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Related papers: Harmful Overfitting in Sobolev Spaces

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Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

Machine Learning · Statistics 2018-10-29 Mikhail Belkin , Daniel Hsu , Partha Mitra

Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. Inspired by this empirical observation, recent work has sought to understand this phenomenon of benign overfitting or harmless…

Machine Learning · Statistics 2022-02-23 Andrew D. McRae , Santhosh Karnik , Mark A. Davenport , Vidya Muthukumar

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

A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We…

Machine Learning · Computer Science 2019-09-10 Vidya Muthukumar , Kailas Vodrahalli , Vignesh Subramanian , Anant Sahai

Understanding how overparameterized neural networks generalize despite perfect interpolation of noisy training data is a fundamental question. Mallinar et. al. 2022 noted that neural networks seem to often exhibit ``tempered overfitting'',…

Machine Learning · Computer Science 2024-03-25 Nirmit Joshi , Gal Vardi , Nathan Srebro

"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, 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

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

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…

Machine Learning · Statistics 2022-06-17 Chen Cheng , John Duchi , Rohith Kuditipudi

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…

Statistics Theory · Mathematics 2024-02-05 Jianfa Lai , Zhifan Li , Dongming Huang , Qian Lin

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

Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both…

Machine Learning · Statistics 2025-11-06 Katharine E Fisher , Matthew TC Li , Youssef Marzouk , Timo Schorlepp

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 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…

Machine Learning · Statistics 2021-06-08 Zhu Li , Zhi-Hua Zhou , Arthur Gretton

Transfer learning is a critical part of real-world machine learning deployments and has been extensively studied in experimental works with overparameterized neural networks. However, even in the simplest setting of linear regression a…

Machine Learning · Computer Science 2024-08-28 Neil Mallinar , Austin Zane , Spencer Frei , Bin Yu

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

Transformers serve as the foundational architecture for many successful large-scale models, demonstrating the ability to overfit the training data while maintaining strong generalization on unseen data, a phenomenon known as benign…

Machine Learning · Computer Science 2025-02-19 Yingying Zhang , Zhenyu Wu , Jian Li , Yong Liu

Recent empirical and theoretical studies have established the generalization capabilities of large machine learning models that are trained to (approximately or exactly) fit noisy data. In this work, we prove a surprising result that even…

Machine Learning · Computer Science 2024-01-26 Yifan Hao , Tong Zhang

The practical success of overparameterized neural networks has motivated the recent scientific study of interpolating methods, which perfectly fit their training data. Certain interpolating methods, including neural networks, can fit noisy…

Machine Learning · Computer Science 2024-07-17 Neil Mallinar , James B. Simon , Amirhesam Abedsoltan , Parthe Pandit , Mikhail Belkin , Preetum Nakkiran

We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…

Numerical Analysis · Mathematics 2021-02-11 Weilin Li
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