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Neural Collapse (NC) is a geometric structure recently observed at the terminal phase of training deep neural networks, which states that last-layer feature vectors for the same class would "collapse" to a single point, while features of…

Machine Learning · Computer Science 2024-09-06 Leyan Pan , Xinyuan Cao

Deep neural networks (DNNs) exhibit a surprising structure in their final layer known as neural collapse (NC), and a growing body of works has currently investigated the propagation of neural collapse to earlier layers of DNNs -- a…

Machine Learning · Computer Science 2024-10-22 Peter Súkeník , Marco Mondelli , Christoph Lampert

The empirical emergence of neural collapse -- a surprising symmetry in the feature representations of the training data in the penultimate layer of deep neural networks -- has spurred a line of theoretical research aimed at its…

Machine Learning · Computer Science 2025-05-22 Peter Súkeník , Christoph H. Lampert , Marco Mondelli

The modern strategy for training deep neural networks for classification tasks includes optimizing the network's weights even after the training error vanishes to further push the training loss toward zero. Recently, a phenomenon termed…

Machine Learning · Computer Science 2022-10-13 Tom Tirer , Joan Bruna

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

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 (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

Recent advances in theoretical Deep Learning have introduced geometric properties that occur during training, past the Interpolation Threshold -- where the training error reaches zero. We inquire into the phenomena coined Neural Collapse in…

Machine Learning · Computer Science 2022-06-14 Ido Ben-Shaul , Shai Dekel

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the $L$-extended unconstrained feature…

Machine Learning · Computer Science 2024-11-27 Haixia Liu

A phenomenon known as ''Neural Collapse (NC)'' in deep classification tasks, in which the penultimate-layer features and the final classifiers exhibit an extremely simple geometric structure, has recently attracted considerable attention,…

Machine Learning · Computer Science 2025-11-05 Chuang Ma , Tomoyuki Obuchi , Toshiyuki Tanaka

With the ever-increasing complexity of large-scale pre-trained models coupled with a shortage of labeled data for downstream training, transfer learning has become the primary approach in many fields, including natural language processing,…

Machine Learning · Computer Science 2024-07-22 Xiao Li , Sheng Liu , Jinxin Zhou , Xinyu Lu , Carlos Fernandez-Granda , Zhihui Zhu , Qing Qu

Neural Collapse (NC) presents an elegant geometric structure that enables individual activations (features), class means and classifier (weights) vectors to reach \textit{optimal} inter-class separability during the terminal phase of…

Machine Learning · Computer Science 2024-08-15 Enhao Zhang , Chaohua Li , Chuanxing Geng , Songcan Chen

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

The recently discovered Neural collapse (NC) phenomenon states that the last-layer weights of Deep Neural Networks (DNN), converge to the so-called Equiangular Tight Frame (ETF) simplex, at the terminal phase of their training. This ETF…

Machine Learning · Computer Science 2024-03-01 Hafiz Tiomoko Ali , Umberto Michieli , Ji Joong Moon , Daehyun Kim , Mete Ozay

Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at…

Machine Learning · Computer Science 2025-10-27 Hancheng Min , Zhihui Zhu , René Vidal

Neural collapse is a phenomenon observed during the terminal phase of neural network training, characterized by the convergence of network activations, class means, and linear classifier weights to a simplex equiangular tight frame (ETF), a…

Machine Learning · Computer Science 2024-12-03 Emily Liu

Recent studies on Neural Collapse (NC) reveal that, under class-balanced conditions, the class feature means and classifier weights spontaneously align into a simplex equiangular tight frame (ETF). In long-tailed regimes, however, severe…

Machine Learning · Computer Science 2025-12-10 Jinping Wang , Zhiqiang Gao , Zhiwu Xie

Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on…

Machine Learning · Computer Science 2023-10-27 Vignesh Kothapalli , Tom Tirer , Joan Bruna

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

We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained with $L^2$ weight decay regularization. Our main contributions…

Machine Learning · Computer Science 2026-02-12 Emanuele Zangrando , Piero Deidda , Simone Brugiapaglia , Nicola Guglielmi , Francesco Tudisco