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Pruning neural network parameters is often viewed as a means to compress models, but pruning has also been motivated by the desire to prevent overfitting. This motivation is particularly relevant given the perhaps surprising observation…

Machine Learning · Computer Science 2020-10-26 Brian R. Bartoldson , Ari S. Morcos , Adrian Barbu , Gordon Erlebacher

Theoretical analysis of the error landscape of deep neural networks has garnered significant interest in recent years. In this work, we theoretically study the importance of noise in the trajectories of gradient descent towards optimal…

Machine Learning · Computer Science 2018-07-24 Adepu Ravi Sankar , Vishwak Srinivasan , Vineeth N Balasubramanian

Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using…

Machine Learning · Computer Science 2026-05-19 Linyu Liu , Pinyan Lu

The stochastic gradient descent (SGD) method is most widely used for deep neural network (DNN) training. However, the method does not always converge to a flat minimum of the loss surface that can demonstrate high generalization capability.…

Machine Learning · Computer Science 2020-09-08 Wonyong Sung , Iksoo Choi , Jinhwan Park , Seokhyun Choi , Sungho Shin

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces neural networks that have classification accuracy…

Machine Learning · Computer Science 2021-02-16 Spencer Frei , Yuan Cao , Quanquan Gu

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Machine Learning · Computer Science 2021-02-24 Shengchao Liu , Dimitris Papailiopoulos , Dimitris Achlioptas

This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best…

Machine Learning · Statistics 2020-12-02 Vatsal Shah , Anastasios Kyrillidis , Sujay Sanghavi

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

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

Machine Learning · Computer Science 2022-06-07 Satrajit Chatterjee , Piotr Zielinski

We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…

Machine Learning · Statistics 2023-11-02 Jung Eun Huh , Patrick Rebeschini

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

Machine Learning · Computer Science 2023-11-30 Avery Ma , Yangchen Pan , Amir-massoud Farahmand

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…

Machine Learning · Statistics 2022-03-28 Sebastian Goldt , Madhu S. Advani , Andrew M. Saxe , Florent Krzakala , Lenka Zdeborová

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…

Computation · Statistics 2015-09-23 Dustin Tran , Panos Toulis , Edoardo M. Airoldi

Label noise and class imbalance are two major issues coexisting in real-world datasets. To alleviate the two issues, state-of-the-art methods reweight each instance by leveraging a small amount of clean and unbiased data. Yet, these methods…

Computer Vision and Pattern Recognition · Computer Science 2021-11-02 Can Chen , Shuhao Zheng , Xi Chen , Erqun Dong , Xue Liu , Hao Liu , Dejing Dou

In spite of advances in understanding lazy training, recent work attributes the practical success of deep learning to the rich regime with complex inductive bias. In this paper, we study rich regime training empirically with benchmark…

Machine Learning · Computer Science 2021-03-01 Xinyan Li , Arindam Banerjee

Stochastic gradient descent (SGD) with momentum is widely used for training modern deep learning architectures. While it is well-understood that using momentum can lead to faster convergence rate in various settings, it has also been…

Machine Learning · Computer Science 2022-07-14 Samy Jelassi , Yuanzhi Li

Deep neural networks are often trained in the over-parametrized regime (i.e. with far more parameters than training examples), and understanding why the training converges to solutions that generalize remains an open problem. Several…

Machine Learning · Statistics 2018-03-23 Hartmut Maennel , Olivier Bousquet , Sylvain Gelly

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

Machine Learning · Computer Science 2021-12-08 Scott Pesme , Loucas Pillaud-Vivien , Nicolas Flammarion

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Machine Learning · Statistics 2020-06-12 Liam Hodgkinson , Michael W. Mahoney

Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's…

Machine Learning · Statistics 2015-06-11 Eric Nalisnick , Anima Anandkumar , Padhraic Smyth