# A Simple Test-Time Method for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2207.08210 · HTML: https://mlsanity.com/paper/2207.08210/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 17 Jul 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [MixNorm: Test-Time Adaptation Through Online Normalization Estimation](https://mlsanity.com/paper/2110.11478/) (2021)
- [Metric Learning for Novelty and Anomaly Detection](https://mlsanity.com/paper/1808.05492/) (2018)

## Built on by (most cited first, 6 of 6)

- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [AdaNeg: Adaptive Negative Proxy Guided OOD Detection with Vision-Language Models](https://mlsanity.com/paper/2410.20149/) (2024)
- [AUTO: Adaptive Outlier Optimization for Test-Time OOD Detection](https://mlsanity.com/paper/2303.12267/) (2023)
- [Taming False Positives in Out-of-Distribution Detection with Human Feedback](https://mlsanity.com/paper/2404.16954/) (2024)
- [Long-Tailed Out-of-Distribution Detection via Normalized Outlier Distribution Adaptation](https://mlsanity.com/paper/2410.20807/) (2024)
- [Iterative Deployment Exposure for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2406.02327/) (2024)

## Abstract (arXiv)

Neural networks are known to produce over-confident predictions on input images, even when these images are out-of-distribution (OOD) samples. This limits the applications of neural network models in real-world scenarios, where OOD samples exist. Many existing approaches identify the OOD instances via exploiting various cues, such as finding irregular patterns in the feature space, logits space, gradient space or the raw space of images. In contrast, this paper proposes a simple Test-time Linear Training (ETLT) method for OOD detection. Empirically, we find that the probabilities of input images being out-of-distribution are surprisingly linearly correlated to the features extracted by neural networks. To be specific, many state-of-the-art OOD algorithms, although designed to measure reliability in different ways, actually lead to OOD scores mostly linearly related to their image features. Thus, by simply learning a linear regression model trained from the paired image features and inferred OOD scores at test-time, we can make a more precise OOD prediction for the test instances. We further propose an online variant of the proposed method, which achieves promising performance and is more practical in real-world applications. Remarkably, we improve FPR95 from 51.37% to 12.30% on CIFAR-10 datasets with maximum softmax probability as the base OOD detector. Extensive experiments on several benchmark datasets show the efficacy of ETLT for OOD detection task.