mlsanityData to 14 Oct 2026

Mahalanobis++: Improving OOD Detection via Feature Normalization

arXiv 2505.18032 ↗First posted 23 May 2025cs.LG cs.CVcited by 32

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Abstract (arXiv)

Detecting out-of-distribution (OOD) examples is an important task for deploying reliable machine learning models in safety-critial applications. While post-hoc methods based on the Mahalanobis distance applied to pre-logit features are among the most effective for ImageNet-scale OOD detection, their performance varies significantly across models. We connect this inconsistency to strong variations in feature norms, indicating severe violations of the Gaussian assumption underlying the Mahalanobis distance estimation. We show that simple ℓ2-normalization of the features mitigates this problem effectively, aligning better with the premise of normally distributed data with shared covariance matrix. Extensive experiments on 44 models across diverse architectures and pretraining schemes show that ℓ2-normalization improves the conventional Mahalanobis distance-based approaches significantly and consistently, and outperforms other recently proposed OOD detection methods.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). Builds on 37 of its 52 references that are in the map. First posted on arXiv 23 May 2025.

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37 of 52 references.

References · 37

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  2. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,385
  3. 2013Describing Textures in the Wildcited by 2,125
  4. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,485
  5. 2020Energy-based Out-of-distribution Detectioncited by 1,299
  6. 2021Swin Transformer V2: Scaling Up Capacity and Resolutioncited by 1,228
  7. 2017SphereFace: Deep Hypersphere Embedding for Face Recognitioncited by 737
  8. 2023ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoderscited by 712
  9. 2022Out-of-Distribution Detection with Deep Nearest Neighborscited by 600
  10. 2021How to train your ViT? Data, Augmentation, and Regularization in Vision Transformerscited by 569
  11. 2021ReAct: Out-of-distribution Detection With Rectified Activationscited by 486
  12. 2019Scaling Out-of-Distribution Detection for Real-World Settingscited by 465
25 more
  1. 2020CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instancescited by 441
  2. 2022DeiT III: Revenge of the ViTcited by 419
  3. 2022ViM: Out-Of-Distribution with Virtual-logit Matchingcited by 405
  4. 2017Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samplescited by 389
  5. 2021Open-Set Recognition: a Good Closed-Set Classifier is All You Need?cited by 353
  6. 2018Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problemcited by 323
  7. 2022OpenOOD: Benchmarking Generalized Out-of-Distribution Detectioncited by 268
  8. 2021SSD: A Unified Framework for Self-Supervised Outlier Detectioncited by 264
  9. 2022Mitigating Neural Network Overconfidence with Logit Normalizationcited by 252
  10. 2022Delving into Out-of-Distribution Detection with Vision-Language Representationscited by 216
  11. 2022Extremely Simple Activation Shaping for Out-of-Distribution Detectioncited by 212
  12. 2021A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detectioncited by 207
  13. 2021Deep Deterministic Uncertainty: A Simple Baselinecited by 200
  14. 2023In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluationcited by 134
  15. 2018Spreading vectors for similarity searchcited by 118
  16. 2023Nearest Neighbor Guidance for Out-of-Distribution Detectioncited by 64
  17. 2022Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifoldcited by 50
  18. 2023Fast Decision Boundary based Out-of-Distribution Detectorcited by 49
  19. 2023A framework for benchmarking class-out-of-distribution detection and its application to ImageNetcited by 31
  20. 2023Understanding the Feature Norm for Out-of-Distribution Detectioncited by 27
  21. 2022Linking Neural Collapse and L2 Normalization with Improved Out-of-Distribution Detection in Deep Neural Networkscited by 23
  22. 2023On the use of Mahalanobis distance for out-of-distribution detection with neural networks for medical imagingcited by 15
  23. 2023Exploring Simple, High Quality Out-of-Distribution Detection with L2 Normalizationcited by 3
  24. 2023Understanding normalization in contrastive representation learning and out-of-distribution detectioncited by 2
  25. 2024How to train your ViT for OOD Detectioncited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 28.

32 papers.

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  1. 2025A Geometry-Based View of Mahalanobis OOD Detectioncited by 4
  2. 2026VLA-FAIL: Efficient Task Failure Detection for Finetuned Vision-Language-Action Modelscited by 3
  3. 2026CANDI: Curated Test-Time Adaptation for Multivariate Time-Series Anomaly Detection Under Distribution Shiftcited by 2
  4. 2026AP-OOD: Attention Pooling for Out-of-Distribution Detectioncited by 1
  5. 2026Vendi Novelty Scores for Out-of-Distribution Detectioncited by 1
  6. 2026Mechanistic Anomaly Detection via Functional Attributioncited by 1
  7. 2026Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuningcited by 1
  8. 2026MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapsecited by 1
  9. 2025Frustratingly Easy Feature Reconstruction for Out-of-Distribution Detectioncited by 0
  10. 2025Adaptive Individual Uncertainty under Out-Of-Distribution Shift with Expert-Routed Conformal Predictioncited by 0
  11. 2025Latent space analysis and generalization to out-of-distribution datacited by 0
  12. 2026Tracking the Discriminative Axis: Dual Prototypes for Test-Time OOD Detection Under Covariate Shiftcited by 0
20 more
  1. 2026Knowledge-Guided Failure Prediction: Detecting When Object Detectors Miss Safety-Critical Objectscited by 0
  2. 2026MATHENA: Mamba-based Architectural Tooth Hierarchical Estimator and Holistic Evaluation Network for Anatomycited by 0
  3. 2026Ranked Activation Shift for Post-Hoc Out-of-Distribution Detectioncited by 0
  4. 2026Sparsity as a Key: Unlocking New Insights from Latent Structures for Out-of-Distribution Detectioncited by 0
  5. 2026Useful Features, Backward Scores: OOD in Language-Model Trajectoriescited by 0
  6. 2026Surviving the Unseen: Predictive Defense for Novel Multi-Turn Multimodal Attackscited by 0
  7. 2026How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learningcited by 0
  8. 2026Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detectioncited by 0
  9. 2026Assessing Sample Quality in Conditional Generation under Compositional Shiftcited by 0
  10. 2026MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusioncited by 0
  11. 2026MaRS: Robust Out-of-Distribution Detection via Mahalanobis Residual Scoringcited by 0
  12. 2026Modality-Aware Out-of-Distribution Detection for Multi-Modal Action Recognitioncited by 0
  13. 2026Exploiting Local Flatness for Efficient Out-of-Distribution Detectioncited by 0
  14. 2026Training-Free Out-of-Distribution Detection for Pathology Whole-Slide Imagescited by 0
  15. 2026Verdict Instability of OOD Scores under Reference Resamplingcited by 0
  16. 2026Fi-ImageNet-1k: An OOD Benchmark From the Inside of the ImageNet-1k Validation Setcited by 0
  17. 2026Unified Multi-Layer Subspace Modeling for Cross-Domain OOD Detectioncited by 0
  18. 2026Dataset Identity, Not Novelty: The Source of an Inflated OOD Detection Gaincited by 0
  19. 2026ReMaD: Tuning-free Domain Adaptation for Classification and Out-of-Distribution Detectioncited by 0
  20. 2026CUBE: Class-conditioned Unknown Boundary Evidence for Open-Set Insect Species Recognitioncited by 0