English
Related papers

Related papers: Neural Collapse in Deep Linear Networks: From Bala…

200 papers

Mixup is a data augmentation strategy that employs convex combinations of training instances and their respective labels to augment the robustness and calibration of deep neural networks. Despite its widespread adoption, the nuanced…

Machine Learning · Computer Science 2024-02-12 Quinn Fisher , Haoming Meng , Vardan Papyan

Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical…

Machine Learning · Computer Science 2024-12-05 Haixiang Sun , Ye Shi

Today, deep neural networks are widely used since they can handle a variety of complex tasks. Their generality makes them very powerful tools in modern technology. However, deep neural networks are often overparameterized. The usage of…

Machine Learning · Computer Science 2024-12-20 Zhu Liao , Nour Hezbri , Victor Quétu , Van-Tam Nguyen , Enzo Tartaglione

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…

Machine Learning · Computer Science 2022-04-26 Wenlong Ji , Yiping Lu , Yiliang Zhang , Zhun Deng , Weijie J. Su

Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically…

Machine Learning · Statistics 2021-11-03 Lu Lu , Yanhui Su , George Em Karniadakis

Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built…

Disordered Systems and Neural Networks · Physics 2025-06-30 Cheng Shi , Liming Pan , Ivan Dokmanić

Deep neural networks have recently achieved notable progress in 3D point cloud recognition, yet their vulnerability to adversarial perturbations poses critical security challenges in practical deployments. Conventional defense mechanisms…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Yuanmin Huang , Wenxuan Li , Mi Zhang , Xiaohan Zhang , Xiaoyu You , Min Yang

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

Predictions made by deep neural networks were shown to be highly sensitive to small changes made in the input space where such maliciously crafted data points containing small perturbations are being referred to as adversarial examples. On…

Machine Learning · Computer Science 2022-06-01 Utku Ozbulak , Manvel Gasparyan , Shodhan Rao , Wesley De Neve , Arnout Van Messem

We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has…

Machine Learning · Computer Science 2018-06-07 Quynh Nguyen , Matthias Hein

Neural collapse describes the geometry of activation in the final layer of a deep neural network when it is trained beyond performance plateaus. Open questions include whether neural collapse leads to better generalization and, if so, why…

Machine Learning · Computer Science 2024-06-28 Siwei Wang , Stephanie E Palmer

Deep learning utilizing deep neural networks (DNNs) has achieved a lot of success recently in many important areas such as computer vision, natural language processing, and recommendation systems. The lack of convexity for DNNs has been…

Machine Learning · Computer Science 2022-06-14 Jingcheng Zhou , Wei Wei , Xing Li , Bowen Pang , Zhiming Zheng

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Machine Learning · Computer Science 2016-03-01 Yixuan Li , Jason Yosinski , Jeff Clune , Hod Lipson , John Hopcroft

Low dimensional structures appear ubiquitously in the eigenspectra of deep learning matrices in classification networks trained in the overparameterized regime. While theoretical advances have aimed to explain this phenomenology, they…

Machine Learning · Computer Science 2026-05-28 Connall Garrod , Jonathan P. Keating

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

Computer Vision and Pattern Recognition · Computer Science 2015-08-04 Axel Angel

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

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

Machine Learning · Computer Science 2025-10-03 Jinshu Huang , Haibin Su , Xue-Cheng Tai , Chunlin Wu

Loss reweighting is a widely used strategy for long-tailed classification, but existing reweighting strategies often rely on heuristics and rarely define a well-specified target. Inspired by Neural Collapse (NC), the ideal simplex…

Machine Learning · Computer Science 2026-05-12 Jinping Wang , Zixin Tong , Zhiwu Xie , Zhiqiang Gao

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI. We use principal component analysis (PCA) to study the performance of a k-nearest neighbors classifier…

Machine Learning · Computer Science 2023-09-28 Amit Harlev , Andrew Engel , Panos Stinis , Tony Chiang

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…

Machine Learning · Computer Science 2025-09-23 Md Yousuf Harun , Jhair Gallardo , Christopher Kanan