Executive Summary
Papers VIII-IX measured domain selectivity as entropy change ratios. Paper XI established that geometric structure bounds achievable selectivity. This paper completes the measurement chain by quantifying the information-theoretic content of domain-selective noise injection.
We measure the KL divergence between noisy and clean output distributions across a sigma sweep at the optimal injection layer (layer 10). The results confirm stochastic resonance in information space and place a tight bound on what domain-selective intervention can achieve.
Key Findings
- Stochastic resonance confirmed: All four domains exhibit inverted-U KL profiles — the signature of stochastic resonance in information space
- Total KL peaks at 14-15 bits: Noise injection produces substantial total information change at optimal sigma
- Domain-specific component is small: +1.3 bits (medical), +1.9 bits (legal), -1.0 bits (code), -1.5 bits (science)
- Information anti-selectivity: Code and science are information-anti-selective — noise reduces their domain-specific content
- Consistent with theoretical bound: Domain-specific differential consistent with C ≤ log2(1 + k2/d_eff) = 2.24 bits from the concentration barrier
Significance
This paper closes the loop between geometry (Paper XI), spectral analysis (Paper X), layer-resolved measurement (Paper IX), and the original terminal measurement limit (Paper VIII). The information-theoretic bound matches the geometric bound, confirming that the concentration barrier is not just a geometric curiosity but a fundamental limit on the information that domain-selective intervention can carry.
Key References
- McEntire (2026) — The Concentration Barrier: geometric bounds (Paper XI)
- McEntire (2026) — Spectral Geometry: Jacobian amplification (Paper X)
- McEntire (2026) — The Generative Lossy Channel: five sufficient conditions for SR (Paper VI)
- Cover & Thomas (2006) — Elements of Information Theory