A Geometry-Based View of Mahalanobis OOD Detection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911483310374912 |
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| author | Janiak, Denis Binkowski, Jakub Kajdanowicz, Tomasz |
| author_facet | Janiak, Denis Binkowski, Jakub Kajdanowicz, Tomasz |
| contents | 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 $\ell_2$ normalization, $ϕ_β(z)=z/\|z\|^β$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Geometry-Based View of Mahalanobis OOD Detection Janiak, Denis Binkowski, Jakub Kajdanowicz, Tomasz Machine Learning Computer Vision and Pattern Recognition 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 $\ell_2$ normalization, $ϕ_β(z)=z/\|z\|^β$, 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. |
| title | A Geometry-Based View of Mahalanobis OOD Detection |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2510.15202 |