# Semantic or Covariate? A Study on the Intractable Case of Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2411.11254 · HTML: https://mlsanity.com/paper/2411.11254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 31 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [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 Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (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)
- [DICE: Leveraging Sparsification for Out-of-Distribution Detection](https://mlsanity.com/paper/2111.09805/) (2021)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [Unsupervised Out-of-Distribution Detection by Maximum Classifier Discrepancy](https://mlsanity.com/paper/1908.04951/) (2019)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [Semantically Coherent Out-of-Distribution Detection](https://mlsanity.com/paper/2108.11941/) (2021)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Provable Guarantees for Understanding Out-of-distribution Detection](https://mlsanity.com/paper/2112.00787/) (2021)
- [Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement](https://mlsanity.com/paper/2310.00227/) (2023)
- [Full-Spectrum Out-of-Distribution Detection](https://mlsanity.com/paper/2204.05306/) (2022)
- [RankFeat: Rank-1 Feature Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2209.08590/) (2022)
- [Learning with Mixture of Prototypes for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.02653/) (2024)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [ImageNet-OOD: Deciphering Modern Out-of-Distribution Detection Algorithms](https://mlsanity.com/paper/2310.01755/) (2023)
- [Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data](https://mlsanity.com/paper/2301.12321/) (2023)
- [When and How Does In-Distribution Label Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2405.18635/) (2024)

## Abstract (arXiv)

The primary goal of out-of-distribution (OOD) detection tasks is to identify inputs with semantic shifts, i.e., if samples from novel classes are absent in the in-distribution (ID) dataset used for training, we should reject these OOD samples rather than misclassifying them into existing ID classes. However, we find the current definition of "semantic shift" is ambiguous, which renders certain OOD testing protocols intractable for the post-hoc OOD detection methods based on a classifier trained on the ID dataset. In this paper, we offer a more precise definition of the Semantic Space and the Covariate Space for the ID distribution, allowing us to theoretically analyze which types of OOD distributions make the detection task intractable. To avoid the flaw in the existing OOD settings, we further define the "Tractable OOD" setting which ensures the distinguishability of OOD and ID distributions for the post-hoc OOD detection methods. Finally, we conduct several experiments to demonstrate the necessity of our definitions and validate the correctness of our theorems.