Early High-Frequency Injection for Geometry-Sensitive OOD Detection

Outlier Exposure (OE) is among the strongest training-based OOD detectors on standard benchmarks but exhibits scorer-dependent tradeoffs (e.g., strong on MSP, weak on KNN) and requires curated auxiliary data. We show why OE works: its features sit at the same geometric locus as real near-OOD data, with the boundary-adjacent quartile driving nearly all of OE's gain. OE is boundary calibration, not OOD coverage. GEODE (GEOmetry-preserving DEtection) replicates this calibration synthetically through an angle-adaptive norm loss in which targets scale per-sample with cosine similarity to the nearest class mean, preserving feature geometry where boundary structure matters. Four theorems grounded in neural collapse justify the design. GEODE works across all seven standard scorers on CIFAR-10 (near-OOD AUROC 89.0-92.3, far-OOD reaching 93.05; no catastrophic failure on any scorer). Since the OOD regime is unknown at deployment, this is the test that matters. GEODE outperforms vanilla CE at matched epoch counts. Combined with OE, GEODE reaches 95.0 MSP / 94.8 KNN on CIFAR-10 and beats OE on every scorer on CIFAR-100. The gains hold on WRN-28-10 (+4.5 Energy, 3 seeds). Unlike methods that push OOD into the classifier null space (e.g., PFS, 14.38 KNN AUROC, worse than random), GEODE's adaptive target preserves the geometry that distance-based scorers depend on.

Long-tailed out-of-distribution (LT-OOD) detection is often addressed with specialized training, including auxiliary out-of-distribution (OOD) data, abstention heads, contrastive objectives, energy losses, or gradient-conflict control. We show that these training mechanisms can obscure a simpler issue: frozen long-tailed representations may already contain useful OOD evidence, but raw Mahalanobis distance is distorted by frequency-coupled feature radius and poorly supported tail covariance. We propose Hyperspherical Pooled Mahalanobis (HPM), a post-hoc detector that normalizes features onto the unit sphere and replaces class-specific covariance with a pooled, ridge-regularized metric while keeping class means as semantic anchors. In CIFAR-LT experiments and an ImageNet-100-LT near-OOD boundary analysis, HPM improves raw Mahalanobis scoring; for Prior-Calibrated ERM (PC-ERM), it raises AUROC from 46.49 to 85.67 on CIFAR-10-LT and from 50.40 to 78.35 on CIFAR-100-LT. This simple PC-ERM+HPM pipeline also achieves the best Log Efficiency Score (LES; 3.08) on CIFAR-100-LT, retaining roughly 95% of the best CIFAR-100-LT AUROC observed among the compared post-hoc scores at substantially lower training-time cost. These results argue for evaluating representation quality, detector geometry, and training complexity as separate factors in LT-OOD detection.

Out-of-distribution (OOD) detection identifies test samples that fall outside a model's training distribution, a capability critical for safe deployment in high-stakes applications. Standard OOD detectors are trained on a specific in-distribution (ID) dataset and detect deviations from that single domain. In contrast, we study few-shot cross-domain OOD detection: given a \emph{single} pre-trained model, can we perform OOD detection on \emph{arbitrary} new ID-OOD task pairs using only a handful of ID samples at inference time, with no additional training? We propose \textbf{UFCOD}, a unified framework that achieves this goal through information-geometric analysis of diffusion trajectories. Our key insight is that diffusion noise predictions are score functions (gradients of log-density), and we extract two energy features: \emph{Path Energy} (integrated score magnitude) and \emph{Dynamics Energy} (score smoothness), that form a discrete Sobolev norm capturing how samples interact with the learned diffusion process. The central contribution is a \textbf{train-once, deploy-anywhere} paradigm: a diffusion model trained on a single dataset (e.g., CelebA) serves as a universal feature extractor for OOD detection across semantically unrelated domains (e.g., CIFAR-10, SVHN, Textures). At deployment, each new task requires only $\sim$100 unlabeled ID samples for inference: no retraining, no fine-tuning, no task-specific adaptation. Using 100 ID samples per task, UFCOD achieves 93.7% average AUROC across 12 cross-domain benchmarks, competitive with methods trained on 50k--163k samples, demonstrating $\sim$500$\times$ improvement in sample efficiency. See our code in https://github.com/lili0415/UFCOD.