# WOOD: Wasserstein-based Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2112.06384 · HTML: https://mlsanity.com/paper/2112.06384/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [Deep Active Learning: Unified and Principled Method for Query and Training](https://mlsanity.com/paper/1911.09162/) (2019)
- [Improving Reconstruction Autoencoder Out-of-distribution Detection with Mahalanobis Distance](https://mlsanity.com/paper/1812.02765/) (2018)
- [Classification Uncertainty of Deep Neural Networks Based on Gradient Information](https://mlsanity.com/paper/1805.08440/) (2018)
- [From GAN to WGAN](https://mlsanity.com/paper/1904.08994/) (2019)
- [Confidence from Invariance to Image Transformations](https://mlsanity.com/paper/1804.00657/) (2018)

## Built on by (most cited first, 9 of 9)

- [Optimal Transport for Unsupervised Hallucination Detection in Neural Machine Translation](https://mlsanity.com/paper/2212.09631/) (2022)
- [Uni-3DAD: GAN-Inversion Aided Universal 3D Anomaly Detection on Model-free Products](https://mlsanity.com/paper/2408.16201/) (2024)
- [Building Trustworthy AI for Materials Discovery: From Autonomous Laboratories to Z-scores](https://mlsanity.com/paper/2512.01080/) (2025)
- [Sliced-Wasserstein-based Anomaly Detection and Open Dataset for Localized Critical Peak Rebates](https://mlsanity.com/paper/2410.21712/) (2024)
- [Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximation](https://mlsanity.com/paper/2505.15284/) (2025)
- [SEE-OoD: Supervised Exploration For Enhanced Out-of-Distribution Detection](https://mlsanity.com/paper/2310.08040/) (2023)
- [ADs: Active Data-sharing for Data Quality Assurance in Advanced Manufacturing Systems](https://mlsanity.com/paper/2404.00572/) (2024)
- [Aortic root landmark localization with optimal transport loss for heatmap regression](https://mlsanity.com/paper/2407.04921/) (2024)
- [Sliced-Wasserstein Distance-based Data Selection](https://mlsanity.com/paper/2504.12918/) (2025)

## Abstract (arXiv)

The training and test data for deep-neural-network-based classifiers are usually assumed to be sampled from the same distribution. When part of the test samples are drawn from a distribution that is sufficiently far away from that of the training samples (a.k.a. out-of-distribution (OOD) samples), the trained neural network has a tendency to make high confidence predictions for these OOD samples. Detection of the OOD samples is critical when training a neural network used for image classification, object detection, etc. It can enhance the classifier's robustness to irrelevant inputs, and improve the system resilience and security under different forms of attacks. Detection of OOD samples has three main challenges: (i) the proposed OOD detection method should be compatible with various architectures of classifiers (e.g., DenseNet, ResNet), without significantly increasing the model complexity and requirements on computational resources; (ii) the OOD samples may come from multiple distributions, whose class labels are commonly unavailable; (iii) a score function needs to be defined to effectively separate OOD samples from in-distribution (InD) samples. To overcome these challenges, we propose a Wasserstein-based out-of-distribution detection (WOOD) method. The basic idea is to define a Wasserstein-distance-based score that evaluates the dissimilarity between a test sample and the distribution of InD samples. An optimization problem is then formulated and solved based on the proposed score function. The statistical learning bound of the proposed method is investigated to guarantee that the loss value achieved by the empirical optimizer approximates the global optimum. The comparison study results demonstrate that the proposed WOOD consistently outperforms other existing OOD detection methods.