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The interplay between optimization and privacy has become a central theme in privacy-preserving machine learning. Noisy stochastic gradient descent (SGD) has emerged as a cornerstone algorithm, particularly in large-scale settings. These…
In this work, we reveal a strong implicit bias of stochastic gradient descent (SGD) that drives overly expressive networks to much simpler subnetworks, thereby dramatically reducing the number of independent parameters, and improving…
We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…
Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…
Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative…
Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…
Previous work has examined the ability of larger capacity neural networks to generalize better than smaller ones, even without explicit regularizers, by analyzing gradient based algorithms such as GD and SGD. The presence of noise and its…
This manuscript investigates the one-pass stochastic gradient descent (SGD) dynamics of a two-layer neural network trained on Gaussian data and labels generated by a similar, though not necessarily identical, target function. We rigorously…
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…
This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional robust regression problems. The number of features is…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Understanding the generalization abilities of modern machine learning algorithms has been a major research topic over the past decades. In recent years, the learning dynamics of Stochastic Gradient Descent (SGD) have been related to…
This article examines the implicit regularization effect of Stochastic Gradient Descent (SGD). We consider the case of SGD without replacement, the variant typically used to optimize large-scale neural networks. We analyze this algorithm in…
Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…
The performance of fully synchronized distributed systems has faced a bottleneck due to the big data trend, under which asynchronous distributed systems are becoming a major popularity due to their powerful scalability. In this paper, we…
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…
Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems. However, some of its learning properties are still not fully understood. We consider least squares learning in…
This paper studies the performance of a recently proposed preconditioned stochastic gradient descent (PSGD) algorithm on recurrent neural network (RNN) training. PSGD adaptively estimates a preconditioner to accelerate gradient descent, and…