ZERO-AD: Learning Normality as a Zero-Level Set for Multivariate Time-Series Anomaly Detection

Multivariate time-series anomaly detection (MTSAD) typically characterizes normal behavior indirectly, for example through reconstruction, forecasting, representation similarity, or normal prototypes. However, these objectives do not explicitly define the properties that normal temporal behavior should satisfy, and as a result, anomalous deviations can become entangled with ordinary modeling uncertainty. We introduce ZERO-AD, a geometric framework that models normal temporal behavior using a small set of learned implicit constraints, $F_{\theta }(Z)=[f_1(Z),\dots ,f_K(Z){]}^{\top }$, such that normal windows satisfy $F_{\theta }(Z)\approx 0$. The common zero-level set of these constraints therefore provides a data-driven representation of normality, while anomalies are identified directly through violations of the learned constraints. To prevent degenerate solutions, ZERO-AD regularizes the local constraint geometry by encouraging complementary Jacobian directions, consistency across observed normal temporal variations, and finite-step sensitivity when moving away from the zero set. During inference, constraint violations are calibrated using held-out normal data and combined through reliability weighting, temporal persistence, and dense–sparse aggregation. ZERO-AD requires neither anomalous training samples nor synthetic anomaly generation, and it does not rely on a reconstruction decoder or forecasting head. On TSB-AD-M, ZERO-AD achieves the best aggregate performance on five of the six reported metrics, including a VUS-PR of 0.437 and a Point-F1 of 0.470, while using only approximately 0.07M parameters. These results demonstrate that directly learning the constraints satisfied by normal temporal behavior provides a compact and geometrically interpretable alternative for normal-only MTSAD.