TLM-SVDD: Dual-Driven Deep Large-Margin ${\ell }_p$-SVDD with Vision Transformers for Anomaly Detection

Deep extensions of the Support Vector Data Description (SVDD) paradigm can jointly learn representations and decision boundaries for anomaly detection. Yet, they typically rely on simplified objectives or use a surrogate objective that does not coincide with the one used to fit the boundary. In this work, we introduce Transformer-based Large-Margin SVDD (TLM-SVDD), a framework that updates the encoder using the exact dual boundary problem to maximize the margin between normal and anomalous samples. By applying Danskin's theorem, we show that at the optimum of the convex dual function, the encoder's hypergradient can be directly derived from a kernel quadratic term evaluated at the optimal dual variables. As such, the encoder update requires no recovered decision thresholds, surrogate losses, or differentiation through a Frank-Wolfe-based solver. Furthermore, we show that this objective is bounded and naturally depends on support vectors. For batch-independent representation learning, we make use of a vision transformer and conduct a controlled ablation study to separately analyze the merits of the backbone architecture for anomaly detection from those of our optimization approach. Through extensive experiments across anomaly detection and long-tailed recognition benchmarks, the proposed TLM-SVDD approach is shown to improve upon convolutional and approximate primal-space predecessors, outperforming state-of-the-art methods in the majority of evaluation settings.