# When and How Does In-Distribution Label Help Out-of-Distribution Detection?

arXiv: https://arxiv.org/abs/2405.18635 · HTML: https://mlsanity.com/paper/2405.18635/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 105 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 71)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [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)
- [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)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [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)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)

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

- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation](https://mlsanity.com/paper/2602.08431/) (2026)
- [Rethinking Out-of-Distribution Detection on Imbalanced Data Distribution](https://mlsanity.com/paper/2407.16430/) (2024)
- [Out-of-Distribution Learning with Human Feedback](https://mlsanity.com/paper/2408.07772/) (2024)
- [Can We Ignore Labels In Out of Distribution Detection?](https://mlsanity.com/paper/2504.14704/) (2025)
- [Semantic or Covariate? A Study on the Intractable Case of Out-of-Distribution Detection](https://mlsanity.com/paper/2411.11254/) (2024)

## Abstract (arXiv)

Detecting data points deviating from the training distribution is pivotal for ensuring reliable machine learning. Extensive research has been dedicated to the challenge, spanning classical anomaly detection techniques to contemporary out-of-distribution (OOD) detection approaches. While OOD detection commonly relies on supervised learning from a labeled in-distribution (ID) dataset, anomaly detection may treat the entire ID data as a single class and disregard ID labels. This fundamental distinction raises a significant question that has yet to be rigorously explored: when and how does ID label help OOD detection? This paper bridges this gap by offering a formal understanding to theoretically delineate the impact of ID labels on OOD detection. We employ a graph-theoretic approach, rigorously analyzing the separability of ID data from OOD data in a closed-form manner. Key to our approach is the characterization of data representations through spectral decomposition on the graph. Leveraging these representations, we establish a provable error bound that compares the OOD detection performance with and without ID labels, unveiling conditions for achieving enhanced OOD detection. Lastly, we present empirical results on both simulated and real datasets, validating theoretical guarantees and reinforcing our insights. Code is publicly available at https://github.com/deeplearning-wisc/id_label.