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MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse

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

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Proposes MahaVar, a post-hoc OOD score that adds a class-wise Mahalanobis distance variance term to the Mahalanobis++ nearest-class score, with a Neural Collapse-based theoretical justification.

Problem

Post-hoc OOD detection with Mahalanobis-based scores ignores the structure of class-wise distances; the paper asks whether the distribution of distances across all classes carries extra ID/OOD signal.

Approach

ID samples show a sharp minimum in sorted class-wise Mahalanobis distances (one small, rest large), producing high variance across classes; under relaxed Neural Collapse (weak NC1, ETF NC2) this variance is provably large for ID samples, so adding alpha times the variance to the negative min-distance gives a complementary OOD score.

Key results

• On CIFAR-100, MahaVar reaches 83.06% AUROC and 68.50% FPR@95, the best among evaluated methods (Mahalanobis++: 82.01%, 70.72%).
• On ImageNet averaged over ResNet-50, Swin-B and ViT-B, MahaVar reports 88.39% AUROC and 45.19% FPR@95, versus 87.50% and 47.90% for Mahalanobis++.
• On CIFAR-10, MahaVar reaches 90.91% AUROC and 46.09% FPR@95; KNN has higher AUROC (91.34%).

Surprising findings

• SCALE and ASH-S, strong on ResNet-50, collapse on Transformer backbones (ASH-S average AUROC about 23% on Swin-B and ViT-B).
• The theoretical separation weakens for ViT-B on ImageNet because its feature dimension (768) is below C-1 = 999, preventing a full simplex ETF.

Limitations

• Theory relies on relaxed Neural Collapse assumptions (ETF class means, bounded within-class deviation) that are not fully met in practice, and the Mahalanobis extension is only claimed analogously.
• Gains over Mahalanobis++ are modest, and MahaVar does not beat KNN on CIFAR-10 AUROC or Texture on ImageNet.
• The implementation drops the centering step used in the theory, so the theoretical guarantees do not directly cover the deployed score.

Experimental setup

Datasets: CIFAR-10 CIFAR-100 ImageNet MNIST SVHN Textures Places365 TIN iNaturalist OpenImage-O SSB-Hard NINCO

Benchmarks: OpenOOD v1.5 CIFAR-10 OpenOOD v1.5 CIFAR-100 OpenOOD v1.5 ImageNet

Metrics: AUROC FPR@95

Baselines: Mahalanobis Mahalanobis++ KNN NCI NCI+filter ViM fDBD MSP MaxLogit KL-matching Energy GEN

Builds on: Mahalanobis distance OOD detection Mahalanobis++ Neural Collapse OpenOOD v1.5

Closest papers by meaning

• Detecting Out-of-Distribution Through the Lens of Neural Collapse (CVPR 2025 · similarity 0.91)
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