# On Out-of-distribution Detection with Energy-based Models

arXiv: https://arxiv.org/abs/2107.08785 · HTML: https://mlsanity.com/paper/2107.08785/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 56 references that are in the map.
- First posted on arXiv 3 Jul 2021.

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

- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [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)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [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)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Flow Contrastive Estimation of Energy-Based Models](https://mlsanity.com/paper/1912.00589/) (2019)
- [Density of States Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2006.09273/) (2020)

## Built on by (most cited first, 17 of 17)

- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Community Forensics: Using Thousands of Generators to Train Fake Image Detectors](https://mlsanity.com/paper/2411.04125/) (2024)
- [Hybrid Energy Based Model in the Feature Space for Out-of-Distribution Detection](https://mlsanity.com/paper/2305.16966/) (2023)
- [A Unified Approach Towards Active Learning and Out-of-Distribution Detection](https://mlsanity.com/paper/2405.11337/) (2024)
- [Joint Out-of-Distribution Filtering and Data Discovery Active Learning](https://mlsanity.com/paper/2503.02491/) (2025)
- [Persistently Trained, Diffusion-assisted Energy-based Models](https://mlsanity.com/paper/2304.10707/) (2023)
- [Latent Space Energy-based Neural ODEs](https://mlsanity.com/paper/2409.03845/) (2024)
- [An Information-Theoretic Framework for Feature Construction in Out-of-Distribution Detection](https://mlsanity.com/paper/2506.14194/) (2025)
- [BOOD: Boundary-based Out-Of-Distribution Data Generation](https://mlsanity.com/paper/2508.00350/) (2025)
- [Federated Learning with Heterogeneous Data Handling for Robust Vehicular Object Detection](https://mlsanity.com/paper/2405.01108/) (2024)
- [Tuning Out-of-Distribution (OOD) Detectors Without Given OOD Data](https://mlsanity.com/paper/2602.05935/) (2026)
- [Mitigating Out-of-Distribution Data Density Overestimation in Energy-Based Models](https://mlsanity.com/paper/2205.14817/) (2022)
- [EBMs vs. CL: Exploring Self-Supervised Visual Pretraining for Visual Question Answering](https://mlsanity.com/paper/2206.14355/) (2022)
- [Exploring Energy-Based Models for Out-of-Distribution Detection in Dialect Identification](https://mlsanity.com/paper/2406.18067/) (2024)
- [DNN-GDITD: Out-of-distribution detection via Deep Neural Network based Gaussian Descriptor for Imbalanced Tabular Data](https://mlsanity.com/paper/2409.00980/) (2024)
- [Score-Based Training for Energy-Based TTS Models](https://mlsanity.com/paper/2505.13771/) (2025)
- [ALSA: Anchors in Logit Space for Out-of-Distribution Accuracy Estimation](https://mlsanity.com/paper/2508.19613/) (2025)

## Abstract (arXiv)

Several density estimation methods have shown to fail to detect out-of-distribution (OOD) samples by assigning higher likelihoods to anomalous data. Energy-based models (EBMs) are flexible, unnormalized density models which seem to be able to improve upon this failure mode. In this work, we provide an extensive study investigating OOD detection with EBMs trained with different approaches on tabular and image data and find that EBMs do not provide consistent advantages. We hypothesize that EBMs do not learn semantic features despite their discriminative structure similar to Normalizing Flows. To verify this hypotheses, we show that supervision and architectural restrictions improve the OOD detection of EBMs independent of the training approach.