# EPA: Neural Collapse Inspired Robust Out-of-Distribution Detector

arXiv: https://arxiv.org/abs/2401.01710 · HTML: https://mlsanity.com/paper/2401.01710/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 28 references that are in the map.
- First posted on arXiv 3 Jan 2024.

## Builds on (most cited first, 23 of 23)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [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)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [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)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Entropy Maximization and Meta Classification for Out-Of-Distribution Detection in Semantic Segmentation](https://mlsanity.com/paper/2012.06575/) (2020)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2302.03004/) (2023)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [Linking Neural Collapse and L2 Normalization with Improved Out-of-Distribution Detection in Deep Neural Networks](https://mlsanity.com/paper/2209.08378/) (2022)
- [Out-Of-Distribution Detection With Subspace Techniques And Probabilistic Modeling Of Features](https://mlsanity.com/paper/2012.04250/) (2020)

## Built on by (most cited first, 10 of 10)

- [Linguistic Collapse: Neural Collapse in (Large) Language Models](https://mlsanity.com/paper/2405.17767/) (2024)
- [Neural Collapse versus Low-rank Bias: Is Deep Neural Collapse Really Optimal?](https://mlsanity.com/paper/2405.14468/) (2024)
- [Wide Neural Networks Trained with Weight Decay Provably Exhibit Neural Collapse](https://mlsanity.com/paper/2410.04887/) (2024)
- [The Persistence of Neural Collapse Despite Low-Rank Bias](https://mlsanity.com/paper/2410.23169/) (2024)
- [Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.17816/) (2024)
- [Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers](https://mlsanity.com/paper/2505.15239/) (2025)
- [Adaptive Multi-prompt Contrastive Network for Few-shot Out-of-distribution Detection](https://mlsanity.com/paper/2506.17633/) (2025)
- [Diagonalizing the Softmax: Hadamard Initialization for Tractable Cross-Entropy Dynamics](https://mlsanity.com/paper/2512.04006/) (2025)
- [Double Descent Meets Out-of-Distribution Detection: Theoretical Insights and Empirical Analysis on the role of model complexity](https://mlsanity.com/paper/2411.02184/) (2024)
- [The Implicit Bias of Depth: From Neural Collapse to Softmax Codes](https://mlsanity.com/paper/2605.23087/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection plays a crucial role in ensuring the security of neural networks. Existing works have leveraged the fact that In-distribution (ID) samples form a subspace in the feature space, achieving state-of-the-art (SOTA) performance. However, the comprehensive characteristics of the ID subspace still leave under-explored. Recently, the discovery of Neural Collapse (NC) sheds light on novel properties of the ID subspace. Leveraging insight from NC, we observe that the Principal Angle between the features and the ID feature subspace forms a superior representation for measuring the likelihood of OOD. Building upon this observation, we propose a novel NC-inspired OOD scoring function, named Entropy-enhanced Principal Angle (EPA), which integrates both the global characteristic of the ID subspace and its inner property. We experimentally compare EPA with various SOTA approaches, validating its superior performance and robustness across different network architectures and OOD datasets.