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In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention.…

Machine Learning · Computer Science 2023-05-29 Mo Zhou , Rong Ge

Recent advances in machine learning have inspired a surge of research into reconstructing specific quantities of interest from measurements that comply with certain physical laws. These efforts focus on inverse problems that are governed by…

Machine Learning · Statistics 2025-04-23 Honam Wong , Wendao Wu , Fanghui Liu , Yiping Lu

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,…

Machine Learning · Computer Science 2020-07-09 Amartya Sanyal , Puneet K Dokania , Varun Kanade , Philip H. S. Torr

Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…

Machine Learning · Statistics 2023-05-15 Liang Ding , Tianyang Hu , Jiahang Jiang , Donghao Li , Wenjia Wang , Yuan Yao

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…

Machine Learning · Computer Science 2026-02-25 Ichiro Hashimoto , Stanislav Volgushev , Piotr Zwiernik

In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex $\eta$-norm loss function…

Statistics Theory · Mathematics 2025-09-30 Yuqing Liu

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

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…

Machine Learning · Statistics 2018-06-18 Mikhail Belkin , Siyuan Ma , Soumik Mandal

We study the overfitting behavior of fully connected deep Neural Networks (NNs) with binary weights fitted to perfectly classify a noisy training set. We consider interpolation using both the smallest NN (having the minimal number of…

Machine Learning · Computer Science 2024-10-28 Itamar Harel , William M. Hoza , Gal Vardi , Itay Evron , Nathan Srebro , Daniel Soudry

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…

Machine Learning · Statistics 2026-02-11 Chen Cheng , Rina Foygel Barber

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

Adversarial training and data augmentation with noise are widely adopted techniques to enhance the performance of neural networks. This paper investigates adversarial training and data augmentation with noise in the context of regularized…

Machine Learning · Statistics 2023-04-20 Teng Zhang , Kang Li

``Benign overfitting'', the ability of certain algorithms to interpolate noisy training data and yet perform well out-of-sample, has been a topic of considerable recent interest. We show, using a fixed design setup, that an important class…

Machine Learning · Computer Science 2023-04-14 Daniel Beaglehole , Mikhail Belkin , Parthe Pandit

We study why overparameterization -- increasing model size well beyond the point of zero training error -- can hurt test error on minority groups despite improving average test error when there are spurious correlations in the data. Through…

Machine Learning · Computer Science 2020-08-28 Shiori Sagawa , Aditi Raghunathan , Pang Wei Koh , Percy Liang

In this paper, we propose to use the general $L^2$-based Sobolev norms, i.e., $H^s$ norms where $s\in \mathbb{R}$, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As…

Numerical Analysis · Mathematics 2022-03-01 Bowen Zhu , Jingwei Hu , Yifei Lou , Yunan Yang

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…

Machine Learning · Computer Science 2025-05-20 Junhyung Park , Patrick Bloebaum , Shiva Prasad Kasiviswanathan

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…

Machine Learning · Computer Science 2024-10-17 Kota Okudo , Kei Kobayashi

Training neural network classifiers on datasets with label noise poses a risk of overfitting them to the noisy labels. To address this issue, researchers have explored alternative loss functions that aim to be more robust. The…

Machine Learning · Computer Science 2024-08-23 William Toner , Amos Storkey

Machine learning models that are overfitted/overtrained are more vulnerable to knowledge leakage, which poses a risk to privacy. Suppose we download or receive a model from a third-party collaborator without knowing its training accuracy.…

Machine Learning · Computer Science 2023-06-01 Hossein Rezaei , Mohammad Sabokrou

Learned classifiers should often possess certain invariance properties meant to encourage fairness, robustness, or out-of-distribution generalization. However, multiple recent works empirically demonstrate that common invariance-inducing…

Machine Learning · Computer Science 2024-07-04 Yoav Wald , Gal Yona , Uri Shalit , Yair Carmon