Evaluation of Saliency-Map Rank-Invariance Audits for Computer Vision Agriculture Weed Detectors Under Variable Soil Backgrounds: An Interpretability Stability Bound for Mechanical Weeding Safety

Saliency maps are increasingly used to audit computer-vision weed detectors before they are coupled to mechanical weeding implements, yet the audit itself has no stated reliability guarantee: a map that reorders its top-ranked pixels when the soil background changes can certify a detector whose actuator command is unsafe. the present analysis treats rank-invariance auditing as a formal decision procedure and derives a stability bound for it. The detector's saliency field is modelled as a random function on the image lattice, and the audit is defined as a rank-preservation test between paired images that differ only in soil background. Under a before-after-control-impact design with a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), the operating characteristics of the audit were characterised across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points.52 clusters are required to detect a 5-percentage-point rank-invariance failure at 80% power, and it yields a closed-form stability bound that links the audit's false-certification rate to the intraclass correlation and the number of clusters. The bound converts an interpretability claim into a safety-relevant tolerance, and it shows that audits conducted on fewer than 24 clusters cannot distinguish a stable detector from one whose ranking is background-dependent.