The Masking Problem

Paper reference: Section 1, "The corrector's effect on σ"; Section 3, Experiment 1

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Masking is the central pathology of delegated systems: the process that preserves output quality also destroys the information needed to calibrate trust.

What masking looks like

Consider a code-generation pipeline. The generator produces code, a reviewer catches bugs. The dashboard shows 90% success rate. Everything looks fine.

But the generator is only 67% competent. The reviewer is catching the rest. If the reviewer degrades (model drift, changed distribution), the dashboard stays green while actual competence silently drops.

This is masking: the corrector hides the agent's weakness from the governance system.

The masking index

\[M^* = \frac{\sigma_\text{corr}^*}{\sigma_\text{raw}^*}\]

When \(M^* = 1\): no masking — what you see is what you get. When \(M^* > 1\): the system appears more competent than it is.

Baseline masking is always present. Even the simplest single-agent delegation has \(M^* \approx 1.35\) with typical parameters. This is not a bug — it's a structural consequence of having a corrector.

Verify the math

from minimal_oversight._formulae import (
    sigma_raw_fixed_point, sigma_corr_fixed_point, masking_index
)

sr = sigma_raw_fixed_point(0.80, eta=10, delta=2)    # 0.667
sc = sigma_corr_fixed_point(sr, catch_rate=0.70)     # 0.900
m = masking_index(sc, sr)                             # 1.35

Why masking is dangerous

The danger isn't that \(M^* > 1\) — it's that governance decisions based on \(\sigma_\text{corr}\) are inflated. The paper's Experiment 1 shows that single-\(\sigma\) governance (which trusts the corrected signal) over-authorizes by 36% compared to dual-\(\sigma\) governance (which uses \(\sigma_\text{raw}\) for authorization).

The fix is simple: track both signals. Authorize based on \(\sigma_\text{raw}\), not \(\sigma_\text{corr}\).

Masking in chains

Masking gets worse with depth. In a linear pipeline where each layer's output feeds the next:

Depth	\(M^*\) per layer	\(M^*_\text{total}\)
1	1.77	1.8
2	1.77, 2.10	3.7
3	1.77, 2.10, 2.17	8.1
5	1.77 → 2.20	38.7

Values: closed-form from Eq. 5-6 at each layer. D=5 total matches the paper's simulation (Table 7: 38.7). Per-layer values from the paper: 1.77, 2.10, 2.17, 2.17, 2.20.

The total masking grows super-multiplicatively — faster than \((M^*_\text{single})^D\) — because each downstream layer receives degraded input and depends more on its corrector.

Detecting masking in practice

The package computes \(M^*\) at every node and alerts when it crosses a threshold:

report = analyze_pipeline(pipeline, p_min=0.80)

for alert in report.alerts:
    if "masking" in alert.message.lower():
        print(f"[{alert.level.value}] {alert.node_name}: {alert.message}")

When to worry

\(M^* > 1.3\): monitoring recommended. Track \(\sigma_\text{raw}\) separately.

\(M^* > 1.5\): corrector is doing heavy lifting. The agent may be coasting.

\(M^* > 2.0\): the dashboard is lying. Raw competence is less than half of apparent quality.

The diagnostic differential

The pair \((\Delta\sigma_\text{raw}, \Delta M^*)\) over time tells you what kind of problem you have:

\(\Delta\sigma_\text{raw}\)	\(\Delta M^*\)	Diagnosis	Action
Stable	Stable	Healthy	None
Rising	Falling	Agent improving	Reduce corrector budget
Falling	Rising	Agent degrading, masked	Retrain agent or add capacity
Falling	Falling	Correlated drift	Retrain both
Stable	Rising	Corrector coasting	Check if agent is coasting