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This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…

Machine Learning · Computer Science 2023-10-17 Jingwen Fu , Nanning Zheng

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

Machine Learning · Statistics 2025-10-29 Hannes Matt , Dominik Stöger

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article…

Statistics Theory · Mathematics 2016-05-31 Lee H. Dicker , Dean P. Foster , Daniel Hsu

This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…

Machine Learning · Statistics 2022-06-06 Gaspard Beugnot , Julien Mairal , Alessandro Rudi

Recent evidence has shown the existence of a so-called double-descent and even triple-descent behavior for the generalization error of deep-learning models. This important phenomenon commonly appears in implemented neural network…

Machine Learning · Computer Science 2021-10-25 Antoine Bodin , Nicolas Macris

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

Machine Learning · Statistics 2012-11-07 Matthew J. Urry , Peter Sollich

Generalisation refers to the ability of a machine learning (ML) model to successfully apply patterns learned from training data to new, unseen data. Quantum devices in the current Noisy Intermediate-Scale Quantum (NISQ) era are inherently…

Quantum Physics · Physics 2026-04-02 Saarisha Govender , Ilya Sinayskiy

Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…

Machine Learning · Computer Science 2022-10-25 Oyebade K. Oyedotun , Konstantinos Papadopoulos , Djamila Aouada

This paper considers a canonical problem in kernel regression: how good are the model performances when it is trained by the popular online first-order algorithms, compared to the offline ones, such as ridge and ridgeless regression? In…

Machine Learning · Statistics 2025-05-29 Haihan Zhang , Weicheng Lin , Yuanshi Liu , Cong Fang

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…

Machine Learning · Statistics 2025-10-20 Dechen Zhang , Zhenmei Shi , Yi Zhang , Yingyu Liang , Difan Zou

In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…

Statistics Theory · Mathematics 2020-07-27 Tengyuan Liang , Alexander Rakhlin

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

Machine Learning · Computer Science 2022-06-22 Sattar Vakili , Jonathan Scarlett , Da-shan Shiu , Alberto Bernacchia

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…

Machine Learning · Statistics 2013-10-01 Matthew Urry , Peter Sollich

We derive a differential equation that governs the evolution of the generalization gap when a deep network is trained by gradient descent. This differential equation is controlled by two quantities, a contraction factor that brings together…

Machine Learning · Computer Science 2025-10-14 Rubing Yang , Pratik Chaudhari

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

In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…

Machine Learning · Computer Science 2025-02-14 Shihong Ding , Haihan Zhang , Hanzhen Zhao , Cong Fang

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

Machine Learning · Computer Science 2021-05-06 Devansh Bisla , Apoorva Nandini Saridena , Anna Choromanska

We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…

Machine Learning · Statistics 2025-05-22 Quanjun Lang , Jianfeng Lu

This article is an overview of supervised machine learning problems for regression and classification. Topics include: kernel methods, training by stochastic gradient descent, deep learning architecture, losses for classification,…

Machine Learning · Computer Science 2019-10-04 Adam M Oberman

The field of Deep Learning is rich with empirical evidence of human-like performance on a variety of prediction tasks. However, despite these successes, the recent Predicting Generalization in Deep Learning (PGDL) NeurIPS 2020 competition…

Machine Learning · Computer Science 2021-10-28 Yair Schiff , Brian Quanz , Payel Das , Pin-Yu Chen