相关论文: Deep Neural Collapse Is Provably Optimal for the D…

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…

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…

Deep neural networks (DNNs) at convergence consistently represent the training data in the last layer via a highly symmetric geometric structure referred to as neural collapse. This empirical evidence has spurred a line of theoretical…

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…

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…

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural…

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,…

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…

Neural collapse (NC) is a phenomenon that emerges at the terminal phase of the training (TPT) of deep neural networks (DNNs). The features of the data in the same class collapse to their respective sample means and the sample means exhibit…

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…

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…

Neural Collapse is a phenomenon where the last-layer representations of a well-trained neural network converge to a highly structured geometry. In this paper, we focus on its first (and most basic) property, known as NC1: the within-class…

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…

Recently it has been observed that neural networks exhibit Neural Collapse (NC) during the final stage of training for the classification problem. We empirically show that multivariate regression, as employed in imitation learning and other…

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…

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…

Neural Collapse (NC) is a recently observed phenomenon in neural networks that characterises the solution space of the final classifier layer when trained until zero training loss. Specifically, NC suggests that the final classifier layer…

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…

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…

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…