Understanding Deep One-Class Classification: A Training-Dynamics Viewpoint

Deep one-class classification (DOCC) maps normal samples toward a fixed center, yet at test time it must distinguish unseen normal and anomalous inputs. How DOCC training shapes representations of inputs that never appear in the training objective remains poorly understood. We study the training dynamics of DOCC under gradient descent and derive a finite-time first-order description of the representation change of an unseen input. We show that its movement is determined by cumulative normal-sample updates transferred through gradient coupling, while the representations of normal training samples are progressively driven toward the center. This analysis identifies two key factors governing the behavior of unseen inputs: their initial separation from the center and the training-induced displacement. These factors explain representative success and failure cases for both unseen normal and anomalous inputs and yield a sufficient condition for an anomaly to remain detectable after training. We further extend the training-dynamics view to anomaly supervision and explain how labeled anomalies induce additional displacements that can correct anomalies missed by one-class training. Experiments support the predicted representation dynamics, anomaly scores, failure modes, and coupling geometry under Gaussian initialization.