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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 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

In classical Machine Learning, "overfitting" is the phenomenon occurring when a given model learns the training data excessively well, and it thus performs poorly on unseen data. A commonly employed technique in Machine Learning is the so…

Quantum Physics · Physics 2024-05-10 Francesco Scala , Andrea Ceschini , Massimo Panella , Dario Gerace

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

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

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

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

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

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

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

"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

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

Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…

Quantum Physics · Physics 2025-03-24 Joachim Tomasi , Sandrine Anthoine , Hachem Kadri

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

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

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

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…

Machine Learning · Statistics 2021-02-08 Zhu Li , Weijie Su , Dino Sejdinovic

The rising performance of deep neural networks is often empirically attributed to an increase in the available computational power, which allows complex models to be trained upon large amounts of annotated data. However, increased model…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Gauthier Tallec , Edouard Yvinec , Arnaud Dapogny , Kevin Bailly

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

Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success…

Machine Learning · Computer Science 2025-07-11 Andrew Gordon Wilson
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