WAND Makes Anomaly Explanations Free by Using the Witness Direction as the Attribution

arXiv 2609.03826·medium signalXBlueskyLinkedInCopy link

Unsupervised anomaly detectors give a score with no account of which features drove it, and SHAP or LIME are bolted on afterward, re-querying the detector thousands of times per point to produce only an approximation. WAND organizes computation around directions on the unit sphere, scoring each point by how far its projection escapes a sub-Gaussian extreme-value baseline, so the witness directions that flag a point are vectors in feature space and therefore are the per-feature explanation, obtained at no cost over scoring and recoverable by gradients. Scoring is linear in sample size, a probe-efficiency bound guarantees every anomaly a witness, and across 47 ADBench datasets WAND attains the best mean Friedman rank at ROC.