8
- Consistent with Paper XI: The effective dimensionality constraint explains the selectivity profile without requiring additional mechanisms
Significance
This paper provides the spatial map that the subsequent papers (X-XII) explain. Varying the injection layer shifts the selectivity profile but does not lift it past the geometric bound, so the terminal measurement limit from Paper VIII generalizes to an all-layer measurement limit: domain-selective intervention via single-layer shaped noise is constrained by activation geometry, not by layer choice.
Key References
- McEntire (2026) — Shaped Noise Injection: the terminal measurement limit (Paper VIII)
- McEntire (2026) — The Concentration Barrier: effective dimensionality bounds (Paper XI)
- McEntire (2026) — Structural Transfer: source of the INLP domain directions (Paper IV)