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Mahalanobis++: Improving OOD Detection via Feature Normalization

ICML 2025 · Label-efficient and robust learning › OOD and anomaly detection · approach: Spurious-aware OOD detection

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Shows that l2-normalizing pre-logit features before post-hoc Mahalanobis OOD detection (Mahalanobis++) fixes feature-norm-driven failures across 44 ImageNet models and improves over Mahalanobis and other post-hoc baselines.

Problem

Post-hoc Mahalanobis-distance OOD detection on pre-logit features performs inconsistently across pretrained models, largely because feature norms vary strongly and violate the Gaussian shared-covariance assumption.

Approach

Discard feature norm by l2-normalizing pre-logit features before estimating class means and the shared covariance and computing the Mahalanobis score, applied purely post-hoc with no training changes.

Key results

• On NINCO with ConvNeXtV2-L-In21k, Mahalanobis++ reaches 18.4% FPR, a new state of the art in the paper's comparison.
• Averaged over 44 ImageNet models on OpenOOD, Mahalanobis++ improves over Mahalanobis by 7.6 FPR points and outperforms the previously best method ViM by about 7 points.
• Mahalanobis++ fails fewer unit tests: 0/17 failed for ConvNeXtV2, SwinV2 and ViT-CLIP, versus 5/17, 10/17 and 14/17 for standard Mahalanobis.

Measured effects reported in the paper

Surprising findings

• Natural OOD images (NINCO) often have larger feature norms than ID images, contradicting the common assumption that OOD features have smaller norms.
• The ViT-augreg models already have well-behaved Gaussian-like features and do not benefit from normalization.

Limitations

• Gains are smaller on CIFAR-100, where the conventional Mahalanobis distance is already fairly effective.
• Normalization does not help the ViT-augreg models, which already have well-behaved feature norms; a few other models also see no improvement.
• Evaluation is limited to post-hoc settings with ImageNet and CIFAR; the paper does not study other ID datasets or training-time methods.

Experimental setup

Datasets: ImageNet-1k CIFAR-10 CIFAR-100

Benchmarks: OpenOOD (NINCO, iNaturalist, SSB-hard, OpenImages-O, Texture) NINCO CIFAR-100 OpenOOD suite unit-test noise distributions

Metrics: FPR at 95% TPR AUC

Baselines: MSP MaxLogit Energy GEN ViM KNN NECO NNguide fDBD ASH Relative Mahalanobis Mahalanobis

Builds on: Mahalanobis distance OOD detection relative Mahalanobis distance KNN OOD detection ViM

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