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Is Complex Training Necessary for Long-Tailed OOD Detection? A Re-think from Feature Geometry

NeurIPS 2026 · Label-efficient and robust learning › OOD and anomaly detection · approach: Spurious-aware OOD detection · 0 citations (OpenAlex)

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Proposes HPM, a post-hoc detector that projects frozen long-tailed features onto the unit sphere and uses class means with a pooled ridge covariance, showing simple PC-ERM plus HPM is competitive for LT-OOD detection without specialized training.

Problem

Long-tailed OOD detection, where rare in-distribution classes must be retained while OOD inputs are rejected; existing methods rely on complex specialized training, and raw Mahalanobis distance performs poorly on long-tailed features.

Approach

Normalize penultimate features onto the hypersphere to remove frequency-coupled feature radius, keep class means as anchors, and replace unstable class-specific covariances with a single pooled ridge-regularized covariance estimated from shared within-class residuals, applied post hoc to frozen models.

Key results

• On PC-ERM, HPM raises AUROC from 46.49 to 85.67 on CIFAR-10-LT and from 50.40 to 78.35 on CIFAR-100-LT versus raw Mahalanobis.
• PC-ERM+HPM achieves the highest CIFAR-100-LT LES (3.08), retaining about 95% of the best CIFAR-100-LT AUROC among compared post-hoc scores.
• On ImageNet-100-LT, HPM substantially improves over raw Mahalanobis (e.g., PC-ERM 52.85 to 63.47 AUROC) but remains a boundary case.

Surprising findings

• Energy and MSP remain stronger than HPM in some CIFAR-10-LT and OE-trained cases, so classifier and feature-geometry evidence are complementary.
• Raw Mahalanobis is weak under long-tailed training, and simple cross-entropy PC-ERM can be underrated under raw distance.

Limitations

• HPM is not a universal substitute for training-time objectives; ImageNet-100-LT remains a boundary case.
• Theoretical results are mechanism statements rather than universal dominance claims.
• The ImageNet-100-LT results are reported with lower absolute AUROC and a near-OOD setting only.

Experimental setup

Datasets: CIFAR-10-LT CIFAR-100-LT ImageNet-100-LT

Benchmarks: CIFAR-10-LT OOD suite CIFAR-100-LT OOD suite ImageNet-100-LT near-OOD

Metrics: AUROC FPR95 ACC LES

Baselines: Energy MSP Mahalanobis RP-MD HC-MD PATT PASCL AdaptOD COCL EAT DARL

Builds on: Mahalanobis distance OOD detection Energy score Prior-Calibrated ERM outlier exposure

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