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Textbook wisdom advocates for smooth function fits and implies that interpolation of noisy data should lead to poor generalization. A related heuristic is that fitting parameters should be fewer than measurements (Occam's Razor).…

Machine Learning · Computer Science 2021-04-02 Partha P Mitra

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…

Statistics Theory · Mathematics 2021-03-17 Peter L. Bartlett , Andrea Montanari , Alexander Rakhlin

The widespread success of deep neural networks has revealed a surprise in classical machine learning: very complex models often generalize well while simultaneously overfitting training data. This phenomenon of benign overfitting has been…

Quantum Physics · Physics 2023-12-20 Evan Peters , Maria Schuld

Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they…

Machine Learning · Statistics 2022-06-10 Andrea Montanari , Yiqiao Zhong

It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the…

Machine Learning · Computer Science 2019-09-27 Rong Ge , Runzhe Wang , Haoyu Zhao

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…

Machine Learning · Computer Science 2025-06-10 Ruichen Xu , Kexin Chen

Overparameterized Neural Networks (NN) display state-of-the-art performance. However, there is a growing need for smaller, energy-efficient, neural networks tobe able to use machine learning applications on devices with limited…

Machine Learning · Statistics 2021-05-21 Soufiane Hayou , Jean-Francois Ton , Arnaud Doucet , Yee Whye Teh

A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the…

Machine Learning · Statistics 2021-07-26 Nicole Mücke , Ingo Steinwart

Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the…

Machine Learning · Computer Science 2019-02-14 Samet Oymak , Mahdi Soltanolkotabi

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…

Machine Learning · Computer Science 2024-10-04 Kedar Karhadkar , Erin George , Michael Murray , Guido Montúfar , Deanna Needell

Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…

Machine Learning · Statistics 2021-09-16 Ke Wang , Christos Thrampoulidis

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…

Machine Learning · Computer Science 2023-10-04 Xuran Meng , Difan Zou , Yuan Cao

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Methodology · Statistics 2019-06-25 Jean Feng , Noah Simon

Modern neural networks are typically trained in an over-parameterized regime where the parameters of the model far exceed the size of the training data. Such neural networks in principle have the capacity to (over)fit any set of labels…

Machine Learning · Computer Science 2019-07-05 Mingchen Li , Mahdi Soltanolkotabi , Samet Oymak

In some studies \citep[e.g.,][]{zhang2016understanding} of deep learning, it is observed that over-parametrized deep neural networks achieve a small testing error even when the training error is almost zero. Despite numerous works towards…

Machine Learning · Statistics 2022-02-25 Yue Xing , Qifan Song , Guang Cheng

In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…

Machine Learning · Statistics 2018-06-22 Yamini Bansal , Madhu Advani , David D Cox , Andrew M Saxe

Neural network models and deep models are one of the leading and state of the art models in machine learning. Most successful deep neural models are the ones with many layers which highly increases their number of parameters. Training such…

Machine Learning · Computer Science 2018-07-17 Soufiane Belharbi

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…

Machine Learning · Computer Science 2023-11-10 Erin George , Michael Murray , William Swartworth , Deanna Needell

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

Recent works show that overparameterized networks contain small subnetworks that exhibit comparable accuracy to the full model when trained in isolation. These results highlight the potential to reduce training costs of deep neural networks…

Machine Learning · Computer Science 2020-06-25 Roger Waleffe , Theodoros Rekatsinas