Title: Topological Alignment: A Universal Framework for Anomaly Detection
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Anomaly Detection, Robustness, Topology, Zero-shot

Abstract: Zero-Shot Anomaly Detection (ZS-AD) methods based on Vision-Language Models face a critical vulnerability: a paradoxical performance collapse when trained on large-scale, diverse data. We identify this phenomenon as {Negative Transfer in Domain Generalization (NTDG)} and diagnose its root cause as a {Domain Conflict}: a fundamental structural incompatibility where a single, rigid geometric decision boundary fails to separate topologically complex data manifolds from multiple domains. To escape this trap, we propose a paradigm shift from geometric separation to robust topological separability, actualized in our {TDA-CLIP} framework. The framework introduces two general-purpose, plug-and-play topological tools: (1) a macro-level {Homology Consistency Loss ($\mathcal{L}_{\text{HC}}$)} that acts as a structural regularizer to enforce a globally consistent feature space, and (2) a micro-level {Topology-Guided Attention (TGA)} module that purifies features by amplifying salient local evidence. Crucially, these topological components are active only during training and are completely pruned at inference time, delivering substantial performance gains while introducing absolutely no extra cost at inference. Extensive experiments demonstrate that our framework is the first to overcome this negative transfer, consistently benefiting from large-scale Domain Generalization where all baselines fail. TDA-CLIP not only establishes a new state-of-the-art across 11 industrial and medical benchmarks but also proves its generalizability by enhancing existing SOTA methods, offering a validated and principled pathway toward building truly universal anomaly detection models.