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Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this…

Machine Learning · Computer Science 2022-01-04 Yuan Cao , Quanquan Gu , Mikhail Belkin

The phenomenon of benign overfitting, where a predictor perfectly fits noisy training data while attaining near-optimal expected loss, has received much attention in recent years, but still remains not fully understood beyond well-specified…

Machine Learning · Computer Science 2023-04-18 Ohad Shamir

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

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…

Machine Learning · Computer Science 2025-07-04 Spencer Frei , Niladri S. Chatterji , Peter L. Bartlett

"Benign overfitting", where classifiers memorize noisy training data yet still achieve a good generalization performance, has drawn great attention in the machine learning community. To explain this surprising phenomenon, a series of works…

Machine Learning · Computer Science 2022-01-03 Jinghui Chen , Yuan Cao , Quanquan Gu

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider…

Machine Learning · Statistics 2022-06-08 Peter L. Bartlett , Philip M. Long , Gábor Lugosi , Alexander Tsigler

Modern machine learning models with a large number of parameters often generalize well despite perfectly interpolating noisy training data - a phenomenon known as benign overfitting. A foundational explanation for this in linear…

Machine Learning · Statistics 2025-11-18 Yuta Kondo

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…

Machine Learning · Computer Science 2023-04-04 Kaiyue Wen , Jiaye Teng , Jingzhao Zhang

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

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as \textit{benign overfitting}. Recently, a few studies have attempted to…

Machine Learning · Computer Science 2023-11-07 Yiwen Kou , Zixiang Chen , Yuanzhou Chen , Quanquan Gu

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…

Machine Learning · Computer Science 2022-06-15 Yuan Cao , Zixiang Chen , Mikhail Belkin , Quanquan Gu

Benign overfitting refers to the phenomenon where an over-parameterized model fits the training data perfectly, including noise in the data, but still generalizes well to the unseen test data. While prior work provides some theoretical…

Machine Learning · Computer Science 2024-12-20 Shange Tang , Jiayun Wu , Jianqing Fan , Chi Jin

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…

Machine Learning · Statistics 2022-09-13 Niladri S. Chatterji , Philip M. Long , Peter L. Bartlett

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…

Statistics Theory · Mathematics 2023-03-23 Andrea Montanari , Feng Ruan , Youngtak Sohn , Jun Yan

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

The phenomenon of benign overfitting, where a trained neural network perfectly fits noisy training data but still achieves near-optimal test performance, has been extensively studied in recent years for linear models and…

Machine Learning · Computer Science 2025-02-13 Roey Magen , Shuning Shang , Zhiwei Xu , Spencer Frei , Wei Hu , Gal Vardi

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

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

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that…

Machine Learning · Computer Science 2022-11-10 Lisha Chen , Songtao Lu , Tianyi Chen

The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…

Machine Learning · Statistics 2023-07-13 Ke Wang , Vidya Muthukumar , Christos Thrampoulidis
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