Same Magnitude, Different Direction: Signed-Orientation Response in Time-Series Anomaly Detection

Modern time-series anomaly detectors respond very differently to signed cross-channel relations, and the corresponding score component can help or harm detection on natural data. We establish these differences using a partial channel sign flip that preserves every coordinatewise magnitude. Across nine released models on 65 multivariate views, responses range from near chance to strong separation; longer training changes them unevenly. An exact even–odd decomposition isolates the flip-sensitive component of the same trained score, linking the controlled comparison to a natural-detection ablation. At 50 epochs, removing this component changes magnitude-matched AUC by more than one percentage point in 19 of 54 model–dataset combinations and by as much as 14.37 points. Yet Anomaly Transformer and GDN, only 1.00 native-AUC point apart on a common panel, differ by 11.36 points in response strength. Similar native performance is therefore insufficient evidence of similar signed response: this behavior and its effect on detection require direct measurement.