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 and science domains consistently exhibit positive selectivity; medical and legal exhibit negative selectivity across all layers
- Modest absolute values: No layer achieves selectivity exceeding 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. The finding that selectivity peaks at intermediate layers — not at the input where INLP directions are defined, and not at the output where effects are measured — is the first indication that the terminal measurement problem is not merely an output-layer phenomenon but reflects a structural property of the full forward pass.
Key References
- McEntire (2026) — Shaped Noise Injection: the terminal measurement limit (Paper VIII)
- McEntire (2026) — The Concentration Barrier: effective dimensionality bounds (Paper XI)
- Ravfogel et al. (2020) — Iterative Nullspace Projection for domain direction identification