English
Related papers

Related papers: Neural Collapse for Unconstrained Feature Model un…

200 papers

Neural collapse (NC) is a simple and symmetric phenomenon for deep neural networks (DNNs) at the terminal phase of training, where the last-layer features collapse to their class means and form a simplex equiangular tight frame aligning…

Machine Learning · Computer Science 2024-05-03 Sicong Wang , Kuo Gai , Shihua Zhang

Recent findings reveal that over-parameterized deep neural networks, trained beyond zero training-error, exhibit a distinctive structural pattern at the final layer, termed as Neural-collapse (NC). These results indicate that the final…

Machine Learning · Computer Science 2024-03-01 Tina Behnia , Christos Thrampoulidis

Neural collapse (NC) and its multi-layer variant, deep neural collapse (DNC), describe a structured geometry that occurs in the features and weights of trained deep networks. Recent theoretical work by Sukenik et al. using a deep…

Machine Learning · Computer Science 2025-10-07 Connall Garrod , Jonathan P. Keating

When training deep neural networks for classification tasks, an intriguing empirical phenomenon has been widely observed in the last-layer classifiers and features, where (i) the class means and the last-layer classifiers all collapse to…

Machine Learning · Computer Science 2022-03-15 Jinxin Zhou , Xiao Li , Tianyu Ding , Chong You , Qing Qu , Zhihui Zhu

Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised. We identify a simple and…

Machine Learning · Computer Science 2026-04-02 Anamika Paul Rupa

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both…

Machine Learning · Computer Science 2023-04-18 Weiyang Liu , Longhui Yu , Adrian Weller , Bernhard Schölkopf

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features…

Machine Learning · Computer Science 2023-05-30 Tom Tirer , Haoxiang Huang , Jonathan Niles-Weed

Neural Collapse (NC) is a well-known phenomenon of deep neural networks in the terminal phase of training (TPT). It is characterized by the collapse of features and classifier into a symmetrical structure, known as simplex equiangular tight…

Machine Learning · Computer Science 2023-10-13 Peifeng Gao , Qianqian Xu , Yibo Yang , Peisong Wen , Huiyang Shao , Zhiyong Yang , Bernard Ghanem , Qingming Huang

Deep classifier neural networks enter the terminal phase of training (TPT) when training error reaches zero and tend to exhibit intriguing Neural Collapse (NC) properties. Neural collapse essentially represents a state at which the…

Machine Learning · Computer Science 2023-04-12 Vignesh Kothapalli

We provide the first global optimization landscape analysis of $Neural\;Collapse$ -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As…

Machine Learning · Computer Science 2021-05-07 Zhihui Zhu , Tianyu Ding , Jinxin Zhou , Xiao Li , Chong You , Jeremias Sulam , Qing Qu

Meta-learning frameworks for few-shot learning aims to learn models that can learn new skills or adapt to new environments rapidly with a few training examples. This has led to the generalizability of the developed model towards new classes…

Machine Learning · Computer Science 2023-10-10 Saaketh Medepalli , Naren Doraiswamy

Neural Collapse (NC) gives a precise description of the representations of classes in the final hidden layer of classification neural networks. This description provides insights into how these networks learn features and generalize well…

Machine Learning · Computer Science 2023-08-08 Liam Parker , Emre Onal , Anton Stengel , Jake Intrater

Modern deep neural networks for classification usually jointly learn a backbone for representation and a linear classifier to output the logit of each class. A recent study has shown a phenomenon called neural collapse that the within-class…

Machine Learning · Computer Science 2022-10-13 Yibo Yang , Shixiang Chen , Xiangtai Li , Liang Xie , Zhouchen Lin , Dacheng Tao

A recent study has shown a phenomenon called neural collapse in that the within-class means of features and the classifier weight vectors converge to the vertices of a simplex equiangular tight frame at the terminal phase of training for…

Computer Vision and Pattern Recognition · Computer Science 2023-01-04 Zhisheng Zhong , Jiequan Cui , Yibo Yang , Xiaoyang Wu , Xiaojuan Qi , Xiangyu Zhang , Jiaya Jia

Neural collapse provides an elegant mathematical characterization of learned last layer representations (a.k.a. features) and classifier weights in deep classification models. Such results not only provide insights but also motivate new…

Machine Learning · Computer Science 2023-10-30 Jiachen Jiang , Jinxin Zhou , Peng Wang , Qing Qu , Dustin Mixon , Chong You , Zhihui Zhu

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More specifically, for the output features of the penultimate…

Machine Learning · Computer Science 2023-03-09 Can Yaras , Peng Wang , Zhihui Zhu , Laura Balzano , Qing Qu

Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which…

Machine Learning · Computer Science 2025-09-30 Li Guo , George Andriopoulos , Zifan Zhao , Shuyang Ling , Zixuan Dong , Keith Ross

While cross entropy (CE) is the most commonly used loss to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is…

Machine Learning · Computer Science 2022-10-11 Jinxin Zhou , Chong You , Xiao Li , Kangning Liu , Sheng Liu , Qing Qu , Zhihui Zhu

Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks.…

Statistics Theory · Mathematics 2024-04-30 Michael Kohler , Sophie Langer

Neural Collapse refers to the remarkable structural properties characterizing the geometry of class embeddings and classifier weights, found by deep nets when trained beyond zero training error. However, this characterization only holds for…

Machine Learning · Computer Science 2022-08-12 Christos Thrampoulidis , Ganesh R. Kini , Vala Vakilian , Tina Behnia