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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

Most Neural Networks (NNs) for classification are trained using Cross-Entropy as a loss function. This approach requires the model to have an explicit classification layer. However, there exist alternative approaches, such as Contrastive…

Machine Learning · Computer Science 2026-04-27 Leonardo Arrighi , Julia Eva Belloni , Aurélie Gallet , Ivan Gentile , Matteo Lippi , Marco Zullich

Contrastive learning applied to self-supervised representation learning has seen a resurgence in recent years, leading to state of the art performance in the unsupervised training of deep image models. Modern batch contrastive approaches…

Machine Learning · Computer Science 2021-03-12 Prannay Khosla , Piotr Teterwak , Chen Wang , Aaron Sarna , Yonglong Tian , Phillip Isola , Aaron Maschinot , Ce Liu , Dilip Krishnan

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

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

Learning robust representations to discriminate cell phenotypes based on microscopy images is important for drug discovery. Drug development efforts typically analyse thousands of cell images to screen for potential treatments. Early works…

Computer Vision and Pattern Recognition · Computer Science 2021-12-28 Alexis Perakis , Ali Gorji , Samriddhi Jain , Krishna Chaitanya , Simone Rizza , Ender Konukoglu

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

Neural Collapse is a phenomenon that helps identify sparse and low rank structures in deep classifiers. Recent work has extended the definition of neural collapse to regression problems, albeit only measuring the phenomenon at the last…

Machine Learning · Computer Science 2026-03-26 Akshay Rangamani , Altay Unal

Recently, self-supervised learning has attracted attention due to its remarkable ability to acquire meaningful representations for classification tasks without using semantic labels. This paper introduces a self-supervised learning…

Computer Vision and Pattern Recognition · Computer Science 2022-02-09 Hyungtae Lee , Heesung Kwon

Convolutional networks have marked their place over the last few years as the best performing model for various visual tasks. They are, however, most suited for supervised learning from large amounts of labeled data. Previous attempts have…

Machine Learning · Computer Science 2018-12-05 Elad Hoffer , Itay Hubara , Nir Ailon

The recently discovered Neural Collapse (NC) phenomenon occurs pervasively in today's deep net training paradigm of driving cross-entropy (CE) loss towards zero. During NC, last-layer features collapse to their class-means, both classifiers…

Machine Learning · Computer Science 2022-05-11 X. Y. Han , Vardan Papyan , David L. Donoho

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

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

A lot of recent advances in unsupervised feature learning are based on designing features which are invariant under semantic data augmentations. A common way to do this is contrastive learning, which uses positive and negative samples. Some…

Machine Learning · Computer Science 2022-03-30 Ashwini Pokle , Jinjin Tian , Yuchen Li , Andrej Risteski

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

Convolutional networks have marked their place over the last few years as the best performing model for various visual tasks. They are, however, most suited for supervised learning from large amounts of labeled data. Previous attempts have…

Machine Learning · Statistics 2016-11-23 Elad Hoffer , Itay Hubara , Nir Ailon

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

While contrastive learning is proven to be an effective training strategy in computer vision, Natural Language Processing (NLP) is only recently adopting it as a self-supervised alternative to Masked Language Modeling (MLM) for improving…

Computation and Language · Computer Science 2021-09-16 Hooman Sedghamiz , Shivam Raval , Enrico Santus , Tuka Alhanai , Mohammad Ghassemi

Supervised contrastive learning (SupCL) has emerged as a prominent approach in representation learning, leveraging both supervised and self-supervised losses. However, achieving an optimal balance between these losses is challenging;…

Machine Learning · Computer Science 2025-03-12 Chungpa Lee , Jeongheon Oh , Kibok Lee , Jy-yong Sohn

Despite its empirical success, the theoretical foundations of self-supervised contrastive learning (CL) are not yet fully established. In this work, we address this gap by showing that standard CL objectives implicitly approximate a…

Machine Learning · Computer Science 2025-11-12 Achleshwar Luthra , Tianbao Yang , Tomer Galanti