# Balanced Energy Regularization Loss for Out-of-distribution Detection

arXiv: https://arxiv.org/abs/2306.10485 · HTML: https://mlsanity.com/paper/2306.10485/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 18 Jun 2023.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [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)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (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)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Evaluating Bayesian Deep Learning Methods for Semantic Segmentation](https://mlsanity.com/paper/1811.12709/) (2018)
- [Detecting the Unexpected via Image Resynthesis](https://mlsanity.com/paper/1904.07595/) (2019)
- [Entropy Maximization and Meta Classification for Out-Of-Distribution Detection in Semantic Segmentation](https://mlsanity.com/paper/2012.06575/) (2020)
- [The Fishyscapes Benchmark: Measuring Blind Spots in Semantic Segmentation](https://mlsanity.com/paper/1904.03215/) (2019)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [Pixel-wise Anomaly Detection in Complex Driving Scenes](https://mlsanity.com/paper/2103.05445/) (2021)
- [Semantically Coherent Out-of-Distribution Detection](https://mlsanity.com/paper/2108.11941/) (2021)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)

## Built on by (most cited first, 16 of 16)

- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [Target before Shooting: Accurate Anomaly Detection and Localization under One Millisecond via Cascade Patch Retrieval](https://mlsanity.com/paper/2308.06748/) (2023)
- [Gradient-Regularized Out-of-Distribution Detection](https://mlsanity.com/paper/2404.12368/) (2024)
- [Extremely Simple Multimodal Outlier Synthesis for Out-of-Distribution Detection and Segmentation](https://mlsanity.com/paper/2505.16985/) (2025)
- [Rethinking Out-of-Distribution Detection on Imbalanced Data Distribution](https://mlsanity.com/paper/2407.16430/) (2024)
- [Zero-Shot Out-of-Distribution Detection with Outlier Label Exposure](https://mlsanity.com/paper/2406.01170/) (2024)
- [Long-Tailed Out-of-Distribution Detection via Normalized Outlier Distribution Adaptation](https://mlsanity.com/paper/2410.20807/) (2024)
- [BOOD: Boundary-based Out-Of-Distribution Data Generation](https://mlsanity.com/paper/2508.00350/) (2025)
- [Panoramic Out-of-Distribution Segmentation](https://mlsanity.com/paper/2505.03539/) (2025)
- [Optimizing Three Critical Factors for Practical and Effective OOD Detection Fine-Tuning](https://mlsanity.com/paper/2308.01030/) (2023)
- [Random Walk on Pixel Manifolds for Anomaly Segmentation of Complex Driving Scenes](https://mlsanity.com/paper/2404.17961/) (2024)
- [Representation Norm Amplification for Out-of-Distribution Detection in Long-Tail Learning](https://mlsanity.com/paper/2408.10676/) (2024)
- [SupLID: Geometrical Guidance for Out-of-Distribution Detection in Semantic Segmentation](https://mlsanity.com/paper/2511.18816/) (2025)
- [RICASSO: Reinforced Imbalance Learning with Class-Aware Self-Supervised Outliers Exposure](https://mlsanity.com/paper/2410.10548/) (2024)
- [Multi-Hierarchical Fine-Grained Feature Mapping Driven by Feature Contribution for Molecular Odor Prediction](https://mlsanity.com/paper/2505.00290/) (2025)
- [Out-of-Distribution Detection Based on Total Variation Estimation](https://mlsanity.com/paper/2601.15867/) (2026)

## Abstract (arXiv)

In the field of out-of-distribution (OOD) detection, a previous method that use auxiliary data as OOD data has shown promising performance. However, the method provides an equal loss to all auxiliary data to differentiate them from inliers. However, based on our observation, in various tasks, there is a general imbalance in the distribution of the auxiliary OOD data across classes. We propose a balanced energy regularization loss that is simple but generally effective for a variety of tasks. Our balanced energy regularization loss utilizes class-wise different prior probabilities for auxiliary data to address the class imbalance in OOD data. The main concept is to regularize auxiliary samples from majority classes, more heavily than those from minority classes. Our approach performs better for OOD detection in semantic segmentation, long-tailed image classification, and image classification than the prior energy regularization loss. Furthermore, our approach achieves state-of-the-art performance in two tasks: OOD detection in semantic segmentation and long-tailed image classification. Code is available at https://github.com/hyunjunChhoi/Balanced_Energy.