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

arXiv: https://arxiv.org/abs/2605.17799 · HTML: https://mlsanity.com/paper/2605.17799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 32 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 1 of 1)

- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)

## Abstract (arXiv)

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.