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Related papers: Deep Double Descent via Smooth Interpolation

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Combining empirical risk minimization with capacity control is a classical strategy in machine learning when trying to control the generalization gap and avoid overfitting, as the model class capacity gets larger. Yet, in modern deep…

Machine Learning · Computer Science 2024-03-18 Marc Lafon , Alexandre Thomas

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Methodology · Statistics 2021-10-25 Anindya Bhadra , Jyotishka Datta , Nick Polson , Vadim Sokolov , Jianeng Xu

Deep double descent is one of the key phenomena underlying the generalization capability of deep learning models. In this study, epoch-wise double descent, which is delayed generalization following overfitting, was empirically investigated…

Machine Learning · Computer Science 2026-01-14 Tomoki Kubo , Ryuken Uda , Yusuke Iida

We study nonparametric regression using an over-parameterized two-layer neural networks trained with algorithmic guarantees in this paper. We consider the setting where the training features are drawn uniformly from the unit sphere in…

Machine Learning · Statistics 2025-10-07 Yingzhen Yang , Ping Li

Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line…

Machine Learning · Computer Science 2024-09-18 Hung-Hsu Chou , Holger Rauhut , Rachel Ward

Optimization plays a key role in the training of deep neural networks. Deciding when to stop training can have a substantial impact on the performance of the network during inference. Under certain conditions, the generalization error can…

Machine Learning · Computer Science 2021-09-20 Florian Dubost , Erin Hong , Max Pike , Siddharth Sharma , Siyi Tang , Nandita Bhaskhar , Christopher Lee-Messer , Daniel Rubin

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

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

In supervised classification tasks, models are trained to predict a label for each data point. In real-world datasets, these labels are often noisy due to annotation errors. While the impact of label noise on the performance of deep…

Machine Learning · Computer Science 2025-10-09 Ali Hussaini Umar , Franky Kevin Nando Tezoh , Jean Barbier , Santiago Acevedo , Alessandro Laio

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

Machine Learning · Computer Science 2025-07-24 Matteo Gamba , Hossein Azizpour , Mårten Björkman

As overparameterized models become increasingly prevalent, training loss alone offers limited insight into generalization performance. While smoothness has been linked to improved generalization across various settings, directly enforcing…

Machine Learning · Computer Science 2025-09-30 Yifan Hao , Yanxin Lu , Hanning Zhang , Xinwei Shen , Tong Zhang

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

There has been a long history of works showing that neural networks have hard time extrapolating beyond the training set. A recent study by Balestriero et al. (2021) challenges this view: defining interpolation as the state of belonging to…

Machine Learning · Computer Science 2022-07-19 Laurent Bonnasse-Gahot

When several models have similar training scores, classical model selection heuristics follow Occam's razor and advise choosing the ones with least capacity. Yet, modern practice with large neural networks has often led to situations where…

Machine Learning · Computer Science 2022-11-29 Luis Sa-Couto , Jose Miguel Ramos , Andreas Wichert

Pruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters.…

Machine Learning · Computer Science 2023-09-27 Viplove Arora , Daniele Irto , Sebastian Goldt , Guido Sanguinetti

Despite being highly over-parametrized, and having the ability to fully interpolate the training data, deep networks are known to generalize well to unseen data. It is now understood that part of the reason for this is that the training…

Machine Learning · Computer Science 2023-02-21 Danil Akhtiamov , Babak Hassibi

Deep neural networks are known to exhibit a `double descent' behavior as the number of parameters increases. Recently, it has also been shown that an `epochwise double descent' effect exists in which the generalization error initially…

Machine Learning · Computer Science 2021-08-30 Cory Stephenson , Tyler Lee

The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized…

Machine Learning · Statistics 2021-09-07 Yehuda Dar , Vidya Muthukumar , Richard G. Baraniuk

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