# Controlling Neural Collapse Enhances Out-of-Distribution Detection and Transfer Learning

arXiv: https://arxiv.org/abs/2502.10691 · HTML: https://mlsanity.com/paper/2502.10691/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 71 of its 96 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 30 of 71)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [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)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Episodic Training for Domain Generalization](https://mlsanity.com/paper/1902.00113/) (2019)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)

## Built on by (most cited first, 11 of 11)

- [NEO: No-Optimization Test-Time Adaptation through Latent Re-Centering](https://mlsanity.com/paper/2510.05635/) (2025)
- [Diagnosing Generalization Failures from Representational Geometry Markers](https://mlsanity.com/paper/2603.01879/) (2026)
- [A Good Start Matters: Enhancing Continual Learning with Data-Driven Weight Initialization](https://mlsanity.com/paper/2503.06385/) (2025)
- [GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models](https://mlsanity.com/paper/2602.00191/) (2026)
- [Unlocking ImageNet's Multi-Object Nature: Automated Large-Scale Multilabel Annotation](https://mlsanity.com/paper/2603.05729/) (2026)
- [Prototype Fusion: A Training-Free Multi-Layer Approach to OOD Detection](https://mlsanity.com/paper/2603.23677/) (2026)
- [Cluster-Aware Neural Collapse Prompt Tuning for Long-Tailed Generalization of Vision-Language Models](https://mlsanity.com/paper/2605.11939/) (2026)
- [Neural Collapse by Design: Learning Class Prototypes on the Hypersphere](https://mlsanity.com/paper/2605.20302/) (2026)
- [MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusion](https://mlsanity.com/paper/2606.17352/) (2026)
- [SwinAD: Multi-stage feature reconstruction for unsupervised industrial anomaly detection](https://mlsanity.com/paper/2607.14534/) (2026)
- [TOOD: Task-Aware Out-of-Distribution Score Calibration for Continual Learners](https://mlsanity.com/paper/2607.29592/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection and OOD generalization are widely studied in Deep Neural Networks (DNNs), yet their relationship remains poorly understood. We empirically show that the degree of Neural Collapse (NC) in a network layer is inversely related with these objectives: stronger NC improves OOD detection but degrades generalization, while weaker NC enhances generalization at the cost of detection. This trade-off suggests that a single feature space cannot simultaneously achieve both tasks. To address this, we develop a theoretical framework linking NC to OOD detection and generalization. We show that entropy regularization mitigates NC to improve generalization, while a fixed Simplex Equiangular Tight Frame (ETF) projector enforces NC for better detection. Based on these insights, we propose a method to control NC at different DNN layers. In experiments, our method excels at both tasks across OOD datasets and DNN architectures. Code for our experiments is available at: https://yousuf907.github.io/ncoodg