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We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with…

Machine Learning · Computer Science 2020-08-21 Yehuda Dar , Paul Mayer , Lorenzo Luzi , Richard G. Baraniuk

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

Numerical Analysis · Mathematics 2021-04-15 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…

Machine Learning · Computer Science 2024-01-17 Maria-Florina Balcan , Mikhail Khodak , Dravyansh Sharma , Ameet Talwalkar

The infrequent occurrence of overfit in deep neural networks is perplexing. On the one hand, theory predicts that as models get larger they should eventually become too specialized for a specific training set, with ensuing decrease in…

Machine Learning · Computer Science 2023-12-29 Uri Stern , Daphna Weinshall

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

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…

Machine Learning · Statistics 2021-09-28 Tianyang Hu , Wenjia Wang , Cong Lin , Guang Cheng

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…

Machine Learning · Computer Science 2024-02-21 Daniel Barzilai , Ohad Shamir

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Statistics Theory · Mathematics 2022-03-28 Federica Gerace , Bruno Loureiro , Florent Krzakala , Marc Mézard , Lenka Zdeborová

Batch normalization is widely used in deep learning to normalize intermediate activations. Deep networks suffer from notoriously increased training complexity, mandating careful initialization of weights, requiring lower learning rates,…

Machine Learning · Statistics 2022-10-19 Lakshmi Annamalai , Chetan Singh Thakur

While metric and similarity learning has been extensively studied from several theoretical perspectives, a rigorous understanding of its generalization performance is still lacking. In this paper, we investigate the generalization behavior…

Machine Learning · Statistics 2026-05-19 Junyu Zhou , Puyu Wang , Ding-Xuan Zhou

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds…

Machine Learning · Computer Science 2023-07-13 Francesco Camilli , Daria Tieplova , Jean Barbier

This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…

Statistics Theory · Mathematics 2021-09-21 Karthik Duraisamy

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

We propose a novel framework for exploring weak and $L_2$ generalization errors of algorithms through the lens of differential calculus on the space of probability measures. Specifically, we consider the KL-regularized empirical risk…

Machine Learning · Statistics 2023-06-21 Gholamali Aminian , Samuel N. Cohen , Łukasz Szpruch

Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this…

Machine Learning · Statistics 2019-01-08 Andrew K. Lampinen , Surya Ganguli

There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…

Data Analysis, Statistics and Probability · Physics 2021-09-22 David W. Hogg , Soledad Villar

The generalization of machine learning models has a complex dependence on the data, model and learning algorithm. We study train and test performance, as well as the generalization gap given by the mean of their difference over different…

Machine Learning · Statistics 2022-06-29 Carlos A. Gomez-Uribe

In this paper, we study the generalization properties of neural networks under input perturbations and show that minimal training data corruption by a few pixel modifications can cause drastic overfitting. We propose an evolutionary…

Machine Learning · Computer Science 2020-03-17 Subhajit Chaudhury , Toshihiko Yamasaki

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…

Machine Learning · Computer Science 2025-03-05 Ali Hasan , Haoming Yang , Yuting Ng , Vahid Tarokh

Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena,…

Machine Learning · Statistics 2020-12-01 Vatsal Shah , Soumya Basu , Anastasios Kyrillidis , Sujay Sanghavi