TopoAD: Resource-Efficient OOD Detection via Multi-Scale Euler Characteristic Curves

Out-of-distribution (OOD) detection is essential for ensuring the reliability of machine learning models deployed in safety-critical applications. Existing methods often rely solely on statistical properties of feature distributions while ignoring the geometric structure of learned representations. We propose TopoAD, a topology-aware OOD detection framework that leverages Euler Characteristic Curves (ECCs) extracted from intermediate convolutional activation maps and fuses them with standardized energy scores. Specifically, we employ a computationally efficient superlevel-set filtration with a local estimator to capture topological invariants, avoiding the high cost of persistent homology. Furthermore, we introduce task-adaptive aggregation strategies to effectively integrate multi-scale topological features based on the complexity of distribution shifts. We evaluate our method on CIFAR-10 against four diverse OOD benchmarks spanning far-OOD (Textures), near-OOD (SVHN), and semantic shift scenarios. Our results demonstrate that TopoAD-Gated achieves superior performance on far-OOD data with 89.98% AUROC on Textures, while the ultra-lightweight TopoAD-Linear provides an efficient alternative for near-OOD detection. Comprehensive ablation studies reveal that cross-layer gating effectively captures multi-scale topological shifts, while threshold-wise attention provides limited benefit and can degrade far-OOD performance. Our analysis demonstrates that topological features are particularly effective for detecting OOD samples with distinct structural characteristics, highlighting TopoAD’s potential as a sustainable solution for resource-constrained applications in texture analysis, medical imaging, and remote sensing.