# VRA: Variational Rectified Activation for Out-of-distribution Detection

arXiv: https://arxiv.org/abs/2302.11716 · HTML: https://mlsanity.com/paper/2302.11716/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 52 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (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)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [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)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [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)
- [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)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)

## Built on by (most cited first, 15 of 15)

- [Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advances](https://mlsanity.com/paper/2409.11884/) (2024)
- [GradOrth: A Simple yet Efficient Out-of-Distribution Detection with Orthogonal Projection of Gradients](https://mlsanity.com/paper/2308.00310/) (2023)
- [Gradient-Regularized Out-of-Distribution Detection](https://mlsanity.com/paper/2404.12368/) (2024)
- [Your Classifier Can Be Secretly a Likelihood-Based OOD Detector](https://mlsanity.com/paper/2408.04851/) (2024)
- [Mitigating the Modality Gap: Few-Shot Out-of-Distribution Detection with Multi-modal Prototypes and Image Bias Estimation](https://mlsanity.com/paper/2502.00662/) (2025)
- [Activation Subspaces for Out-of-Distribution Detection](https://mlsanity.com/paper/2508.21695/) (2025)
- [Tuning Out-of-Distribution (OOD) Detectors Without Given OOD Data](https://mlsanity.com/paper/2602.05935/) (2026)
- [RankFeat&RankWeight: Rank-1 Feature/Weight Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2311.13959/) (2023)
- [Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximation](https://mlsanity.com/paper/2505.15284/) (2025)
- [MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse](https://mlsanity.com/paper/2605.14413/) (2026)
- [Resultant: Incremental Effectiveness on Likelihood for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2409.03801/) (2024)
- [Beyond Perceptual Distance: Discrepancy Assessment on Deep Representation for Out-of-Distribution Detection with Diffusion Model](https://mlsanity.com/paper/2409.10094/) (2024)
- [Multi-Method Ensemble for Out-of-Distribution Detection](https://mlsanity.com/paper/2508.21463/) (2025)
- [From Local Geometry to Global Pseudo Labeling for Robust Positive Unlabeled Learning under Covariate Shift](https://mlsanity.com/paper/2605.31187/) (2026)
- [Out-of-Distribution (OOD) Detectors for Open-Set RF Fingerprinting](https://mlsanity.com/paper/2606.12718/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is critical to building reliable machine learning systems in the open world. Researchers have proposed various strategies to reduce model overconfidence on OOD data. Among them, ReAct is a typical and effective technique to deal with model overconfidence, which truncates high activations to increase the gap between in-distribution and OOD. Despite its promising results, is this technique the best choice for widening the gap? To answer this question, we leverage the variational method to find the optimal operation and verify the necessity of suppressing abnormally low and high activations and amplifying intermediate activations in OOD detection, rather than focusing only on high activations like ReAct. This motivates us to propose a novel technique called ``Variational Rectified Activation (VRA)'', which simulates these suppression and amplification operations using piecewise functions. Experimental results on multiple benchmark datasets demonstrate that our method outperforms existing post-hoc strategies. Meanwhile, VRA is compatible with different scoring functions and network architectures. textcolor[rgb]0.93,0.0,0.47Our code can be found in Supplementary Material.