# Subspace Modeling for Fast Out-Of-Distribution and Anomaly Detection

arXiv: https://arxiv.org/abs/2203.10422 · HTML: https://mlsanity.com/paper/2203.10422/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 20 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [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)
- [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)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Anomalib: A Deep Learning Library for Anomaly Detection](https://mlsanity.com/paper/2202.08341/) (2022)
- [Probabilistic Modeling of Deep Features for Out-of-Distribution and Adversarial Detection](https://mlsanity.com/paper/1909.11786/) (2019)
- [Novelty Detection Through Model-Based Characterization of Neural Networks](https://mlsanity.com/paper/2008.06094/) (2020)

## Built on by (most cited first, 3 of 3)

- [FRE: A Fast Method For Anomaly Detection And Segmentation](https://mlsanity.com/paper/2211.12650/) (2022)
- [CONCLAD: COntinuous Novel CLAss Detector](https://mlsanity.com/paper/2412.10473/) (2024)
- [Incremental dimension reduction for efficient and accurate visual anomaly detection](https://mlsanity.com/paper/2602.23595/) (2026)

## Abstract (arXiv)

This paper presents a fast, principled approach for detecting anomalous and out-of-distribution (OOD) samples in deep neural networks (DNN). We propose the application of linear statistical dimensionality reduction techniques on the semantic features produced by a DNN, in order to capture the low-dimensional subspace truly spanned by said features. We show that the "feature reconstruction error" (FRE), which is the ℓ2-norm of the difference between the original feature in the high-dimensional space and the pre-image of its low-dimensional reduced embedding, is highly effective for OOD and anomaly detection. To generalize to intermediate features produced at any given layer, we extend the methodology by applying nonlinear kernel-based methods. Experiments using standard image datasets and DNN architectures demonstrate that our method meets or exceeds best-in-class quality performance, but at a fraction of the computational and memory cost required by the state of the art. It can be trained and run very efficiently, even on a traditional CPU.