相关论文: Large Stepsize Gradient Descent for Non-Homogeneou…
Deep neural networks are known to exhibit a `double descent' behavior as the number of parameters increases. Recently, it has also been shown that an `epochwise double descent' effect exists in which the generalization error initially…
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…
Modern deep learning techniques focus on extracting intricate information from data to achieve accurate predictions. However, the training datasets may be crowdsourced and include sensitive information, such as personal contact details,…
Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on \emph{very small or even…
Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…
We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…
We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
Recent theoretical results show that gradient descent on deep neural networks under exponential loss functions locally maximizes classification margin, which is equivalent to minimizing the norm of the weight matrices under margin…
We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a…
Gradient descent (GD) methods for the training of artificial neural networks (ANNs) belong nowadays to the most heavily employed computational schemes in the digital world. Despite the compelling success of such methods, it remains an open…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
We analyze speed of convergence to global optimum for gradient descent training a deep linear neural network (parameterized as $x \mapsto W_N W_{N-1} \cdots W_1 x$) by minimizing the $\ell_2$ loss over whitened data. Convergence at a linear…
Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the…
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale…
The study of Deep Network (DN) training dynamics has largely focused on the evolution of the loss function, evaluated on or around train and test set data points. In fact, many DN phenomenon were first introduced in literature with that…
We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations…
This paper presents a comprehensive study on the convergence rates of the stochastic gradient descent (SGD) algorithm when applied to overparameterized two-layer neural networks. Our approach combines the Neural Tangent Kernel (NTK)…
The choice of step-size used in Stochastic Gradient Descent (SGD) optimization is empirically selected in most training procedures. Moreover, the use of scheduled learning techniques such as Step-Decaying, Cyclical-Learning, and Warmup to…