Evaluation of Concept-Activation Sparsity Probes for Artificial Intelligence Agriculture Disease Classifiers Under Field-Sensor Fusion: An Interpretability Decomposition-Reliability Bound for Smallholder Fungicide Timing

Concept-activation sparsity probes are increasingly proposed as a route to trustworthy disease classifiers that fuse leaf imagery with field-sensor streams, yet the reliability of the resulting explanations has not been bounded for the decision they are meant to serve: whether a smallholder should spray fungicide now. The bound separates an explanation's activation mass into a concept-attributable component, a sensor-fusion component and a residual, and shows that the reliability of a sparsity probe is governed by the ratio of concept-attributable mass to fusion-induced variance rather than by sparsity alone. A before-after-control-impact design was used to characterise the operating characteristics of the bound under a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64; power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. The design required 54 clusters to detect a 5-percentage-point effect at 80% power. The analysis is theoretical and methodological: it proposes the bound, derives its properties and characterises the design under which it can be validated, without claiming observational data. The contribution is a decision-relevant reliability criterion that ties explanation sparsity to fungicide-timing error rather than to visual plausibility.