# Provable Guarantees for Understanding Out-of-distribution Detection

arXiv: https://arxiv.org/abs/2112.00787 · HTML: https://mlsanity.com/paper/2112.00787/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 30 of 33)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (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)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [Towards Open World Recognition](https://mlsanity.com/paper/1412.5687/) (2014)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [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)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Can multi-label classification networks know what they don't know?](https://mlsanity.com/paper/2109.14162/) (2021)
- [On the Impact of Spurious Correlation for Out-of-distribution Detection](https://mlsanity.com/paper/2109.05642/) (2021)
- [Out-of-distribution Detection in Classifiers via Generation](https://mlsanity.com/paper/1910.04241/) (2019)

## Built on by (most cited first, 30 of 78)

- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [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)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)
- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Training OOD Detectors in their Natural Habitats](https://mlsanity.com/paper/2202.03299/) (2022)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Unknown-Aware Object Detection: Learning What You Don't Know from Videos in the Wild](https://mlsanity.com/paper/2203.03800/) (2022)
- [Learning to Augment Distributions for Out-of-Distribution Detection](https://mlsanity.com/paper/2311.01796/) (2023)
- [LINe: Out-of-Distribution Detection by Leveraging Important Neurons](https://mlsanity.com/paper/2303.13995/) (2023)
- [OpenCon: Open-world Contrastive Learning](https://mlsanity.com/paper/2208.02764/) (2022)
- [A Survey on Out-of-Distribution Detection in NLP](https://mlsanity.com/paper/2305.03236/) (2023)
- [Out-of-distribution Detection Learning with Unreliable Out-of-distribution Sources](https://mlsanity.com/paper/2311.03236/) (2023)
- [Watermarking for Out-of-distribution Detection](https://mlsanity.com/paper/2210.15198/) (2022)
- [Understanding the Feature Norm for Out-of-Distribution Detection](https://mlsanity.com/paper/2310.05316/) (2023)
- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.17888/) (2024)
- [DOS: Diverse Outlier Sampling for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.02031/) (2023)
- [Far Away in the Deep Space: Dense Nearest-Neighbor-Based Out-of-Distribution Detection](https://mlsanity.com/paper/2211.06660/) (2022)
- [Average of Pruning: Improving Performance and Stability of Out-of-Distribution Detection](https://mlsanity.com/paper/2303.01201/) (2023)
- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [AUTO: Adaptive Outlier Optimization for Test-Time OOD Detection](https://mlsanity.com/paper/2303.12267/) (2023)
- [Conjugated Semantic Pool Improves OOD Detection with Pre-trained Vision-Language Models](https://mlsanity.com/paper/2410.08611/) (2024)
- [Mixture of Gaussian-distributed Prototypes with Generative Modelling for Interpretable and Trustworthy Image Recognition](https://mlsanity.com/paper/2312.00092/) (2023)
- [Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation](https://mlsanity.com/paper/2408.03915/) (2024)
- [Energy-based Hopfield Boosting for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.08766/) (2024)
- [Unlocking the Power of Open Set : A New Perspective for Open-Set Noisy Label Learning](https://mlsanity.com/paper/2305.04203/) (2023)
- [Concurrent Misclassification and Out-of-Distribution Detection for Semantic Segmentation via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2305.09610/) (2023)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is important for deploying machine learning models in the real world, where test data from shifted distributions can naturally arise. While a plethora of algorithmic approaches have recently emerged for OOD detection, a critical gap remains in theoretical understanding. In this work, we develop an analytical framework that characterizes and unifies the theoretical understanding for OOD detection. Our analytical framework motivates a novel OOD detection method for neural networks, GEM, which demonstrates both theoretical and empirical superiority. In particular, on CIFAR-100 as in-distribution data, our method outperforms a competitive baseline by 16.57% (FPR95). Lastly, we formally provide provable guarantees and comprehensive analysis of our method, underpinning how various properties of data distribution affect the performance of OOD detection.