CovDiff-PaAno: Covariance-Aware Differential Patch Scoring with a Shared Encoder for Time-Series Anomaly Detection

Abstract Patch-based time-series anomaly detectors often score raw-patch embeddings by angular distance to normal memories. This assumes that angular similarity sufficiently captures abnormality, although it can underrepresent deviations along low-variance embedding directions and temporal changes in slope or curvature. We propose CovDiff-PaAno, a scoring-stage extension of PaAno that combines regularized Mahalanobis memory scoring with raw, first-order-difference, and second-order-difference views. A single frozen encoder processes all views, while each view maintains its own memory bank and covariance estimate. Fixed score-level fusion combines their point-level anomaly evidence without adding trainable backbone parameters. We evaluated the method across ten seeds on the multivariate collection of the Time-Series Benchmark for Anomaly Detection (TSB-AD-M). CovDiff-PaAno increased the area under the receiver operating characteristic curve (AUC-ROC) from 0.7612 to 0.7843 and the range-based F1 score (Range-F1) from 0.4043 to 0.4384. On the univariate collection (TSB-AD-U), the corresponding scores increased from 0.8532 to 0.8626 and from 0.4822 to 0.4924. A three-seed encoder comparison showed that view-dependent encoders improved every metric by less than 0.005, supporting the shared encoder as a parameter-efficient compromise. Conventional label-free score normalization produced only marginal changes, although empirical cumulative distribution function normalization substantially degraded performance. The method retained PaAno's encoder parameter count, but required 3.47 times the inference time and 10.01 times the peak allocated inference memory. These findings show that inference-stage scoring geometry and temporal views can strengthen patch-based detection without enlarging the backbone, while introducing a measurable deployment trade-off.