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

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…

A recent study by De et al. (2022) has reported that large-scale representation learning through pre-training on a public dataset significantly enhances differentially private (DP) learning in downstream tasks, despite the high…

Recent years have witnessed the huge success of deep neural networks (DNNs) in various tasks of computer vision and text processing. Interestingly, these DNNs with massive number of parameters share similar structural properties on their…

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase…

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,…

This work bridges two important concepts: the Neural Tangent Kernel (NTK), which captures the evolution of deep neural networks (DNNs) during training, and the Neural Collapse (NC) phenomenon, which refers to the emergence of symmetry and…

Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs). Though the phenomenon has been measured in a variety of settings, its emergence is…

We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC). Previous works have been restricted to the multi-class classification setting and discovered a prevalent NC phenomenon…

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…

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…

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…

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…

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…

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…

The recent work of Papyan, Han, & Donoho (2020) presented an intriguing "Neural Collapse" phenomenon, showing a structural property of interpolating classifiers in the late stage of training. This opened a rich area of exploration studying…

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…

We study regularized deep neural networks (DNNs) and introduce a convex analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weights for a norm regularized DNN training problem…

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…

Interpretability of Deep Neural Networks has become a major area of exploration. Although these networks have achieved state of the art accuracy in many tasks, it is extremely difficult to interpret and explain their decisions. In this work…

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…