# A Geometry-Based View of Mahalanobis OOD Detection

arXiv: https://arxiv.org/abs/2510.15202 · HTML: https://mlsanity.com/paper/2510.15202/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 22 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 17 of 17)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation](https://mlsanity.com/paper/2306.00826/) (2023)
- [Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement](https://mlsanity.com/paper/2310.00227/) (2023)
- [How Does Fine-Tuning Impact Out-of-Distribution Detection for Vision-Language Models?](https://mlsanity.com/paper/2306.06048/) (2023)
- [Mahalanobis++: Improving OOD Detection via Feature Normalization](https://mlsanity.com/paper/2505.18032/) (2025)
- [On the Importance of Feature Separability in Predicting Out-Of-Distribution Error](https://mlsanity.com/paper/2303.15488/) (2023)
- [Towards Optimal Feature-Shaping Methods for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.00865/) (2024)
- [Exploiting Layer Normalization Fine-tuning in Visual Transformer Foundation Models for Classification](https://mlsanity.com/paper/2508.07577/) (2025)
- [Understanding normalization in contrastive representation learning and out-of-distribution detection](https://mlsanity.com/paper/2312.15288/) (2023)
- [How to train your ViT for OOD Detection](https://mlsanity.com/paper/2405.17447/) (2024)

## Built on by (most cited first, 4 of 4)

- [Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning](https://mlsanity.com/paper/2605.05638/) (2026)
- [Useful Features, Backward Scores: OOD in Language-Model Trajectories](https://mlsanity.com/paper/2605.00269/) (2026)
- [MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusion](https://mlsanity.com/paper/2606.17352/) (2026)
- [Verdict Instability of OOD Scores under Reference Resampling](https://mlsanity.com/paper/2609.00691/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is critical for reliable deployment of vision models. Mahalanobis-based detectors remain strong baselines, yet their performance varies widely across modern pretrained representations, and it is unclear which properties of a feature space cause these methods to succeed or fail. We conduct a large-scale study across diverse foundation-model backbones and Mahalanobis variants. First, we show that Mahalanobis-style OOD detection is not universally reliable: performance is highly representation-dependent and can shift substantially with pretraining data and fine-tuning regimes. Second, we link this variability to in-distribution geometry and identify a two-term ID summary that consistently tracks Mahalanobis OOD behavior across detectors: within-class spectral structure and local intrinsic dimensionality. Finally, we treat normalization as a geometric control mechanism and introduce radially scaled ℓ2 normalization, φβ(z)=z/|z|β, which preserves directions while contracting or expanding feature radii. Varying β changes the radii while preserving directions, so the same quadratic detector sees a different ID geometry. We choose β from ID-only geometry signals and typically outperform fixed normalization baselines.