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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 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 studies have noted an intriguing phenomenon termed Neural Collapse, that is, when the neural networks establish the right correlation between feature spaces and the training targets, their last-layer features, together with the…

Computer Vision and Pattern Recognition · Computer Science 2025-09-22 Yining Wang , Junjie Sun , Chenyue Wang , Mi Zhang , Min Yang

Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2…

Machine Learning · Computer Science 2026-05-25 Connall Garrod , Jonathan P. Keating , Christos Thrampoulidis

Recent work has observed an intriguing ''Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the…

Machine Learning · Computer Science 2023-06-30 Yongyi Yang , Jacob Steinhardt , Wei Hu

What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…

Machine Learning · Computer Science 2025-07-08 Shikai Qiu , Lechao Xiao , Andrew Gordon Wilson , Jeffrey Pennington , Atish Agarwala

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

Machine Learning · Computer Science 2022-06-23 Chao Ma , Daniel Kunin , Lei Wu , Lexing Ying

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

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

Recent results in the literature suggest that the penultimate (second-to-last) layer representations of neural networks that are trained for classification exhibit a clustering property called neural collapse (NC). We study the implicit…

Machine Learning · Computer Science 2022-09-29 Tomer Galanti , Liane Galanti , Ido Ben-Shaul

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned…

Machine Learning · Computer Science 2023-02-27 Xuantong Liu , Jianfeng Zhang , Tianyang Hu , He Cao , Lujia Pan , Yuan Yao

The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…

Machine Learning · Computer Science 2023-04-05 Duc Anh Nguyen , Ron Levie , Julian Lienen , Gitta Kutyniok , Eyke Hüllermeier

Modern practice for training classification deepnets involves a Terminal Phase of Training (TPT), which begins at the epoch where training error first vanishes; During TPT, the training error stays effectively zero while training loss is…

Machine Learning · Computer Science 2020-09-23 Vardan Papyan , X. Y. Han , David L. Donoho

Deep learning has achieved impressive performance across various medical imaging tasks. However, its inherent bias against specific groups hinders its clinical applicability in equitable healthcare systems. A recently discovered phenomenon,…

Computer Vision and Pattern Recognition · Computer Science 2024-11-01 Kaouther Mouheb , Marawan Elbatel , Stefan Klein , Esther E. Bron

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

Supervised classification has a theoretical optimum, Neural Collapse (NC), yet neither of its two dominant paradigms reaches it in practice. Cross entropy (CE) leaves radial degrees of freedom unconstrained and converges to a degenerate…

Machine Learning · Computer Science 2026-05-22 Panagiotis Koromilas , Theodoros Giannakopoulos , Mihalis A. Nicolaou , Yannis Panagakis

This paper explores the connection between two recently identified phenomena in deep learning: plasticity loss and neural collapse. We analyze their correlation in different scenarios, revealing a significant association during the initial…

Machine Learning · Computer Science 2024-04-04 Guglielmo Bonifazi , Iason Chalas , Gian Hess , Jakub Łucki

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

When training a neural network for classification, the feature vectors of the training set are known to collapse to the vertices of a regular simplex, provided the dimension $d$ of the feature space and the number $n$ of classes satisfies…

Machine Learning · Computer Science 2026-03-24 James Alcala , Rayna Andreeva , Vladimir A. Kobzar , Dustin G. Mixon , Sanghoon Na , Shashank Sule , Yangxinyu Xie

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes…

Machine Learning · Computer Science 2022-01-05 Tomer Galanti , András György , Marcus Hutter