# Dimensionality-induced information loss of outliers in deep neural networks

arXiv: https://arxiv.org/abs/2410.21656 · HTML: https://mlsanity.com/paper/2410.21656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [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)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [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)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection](https://mlsanity.com/paper/2005.14140/) (2020)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [MOOD: Multi-level Out-of-distribution Detection](https://mlsanity.com/paper/2104.14726/) (2021)
- [Why Do Better Loss Functions Lead to Less Transferable Features?](https://mlsanity.com/paper/2010.16402/) (2020)
- [RankFeat: Rank-1 Feature Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2209.08590/) (2022)
- [Stable Rank Normalization for Improved Generalization in Neural Networks and GANs](https://mlsanity.com/paper/1906.04659/) (2019)
- [Compression based bound for non-compressed network: unified generalization error analysis of large compressible deep neural network](https://mlsanity.com/paper/1909.11274/) (2019)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is a critical issue for the stable and reliable operation of systems using a deep neural network (DNN). Although many OOD detection methods have been proposed, it remains unclear how the differences between in-distribution (ID) and OOD samples are generated by each processing step inside DNNs. We experimentally clarify this issue by investigating the layer dependence of feature representations from multiple perspectives. We find that intrinsic low dimensionalization of DNNs is essential for understanding how OOD samples become more distinct from ID samples as features propagate to deeper layers. Based on these observations, we provide a simple picture that consistently explains various properties of OOD samples. Specifically, low-dimensional weights eliminate most information from OOD samples, resulting in misclassifications due to excessive attention to dataset bias. In addition, we demonstrate the utility of dimensionality by proposing a dimensionality-aware OOD detection method based on alignment of features and weights, which consistently achieves high performance for various datasets with lower computational cost.