# Why Out-of-distribution Detection in CNNs Does Not Like Mahalanobis -- and What to Use Instead

arXiv: https://arxiv.org/abs/2110.07043 · HTML: https://mlsanity.com/paper/2110.07043/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Meta Pseudo Labels](https://mlsanity.com/paper/2003.10580/) (2020)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Large-Scale Image Retrieval with Attentive Deep Local Features](https://mlsanity.com/paper/1612.06321/) (2016)
- [Towards Open World Recognition](https://mlsanity.com/paper/1412.5687/) (2014)
- [Towards Safe Autonomous Driving: Capture Uncertainty in the Deep Neural Network For Lidar 3D Vehicle Detection](https://mlsanity.com/paper/1804.05132/) (2018)
- [The Extreme Value Machine](https://mlsanity.com/paper/1506.06112/) (2015)
- [Selective Convolutional Descriptor Aggregation for Fine-Grained Image Retrieval](https://mlsanity.com/paper/1604.04994/) (2016)
- [Cross-dimensional Weighting for Aggregated Deep Convolutional Features](https://mlsanity.com/paper/1512.04065/) (2015)
- [Humans can decipher adversarial images](https://mlsanity.com/paper/1809.04120/) (2018)

## Built on by (most cited first, 1 of 1)

- [The Invisible Gorilla Effect in Out-of-distribution Detection](https://mlsanity.com/paper/2602.20068/) (2026)

## Abstract (arXiv)

Convolutional neural networks applied for real-world classification tasks need to recognize inputs that are far or out-of-distribution (OoD) with respect to the known or training data. To achieve this, many methods estimate class-conditional posterior probabilities and use confidence scores obtained from the posterior distributions. Recent works propose to use multivariate Gaussian distributions as models of posterior distributions at different layers of the CNN (i.e., for low- and upper-level features), which leads to the confidence scores based on the Mahalanobis distance. However, this procedure involves estimating probability density in high dimensional data using the insufficient number of observations (e.g. the dimensionality of features at the last two layers in the ResNet-101 model are 2048 and 1024, with ca. 1000 observations per class used to estimate density). In this work, we want to address this problem. We show that in many OoD studies in high-dimensional data, LOF-based (Local Outlierness-Factor) methods outperform the parametric, Mahalanobis distance-based methods. This motivates us to propose the nonparametric, LOF-based method of generating the confidence scores for CNNs. We performed several feasibility studies involving ResNet-101 and EffcientNet-B3, based on CIFAR-10 and ImageNet (as known data), and CIFAR-100, SVHN, ImageNet2010, Places365, or ImageNet-O (as outliers). We demonstrated that nonparametric LOF-based confidence estimation can improve current Mahalanobis-based SOTA or obtain similar performance in a simpler way.