Reconstruction residuals miss a drifting sensor: CLOSURE adds a second, separately learned channel-consistency score and reaches 88.13 Aff-F1 on SMD
Synopsis
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.
Interpretation
Detection evidence expands from a single reconstruction residual to two independently scored paths, recoverability and cross-channel consistency, which meet only at the decision stage after calibration on normal data. Earlier reconstruction-based detectors, including those folding channel dependencies into the reconstruction objective, still supervise their relational evidence with the same recovery loss, so they cannot separate hard-to-recover from broken channel relations. On SMD, the reconstruction-only path reaches 78.10 Aff-F1 and the relation-only path 75.79, while the two combined reach 88.13; on SWaT the same three are 69.99, 68.08 and 73.07.
The consistency path is carried by a relation-closure operator in which each target channel receives nonlinear messages only from its peers, its own trajectory is withheld, and sparse signed gates decide which peers are actually used. A predictor able to read its target could copy that trajectory and report agreement without consulting any peer, and row normalization erases absolute relation strength so that uniformly weak associations still receive nearly unit total weight. On SMAP, holding observations fixed and perturbing only the relational reference, both rewiring and sign reassignment at the largest perturbation level raise the closure residual relative to its unperturbed value, showing sensitivity to peer identity and relation sign; the two perturbations are not budget-matched, so their ordering does not establish which aspect matters more.
The recoverability path uses a diffusion reconstructor that recovers the whole window in a forward pass at one fixed diffusion index, conditioned on normal time-frequency bases stored in a discrete codebook. Earlier diffusion detectors recover observations through denoising or imputation conditioned on the test window itself; here the recovery condition becomes a discrete basis memory learned from normal training windows. On SWaT and SMD, replacing the learned codebook with the raw basis memory while keeping both scoring paths lowers Aff-F1 by 1.50 and 7.60 percentage points respectively.
Perspective
Evaluation covers five real multivariate datasets, SMD, MSL, SMAP, SWaT and PSM, plus the NeurIPS-TS Creditcard and GECCO scenarios, all split into training, validation and calibration, with affiliation precision, recall and F1 reported without point adjustment and averaged over five independent runs. The method targets unlabeled monitoring fitted on normal data, and the closure residual scores the window endpoint relative to that window's own background, so it does not measure anomaly duration.
The authors note that the endpoint ratio emphasizes localized changes in coordination within a window, since a departure sustained across the window raises numerator and background alike; the normal-data quantile is an operating point, not a guarantee of false-alarm control under distribution shift. The rewiring and sign-reassignment perturbations are not budget-matched, so their ordering does not establish which aspect matters more, and that experiment does not by itself establish relation-recovery accuracy or detection performance. Fusion-weight sensitivity shows the best balance can vary across processes, and equal weighting is only an effective choice in the evaluated cases.