# Relation-Closure Operator

Multivariate time series anomaly detection has long leaned on reconstruction residuals, but a residual only certifies that a window can be reproduced, not that its channels still explain one another as they do under normal operation. CLOSURE splits recoverability and cross-channel consistency into two prediction tasks trained separately on normal data: a diffusion reconstructor conditioned on a discrete memory of normal temporal bases scores the first, and a relation operator that predicts each channel only from its peers scores the second, with the two combined after calibration on normal data. Across the five public benchmarks SMD, MSL, SMAP, SWaT and PSM, its Aff-F1 exceeds the listed methods, reaching 88.13 on SMD.

Multivariate time series anomaly detection has long leaned on reconstruction residuals, but a residual only certifies that a window can be reproduced, not that its channels still explain one another as they do under normal operation. CLOSURE splits recoverability and cross-channel consistency into two prediction tasks trained separately on normal data: a diffusion reconstructor conditioned on a discrete memory of normal temporal bases scores the first, and a relation operator that predicts each channel only from its peers scores the second, with the two combined after calibration on normal data. Across the five public benchmarks SMD, MSL, SMAP, SWaT and PSM, its Aff-F1 exceeds the listed methods, reaching 88.13 on SMD.