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Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and…

Machine Learning · Computer Science 2019-05-28 Sanjeev Arora , Simon S. Du , Wei Hu , Zhiyuan Li , Ruosong Wang

This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning where data from diverse distributions are available. Min-norm interpolators emerge naturally as implicit regularized limits of…

Statistics Theory · Mathematics 2024-06-21 Yanke Song , Sohom Bhattacharya , Pragya Sur

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

Statistics Theory · Mathematics 2011-11-10 Xiaotong Shen , Lifeng Wang

Overparameterization is known to permit strong generalization performance in neural networks. In this work, we provide an initial theoretical analysis of its effect on catastrophic forgetting in a continual learning setup. We show…

Machine Learning · Computer Science 2022-07-15 Daniel Goldfarb , Paul Hand

This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…

Machine Learning · Statistics 2024-05-24 Samuel Lanthaler , Nicholas H. Nelsen

The practice of deep learning has shown that neural networks generalize remarkably well even with an extreme number of learned parameters. This appears to contradict traditional statistical wisdom, in which a trade-off between model…

Machine Learning · Computer Science 2023-02-21 Yifei Wang , Yixuan Hua , Emmanuel Candés , Mert Pilanci

Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made…

Machine Learning · Computer Science 2026-04-09 Hao Yu

We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…

Machine Learning · Computer Science 2022-07-12 Sharan Vaswani , Reza Babanezhad , Jose Gallego-Posada , Aaron Mishkin , Simon Lacoste-Julien , Nicolas Le Roux

Overparameterization, the condition where models have more parameters than necessary to fit their training loss, is a crucial factor for the success of deep learning. However, the characteristics of the features learned by overparameterized…

Machine Learning · Computer Science 2024-07-02 Ahmet Cagri Duzgun , Samy Jelassi , Yuanzhi Li

Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal…

Computation and Language · Computer Science 2024-06-07 Nur Lan , Emmanuel Chemla , Roni Katzir

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

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…

Machine Learning · Computer Science 2019-04-09 Daniel Jakubovitz , Raja Giryes , Miguel R. D. Rodrigues

We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by…

Machine Learning · Computer Science 2021-10-15 Vidya Muthukumar , Adhyyan Narang , Vignesh Subramanian , Mikhail Belkin , Daniel Hsu , Anant Sahai

Despite the superior empirical success of deep meta-learning, theoretical understanding of overparameterized meta-learning is still limited. This paper studies the generalization of a widely used meta-learning approach, Model-Agnostic…

Machine Learning · Computer Science 2022-06-22 Yu Huang , Yingbin Liang , Longbo Huang

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

We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples exceeds a certain threshold. Understanding the high…

Machine Learning · Computer Science 2025-12-09 Naoki Yoshida , Isao Ishikawa , Masaaki Imaizumi

A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schemes as well as general…

Machine Learning · Computer Science 2020-02-27 Weinan E , Chao Ma , Lei Wu

The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps, and provides a good approximation to the Newton method for large-scale optimization problems. GGN has been found particularly…

Machine Learning · Computer Science 2024-04-24 Adeyemi D. Adeoye , Philipp Christian Petersen , Alberto Bemporad

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding…

Quantum Physics · Physics 2024-03-14 Elies Gil-Fuster , Jens Eisert , Carlos Bravo-Prieto