GEODE: Angle-Adaptive OOD Detection with Universal Scorer Compatibility

arXiv cs.LG / 5/5/2026

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Key Points

The paper explains why Outlier Exposure (OE) performs well: its gains mainly come from boundary calibration rather than broad OOD coverage, with the boundary-adjacent quartile driving most improvements.
It introduces GEODE, a geometry-preserving OOD detection approach that uses an angle-adaptive norm loss to scale per-sample targets by cosine similarity to the nearest class mean.
GEODE is designed to be compatible with multiple “scorers,” addressing OE’s known scorer-dependent tradeoffs (e.g., strong with MSP but weak with KNN).
Experiments on CIFAR-10 show near-OOD AUROC of 89.0–92.3 and far-OOD up to 93.05, with no catastrophic failures across seven standard scorers, and GEODE improves over vanilla cross-entropy at matched training.
On CIFAR-10 and CIFAR-100, GEODE+OE achieves strong results (e.g., 95.0 MSP / 94.8 KNN on CIFAR-10) and also avoids failure modes where other methods distort the classifier geometry relied on by distance-based scorers.

Abstract

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.