# Mahalanobis++: Improving OOD Detection via Feature Normalization

arXiv: https://arxiv.org/abs/2505.18032 · HTML: https://mlsanity.com/paper/2505.18032/

## 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.

## Builds on (most cited first, 30 of 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Delving into Out-of-Distribution Detection with Vision-Language Representations](https://mlsanity.com/paper/2211.13445/) (2022)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation](https://mlsanity.com/paper/2306.00826/) (2023)
- [Spreading vectors for similarity search](https://mlsanity.com/paper/1806.03198/) (2018)
- [Nearest Neighbor Guidance for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.14888/) (2023)
- [Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold](https://mlsanity.com/paper/2209.09211/) (2022)
- [Fast Decision Boundary based Out-of-Distribution Detector](https://mlsanity.com/paper/2312.11536/) (2023)

## Built on by (most cited first, 30 of 32)

- [A Geometry-Based View of Mahalanobis OOD Detection](https://mlsanity.com/paper/2510.15202/) (2025)
- [VLA-FAIL: Efficient Task Failure Detection for Finetuned Vision-Language-Action Models](https://mlsanity.com/paper/2606.21386/) (2026)
- [CANDI: Curated Test-Time Adaptation for Multivariate Time-Series Anomaly Detection Under Distribution Shift](https://mlsanity.com/paper/2604.01845/) (2026)
- [AP-OOD: Attention Pooling for Out-of-Distribution Detection](https://mlsanity.com/paper/2602.06031/) (2026)
- [Vendi Novelty Scores for Out-of-Distribution Detection](https://mlsanity.com/paper/2602.10062/) (2026)
- [Mechanistic Anomaly Detection via Functional Attribution](https://mlsanity.com/paper/2604.18970/) (2026)
- [Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning](https://mlsanity.com/paper/2605.05638/) (2026)
- [MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse](https://mlsanity.com/paper/2605.14413/) (2026)
- [Frustratingly Easy Feature Reconstruction for Out-of-Distribution Detection](https://mlsanity.com/paper/2509.06988/) (2025)
- [Adaptive Individual Uncertainty under Out-Of-Distribution Shift with Expert-Routed Conformal Prediction](https://mlsanity.com/paper/2510.15233/) (2025)
- [Latent space analysis and generalization to out-of-distribution data](https://mlsanity.com/paper/2511.15010/) (2025)
- [Tracking the Discriminative Axis: Dual Prototypes for Test-Time OOD Detection Under Covariate Shift](https://mlsanity.com/paper/2603.15213/) (2026)
- [Knowledge-Guided Failure Prediction: Detecting When Object Detectors Miss Safety-Critical Objects](https://mlsanity.com/paper/2603.25499/) (2026)
- [MATHENA: Mamba-based Architectural Tooth Hierarchical Estimator and Holistic Evaluation Network for Anatomy](https://mlsanity.com/paper/2604.00537/) (2026)
- [Ranked Activation Shift for Post-Hoc Out-of-Distribution Detection](https://mlsanity.com/paper/2604.08572/) (2026)
- [Sparsity as a Key: Unlocking New Insights from Latent Structures for Out-of-Distribution Detection](https://mlsanity.com/paper/2604.26409/) (2026)
- [Useful Features, Backward Scores: OOD in Language-Model Trajectories](https://mlsanity.com/paper/2605.00269/) (2026)
- [Surviving the Unseen: Predictive Defense for Novel Multi-Turn Multimodal Attacks](https://mlsanity.com/paper/2605.18988/) (2026)
- [How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learning](https://mlsanity.com/paper/2605.25414/) (2026)
- [Learning Hyperspherical Time-Frequency Representations for Time-Series Out-of-Distribution Detection](https://mlsanity.com/paper/2605.31155/) (2026)
- [Assessing Sample Quality in Conditional Generation under Compositional Shift](https://mlsanity.com/paper/2606.09601/) (2026)
- [MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusion](https://mlsanity.com/paper/2606.17352/) (2026)
- [MaRS: Robust Out-of-Distribution Detection via Mahalanobis Residual Scoring](https://mlsanity.com/paper/2606.22649/) (2026)
- [Modality-Aware Out-of-Distribution Detection for Multi-Modal Action Recognition](https://mlsanity.com/paper/2606.24404/) (2026)
- [Exploiting Local Flatness for Efficient Out-of-Distribution Detection](https://mlsanity.com/paper/2606.29952/) (2026)
- [Training-Free Out-of-Distribution Detection for Pathology Whole-Slide Images](https://mlsanity.com/paper/2608.01407/) (2026)
- [Verdict Instability of OOD Scores under Reference Resampling](https://mlsanity.com/paper/2609.00691/) (2026)
- [Fi-ImageNet-1k: An OOD Benchmark From the Inside of the ImageNet-1k Validation Set](https://mlsanity.com/paper/2609.01027/) (2026)
- [Unified Multi-Layer Subspace Modeling for Cross-Domain OOD Detection](https://mlsanity.com/paper/2609.06785/) (2026)
- [Dataset Identity, Not Novelty: The Source of an Inflated OOD Detection Gain](https://mlsanity.com/paper/2610.01096/) (2026)

## 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.