Related papers: Benign Overfitting for Two-layer ReLU Convolutiona…
Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance. This phenomenon is referred to as "benign overfitting". Recently, there emerges a line…
Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss; yet surprisingly, they possess near-optimal prediction performance, contradicting classical learning theory. We…
Modern deep learning models are usually highly over-parameterized so that they can overfit the training data. Surprisingly, such overfitting neural networks can usually still achieve high prediction accuracy. To study this "benign…
The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer leaky ReLU networks trained with the hinge loss on a binary…
Benign overfitting, the phenomenon where interpolating models generalize well in the presence of noisy data, was first observed in neural network models trained with gradient descent. To better understand this empirical observation, we…
We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the…
Benign overfitting is a phenomenon in machine learning where a model perfectly fits (interpolates) the training data, including noisy examples, yet still generalizes well to unseen data. Understanding this phenomenon has attracted…
Benign overfitting refers to how over-parameterized neural networks can fit training data perfectly and generalize well to unseen data. While this has been widely investigated theoretically, existing works are limited to two-layer networks…
We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification. In particular, we consider linearly separable data for which a relatively small proportion of…
Overparameterized neural networks (NNs) are observed to generalize well even when trained to perfectly fit noisy data. This phenomenon motivated a large body of work on "benign overfitting", where interpolating predictors achieve…
In this paper, we provide sufficient conditions of benign overfitting of fixed width leaky ReLU two-layer neural network classifiers trained on mixture data via gradient descent. Our results are derived by establishing directional…
Studies on benign overfitting provide insights for the success of overparameterized deep learning models. In this work, we examine whether overfitting is truly benign in real-world classification tasks. We start with the observation that a…
Recent theoretical studies (Kou et al., 2023; Cao et al., 2022) have revealed a sharp phase transition from benign to harmful overfitting when the noise-to-feature ratio exceeds a threshold-a situation common in long-tailed data…
The practical success of deep learning has led to the discovery of several surprising phenomena. One of these phenomena, that has spurred intense theoretical research, is ``benign overfitting'': deep neural networks seem to generalize well…
This paper investigates the phenomenon of benign overfitting in binary classification problems with heavy-tailed input distributions, extending the analysis of maximum margin classifiers to $\alpha$ sub-exponential distributions ($\alpha…
Modern machine learning often operates in the regime where the number of parameters is much higher than the number of data points, with zero training loss and yet good generalization, thereby contradicting the classical bias-variance…
The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…
Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can…
The success of over-parameterized neural networks trained to near-zero training error has caused great interest in the phenomenon of benign overfitting, where estimators are statistically consistent even though they interpolate noisy…
We investigate two causes for adversarial vulnerability in deep neural networks: bad data and (poorly) trained models. When trained with SGD, deep neural networks essentially achieve zero training error, even in the presence of label noise,…