VACE: Learning Geometrically Structured Representations for Time Series Anomaly Detection

Abstract: Anomaly detection in multivariate time series is a critical task across a wide range of real-world applications, where abnormal behaviour is rare, labels are unavailable, and the cost of a miss is high. The central challenge is learning a characterisation of normality precise enough to flag deviations. Representation self-supervised learning, typically through contrastive approaches, addresses this by embedding temporal patches into a latent space where normality occupies a well-defined region, with anomalies detected by geometric deviation. However, contrastive approaches shape this space indirectly through pair-sampling heuristics, providing no explicit control over the geometric structure that distance-based scoring requires. This means how tightly normal representations are grouped, and whether distances are directionally meaningful. We present VACE (Velocity-Aligned Channel Embeddings), a self-supervised anomaly detection method that represents normality as a compact, directionally coherent region in the embedding space. To this end, VACE trains a channel-aware encoder through a velocity-consistency objective, with no negatives and no synthetic anomalies, so that normal trajectories are locally smooth and aligned. At test time, a Mahalanobis positional score and a velocity-bank directional score are combined multiplicatively, flagging points that are simultaneously off-distribution and dynamically atypical. Despite its simplicity, VACE achieves state-of-the-art performance on TSB-AD-M under rigorous evaluation, significantly outperforming more complex methods trained on substantially larger budgets.