# Out-of-Distribution Example Detection in Deep Neural Networks using Distance to Modelled Embedding

arXiv: https://arxiv.org/abs/2108.10673 · HTML: https://mlsanity.com/paper/2108.10673/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 24 Aug 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [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)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Safe Reinforcement Learning with Model Uncertainty Estimates](https://mlsanity.com/paper/1810.08700/) (2018)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Distance-based Confidence Score for Neural Network Classifiers](https://mlsanity.com/paper/1709.09844/) (2017)
- [Confidence Scoring Using Whitebox Meta-models with Linear Classifier Probes](https://mlsanity.com/paper/1805.05396/) (2018)
- [PsyPhy: A Psychophysics Driven Evaluation Framework for Visual Recognition](https://mlsanity.com/paper/1611.06448/) (2016)
- [Outlier Exposure with Confidence Control for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.03509/) (2019)

## Built on by (most cited first, 2 of 2)

- [phepy: Visual benchmarks and improvements for out-of-distribution detectors](https://mlsanity.com/paper/2503.05169/) (2025)
- [Vmem-varphi: Low-Compute Out-of-Distribution Detection in Spiking Neural Networks from Membrane-Potential Statistics](https://mlsanity.com/paper/2610.00350/) (2026)

## Abstract (arXiv)

Adoption of deep learning in safety-critical systems raise the need for understanding what deep neural networks do not understand after models have been deployed. The behaviour of deep neural networks is undefined for so called out-of-distribution examples. That is, examples from another distribution than the training set. Several methodologies to detect out-of-distribution examples during prediction-time have been proposed, but these methodologies constrain either neural network architecture, how the neural network is trained, suffer from performance overhead, or assume that the nature of out-of-distribution examples are known a priori. We present Distance to Modelled Embedding (DIME) that we use to detect out-of-distribution examples during prediction time. By approximating the training set embedding into feature space as a linear hyperplane, we derive a simple, unsupervised, highly performant and computationally efficient method. DIME allows us to add prediction-time detection of out-of-distribution examples to neural network models without altering architecture or training while imposing minimal constraints on when it is applicable. In our experiments, we demonstrate that by using DIME as an add-on after training, we efficiently detect out-of-distribution examples during prediction and match state-of-the-art methods while being more versatile and introducing negligible computational overhead.