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A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection

arXiv 2106.09022 ↗First posted 16 Jun 2021cs.LGcited by 206

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Abstract (arXiv)

Mahalanobis distance (MD) is a simple and popular post-processing method for detecting out-of-distribution (OOD) inputs in neural networks. We analyze its failure modes for near-OOD detection and propose a simple fix called relative Mahalanobis distance (RMD) which improves performance and is more robust to hyperparameter choice. On a wide selection of challenging vision, language, and biology OOD benchmarks (CIFAR-100 vs CIFAR-10, CLINC OOD intent detection, Genomics OOD), we show that RMD meaningfully improves upon MD performance (by up to 15% AUROC on genomics OOD).

Key facts. Cited by 206 papers in the map (data through 7 Oct 2026). Builds on 20 of its 25 references that are in the map. First posted on arXiv 16 Jun 2021.

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20 of 25 references.

References · 20

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  4. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
  5. 2016Concrete Problems in AI Safetycited by 1,582
  6. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,472
  7. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  8. 2018Deep Anomaly Detection with Outlier Exposurecited by 939
  9. 2019Big Transfer (BiT): General Visual Representation Learningcited by 766
  10. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  11. 2019Likelihood Ratios for Out-of-Distribution Detectioncited by 451
  12. 2020Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awarenesscited by 389
8 more
  1. 2019An Evaluation Dataset for Intent Classification and Out-of-Scope Predictioncited by 378
  2. 2019Using Pre-Training Can Improve Model Robustness and Uncertaintycited by 373
  3. 2021Exploring the Limits of Out-of-Distribution Detectioncited by 283
  4. 2021Vision Transformers are Robust Learnerscited by 208
  5. 2020Contrastive Training for Improved Out-of-Distribution Detectioncited by 186
  6. 2020Hybrid Models for Open Set Recognitioncited by 109
  7. 2020Density of States Estimation for Out-of-Distribution Detectioncited by 74
  8. 2020Why is the Mahalanobis Distance Effective for Anomaly Detection?cited by 28

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 25; 2023: 49; 2024: 48; 2025: 41; 2026: 36.

206 papers.

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  1. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedbackcited by 3,634
  2. 2021Generalized Out-of-Distribution Detection: A Surveycited by 796
  3. 2022OpenOOD: Benchmarking Generalized Out-of-Distribution Detectioncited by 267
  4. 2022Out-of-Distribution Detection and Selective Generation for Conditional Language Modelscited by 193
  5. 2023OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detectioncited by 178
  6. 2023Towards Open Vocabulary Learning: A Surveycited by 165
  7. 2021A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challengescited by 154
  8. 2023In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluationcited by 132
  9. 2022Is Out-of-Distribution Detection Learnable?cited by 109
  10. 2022Plex: Towards Reliability using Pretrained Large Model Extensionscited by 102
  11. 2023Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancementcited by 77
  12. 2024Variational Bayesian Last Layerscited by 67
38 more
  1. 2022A Call to Reflect on Evaluation Practices for Failure Detection in Image Classificationcited by 51
  2. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
  3. 2023NECO: NEural Collapse Based Out-of-distribution detectioncited by 41
  4. 2022Test-Time Robust Personalization for Federated Learningcited by 39
  5. 2023A Simple Zero-shot Prompt Weighting Technique to Improve Prompt Ensembling in Text-Image Modelscited by 39
  6. 2024How Does Unlabeled Data Provably Help Out-of-Distribution Detection?cited by 36
  7. 2023LINe: Out-of-Distribution Detection by Leveraging Important Neuronscited by 34
  8. 2024Outlier detection by ensembling uncertainty with negative objectnesscited by 34
  9. 2022SAFE: Sensitivity-Aware Features for Out-of-Distribution Object Detectioncited by 33
  10. 2021No True State-of-the-Art? OOD Detection Methods are Inconsistent across Datasetscited by 31
  11. 2025Mahalanobis++: Improving OOD Detection via Feature Normalizationcited by 30
  12. 2022Watermarking for Out-of-distribution Detectioncited by 28
  13. 2023Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalizationcited by 28
  14. 2022Rainproof: An Umbrella To Shield Text Generators From Out-Of-Distribution Datacited by 21
  15. 2024LAPT: Label-driven Automated Prompt Tuning for OOD Detection with Vision-Language Modelscited by 21
  16. 2022Igeood: An Information Geometry Approach to Out-of-Distribution Detectioncited by 20
  17. 2022A Learning Based Hypothesis Test for Harmful Covariate Shiftcited by 18
  18. 2023From Global to Local: Multi-scale Out-of-distribution Detectioncited by 18
  19. 2024Embedding Trajectory for Out-of-Distribution Detection in Mathematical Reasoningcited by 18
  20. 2024Robust AI-Generated Text Detection by Restricted Embeddingscited by 18
  21. 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 17
  22. 2022Adversarial vulnerability of powerful near out-of-distribution detectioncited by 16
  23. 2022Back to the Basics: Revisiting Out-of-Distribution Detection Baselinescited by 16
  24. 2022Your Out-of-Distribution Detection Method is Not Robust!cited by 16
  25. 2023Devil is in the Queries: Advancing Mask Transformers for Real-world Medical Image Segmentation and Out-of-Distribution Localizationcited by 16
  26. 2024AdaNeg: Adaptive Negative Proxy Guided OOD Detection with Vision-Language Modelscited by 16
  27. 2023Learning Sample Difficulty from Pre-trained Models for Reliable Predictioncited by 15
  28. 2023On the use of Mahalanobis distance for out-of-distribution detection with neural networks for medical imagingcited by 15
  29. 2024TrustSQL: Benchmarking Text-to-SQL Reliability with Penalty-Based Scoringcited by 15
  30. 2023A Data-Driven Measure of Relative Uncertainty for Misclassification Detectioncited by 14
  31. 2025Out-of-Distribution Detection Methods Answer the Wrong Questionscited by 14
  32. 2021Hyperdimensional Feature Fusion for Out-Of-Distribution Detectioncited by 13
  33. 2024A noisy elephant in the room: Is your out-of-distribution detector robust to label noise?cited by 13
  34. 2025OpenMIBOOD: Open Medical Imaging Benchmarks for Out-Of-Distribution Detectioncited by 13
  35. 2023Gaussian Process Probes (GPP) for Uncertainty-Aware Probingcited by 11
  36. 2022Fine-grain Inference on Out-of-Distribution Data with Hierarchical Classificationcited by 10
  37. 2023Gaussian Latent Representations for Uncertainty Estimation using Mahalanobis Distance in Deep Classifierscited by 10
  38. 2024Can OOD Object Detectors Learn from Foundation Models?cited by 10

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