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Related papers: Implicit Regularization of Stochastic Gradient Des…

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We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance…

Machine Learning · Computer Science 2019-05-29 Preetum Nakkiran , Gal Kaplun , Dimitris Kalimeris , Tristan Yang , Benjamin L. Edelman , Fred Zhang , Boaz Barak

Works on implicit regularization have studied gradient trajectories during the optimization process to explain why deep networks favor certain kinds of solutions over others. In deep linear networks, it has been shown that gradient descent…

Machine Learning · Computer Science 2023-06-02 Dan Zhao

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of…

Machine Learning · Computer Science 2023-06-08 Maksym Andriushchenko , Aditya Varre , Loucas Pillaud-Vivien , Nicolas Flammarion

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

Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…

Machine Learning · Computer Science 2019-10-30 Mingwei Wei , David J Schwab

We investigate the ability of deep neural networks to identify the support of the target function. Our findings reveal that mini-batch SGD effectively learns the support in the first layer of the network by shrinking to zero the weights…

Machine Learning · Computer Science 2024-06-18 Pierfrancesco Beneventano , Andrea Pinto , Tomaso Poggio

Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…

Machine Learning · Computer Science 2025-12-10 Jianhao Ma , Geyu Liang , Salar Fattahi

Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes…

Machine Learning · Computer Science 2020-07-03 Erhan Bilal

We investigate the inherent bias of Stochastic Gradient Descent (SGD) toward learning low-rank weight matrices during the training of deep neural networks. Our results demonstrate that training with mini-batch SGD and weight decay induces a…

Machine Learning · Computer Science 2024-10-22 Tomer Galanti , Zachary S. Siegel , Aparna Gupte , Tomaso Poggio

A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show…

Machine Learning · Computer Science 2021-12-14 Yatin Dandi , Luis Barba , Martin Jaggi

The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with respect to parameters and the landscape of the model function…

Machine Learning · Computer Science 2021-11-30 Chao Ma , Lexing Ying

Training Deep Neural Networks (DNNs) with small batches using Stochastic Gradient Descent (SGD) yields superior test performance compared to larger batches. The specific noise structure inherent to SGD is known to be responsible for this…

Machine Learning · Statistics 2024-02-14 Tom Sander , Maxime Sylvestre , Alain Durmus

The capacity of deep learning models is often large enough to both learn the underlying statistical signal and overfit to noise in the training set. This noise memorization can be harmful especially for data with a low signal-to-noise ratio…

Machine Learning · Computer Science 2025-10-21 Wei Huang , Andi Han , Yujin Song , Yilan Chen , Denny Wu , Difan Zou , Taiji Suzuki

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…

Machine Learning · Computer Science 2023-01-10 Matteo Cacciola , Antonio Frangioni , Masoud Asgharian , Alireza Ghaffari , Vahid Partovi Nia

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…

Machine Learning · Computer Science 2026-03-17 Jonathan Wenger , Beau Coker , Juraj Marusic , John P. Cunningham

Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…

Machine Learning · Computer Science 2023-05-30 Mingze Wang , Chao Ma

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

Machine Learning · Computer Science 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the…

Machine Learning · Computer Science 2023-04-04 Haoyi Xiong , Xuhong Li , Boyang Yu , Zhanxing Zhu , Dongrui Wu , Dejing Dou

Regularization plays a major role in modern deep learning. From classic techniques such as L1,L2 penalties to other noise-based methods such as Dropout, regularization often yields better generalization properties by avoiding overfitting.…

Machine Learning · Statistics 2021-06-08 Soufiane Hayou , Fadhel Ayed

Dropout is a widely-used regularization technique, often required to obtain state-of-the-art for a number of architectures. This work demonstrates that dropout introduces two distinct but entangled regularization effects: an explicit effect…

Machine Learning · Computer Science 2020-10-16 Colin Wei , Sham Kakade , Tengyu Ma