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

arXiv: https://arxiv.org/abs/2106.09022 · HTML: https://mlsanity.com/paper/2106.09022/

## Key facts

- Cited by 207 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [An Evaluation Dataset for Intent Classification and Out-of-Scope Prediction](https://mlsanity.com/paper/1909.02027/) (2019)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Vision Transformers are Robust Learners](https://mlsanity.com/paper/2105.07581/) (2021)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [Hybrid Models for Open Set Recognition](https://mlsanity.com/paper/2003.12506/) (2020)
- [Density of States Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2006.09273/) (2020)
- [Why is the Mahalanobis Distance Effective for Anomaly Detection?](https://mlsanity.com/paper/2003.00402/) (2020)

## Built on by (most cited first, 30 of 207)

- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Towards Open Vocabulary Learning: A Survey](https://mlsanity.com/paper/2306.15880/) (2023)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation](https://mlsanity.com/paper/2306.00826/) (2023)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [Plex: Towards Reliability using Pretrained Large Model Extensions](https://mlsanity.com/paper/2207.07411/) (2022)
- [Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement](https://mlsanity.com/paper/2310.00227/) (2023)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [A Call to Reflect on Evaluation Practices for Failure Detection in Image Classification](https://mlsanity.com/paper/2211.15259/) (2022)
- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [NECO: NEural Collapse Based Out-of-distribution detection](https://mlsanity.com/paper/2310.06823/) (2023)
- [Test-Time Robust Personalization for Federated Learning](https://mlsanity.com/paper/2205.10920/) (2022)
- [A Simple Zero-shot Prompt Weighting Technique to Improve Prompt Ensembling in Text-Image Models](https://mlsanity.com/paper/2302.06235/) (2023)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [LINe: Out-of-Distribution Detection by Leveraging Important Neurons](https://mlsanity.com/paper/2303.13995/) (2023)
- [Outlier detection by ensembling uncertainty with negative objectness](https://mlsanity.com/paper/2402.15374/) (2024)
- [SAFE: Sensitivity-Aware Features for Out-of-Distribution Object Detection](https://mlsanity.com/paper/2208.13930/) (2022)
- [Mahalanobis++: Improving OOD Detection via Feature Normalization](https://mlsanity.com/paper/2505.18032/) (2025)
- [No True State-of-the-Art? OOD Detection Methods are Inconsistent across Datasets](https://mlsanity.com/paper/2109.05554/) (2021)
- [Watermarking for Out-of-distribution Detection](https://mlsanity.com/paper/2210.15198/) (2022)
- [Neuron Activation Coverage: Rethinking Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2306.02879/) (2023)
- [Rainproof: An Umbrella To Shield Text Generators From Out-Of-Distribution Data](https://mlsanity.com/paper/2212.09171/) (2022)
- [LAPT: Label-driven Automated Prompt Tuning for OOD Detection with Vision-Language Models](https://mlsanity.com/paper/2407.08966/) (2024)
- [Igeood: An Information Geometry Approach to Out-of-Distribution Detection](https://mlsanity.com/paper/2203.07798/) (2022)
- [A Learning Based Hypothesis Test for Harmful Covariate Shift](https://mlsanity.com/paper/2212.02742/) (2022)
- [From Global to Local: Multi-scale Out-of-distribution Detection](https://mlsanity.com/paper/2308.10239/) (2023)

## 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).