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We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the…

机器学习 · 计算机科学 2015-06-09 Behnam Neyshabur , Ruslan Salakhutdinov , Nathan Srebro

Weight decay is a simple yet powerful regularization technique that has been very widely used in training of deep neural networks (DNNs). While weight decay has attracted much attention, previous studies fail to discover some overlooked…

机器学习 · 计算机科学 2024-08-19 Zeke Xie , Zhiqiang Xu , Jingzhao Zhang , Issei Sato , Masashi Sugiyama

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…

机器学习 · 计算机科学 2023-11-30 Avery Ma , Yangchen Pan , Amir-massoud Farahmand

Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning.…

机器学习 · 统计学 2022-07-21 Adarsh M. Subramaniam , Akshayaa Magesh , Venugopal V. Veeravalli

Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored,…

机器学习 · 计算机科学 2020-04-21 Huanrui Yang , Minxue Tang , Wei Wen , Feng Yan , Daniel Hu , Ang Li , Hai Li , Yiran Chen

Distributed Deep Learning (DDL) is essential for large-scale Deep Learning (DL) training. Synchronous Stochastic Gradient Descent (SSGD) 1 is the de facto DDL optimization method. Using a sufficiently large batch size is critical to…

机器学习 · 计算机科学 2021-12-03 Wei Zhang , Mingrui Liu , Yu Feng , Xiaodong Cui , Brian Kingsbury , Yuhai Tu

With an increasing demand for training powers for deep learning algorithms and the rapid growth of computation resources in data centers, it is desirable to dynamically schedule different distributed deep learning tasks to maximize resource…

机器学习 · 计算机科学 2019-05-03 Haibin Lin , Hang Zhang , Yifei Ma , Tong He , Zhi Zhang , Sheng Zha , Mu Li

It has long been argued that minibatch stochastic gradient descent can generalize better than large batch gradient descent in deep neural networks. However recent papers have questioned this claim, arguing that this effect is simply a…

机器学习 · 计算机科学 2020-06-29 Samuel L. Smith , Erich Elsen , Soham De

The stochastic gradient descent (SGD) algorithm has been widely used to optimize deep Cox neural network (Cox-NN) by updating model parameters using mini-batches of data. We show that SGD aims to optimize the average of mini-batch…

机器学习 · 统计学 2026-04-16 Lang Zeng , Weijing Tang , Zhao Ren , Ying Ding

Training machine learning models based on neural networks requires large datasets, which may contain sensitive information. The models, however, should not expose private information from these datasets. Differentially private SGD [DP-SGD]…

机器学习 · 计算机科学 2024-09-26 Francisco Aguilera-Martínez , Fernando Berzal

We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning…

机器学习 · 计算机科学 2016-06-07 Tim Salimans , Diederik P. Kingma

Stochastic gradient descent (SGD), which updates the model parameters by adding a local gradient times a learning rate at each step, is widely used in model training of machine learning algorithms such as neural networks. It is observed…

机器学习 · 计算机科学 2017-06-01 Chang Xu , Tao Qin , Gang Wang , Tie-Yan Liu

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD,…

机器学习 · 计算机科学 2019-02-26 Pavel Izmailov , Dmitrii Podoprikhin , Timur Garipov , Dmitry Vetrov , Andrew Gordon Wilson

When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…

机器学习 · 计算机科学 2018-12-24 Kanghoon Lee , Jihye Choi , Moonsu Cha , Jung-Kwon Lee , Taeyoon Kim

Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer…

机器学习 · 计算机科学 2018-02-15 Aditya Devarakonda , Maxim Naumov , Michael Garland

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

机器学习 · 计算机科学 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

Synchronous strategies with data parallelism, such as the Synchronous StochasticGradient Descent (S-SGD) and the model averaging methods, are widely utilizedin distributed training of Deep Neural Networks (DNNs), largely owing to itseasy…

机器学习 · 计算机科学 2022-11-04 Qing Ye , Yuhao Zhou , Mingjia Shi , Yanan Sun , Jiancheng Lv

Batch normalization is currently the most widely used variant of internal normalization for deep neural networks. Additional work has shown that the normalization of weights and additional conditioning as well as the normalization of…

计算机视觉与模式识别 · 计算机科学 2021-01-19 Wolfgang Fuhl , Enkelejda Kasneci

This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…

最优化与控制 · 数学 2026-04-07 Runze Li , Jintao Xu , Wenxun Xing

Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of a feature extractor (i.e. last hidden layer) and a linear classifier (i.e. output layer) that is trained jointly with stochastic gradient descent (SGD). In…

机器学习 · 计算机科学 2020-02-28 Xiangrui Li , Deng Pan , Xin Li , Dongxiao Zhu