Related papers: Implicit Bias in Noisy-SGD: With Applications to D…

Differentially private stochastic gradient descent (DP-SGD) is known to have poorer training and test performance on large neural networks, compared to ordinary stochastic gradient descent (SGD). In this paper, we perform a detailed study…

Learning often involves sensitive data and as such, privacy preserving extensions to Stochastic Gradient Descent (SGD) and other machine learning algorithms have been developed using the definitions of Differential Privacy (DP). In…

Differentially private stochastic gradient descent (DP-SGD) has been widely adopted in deep learning to provide rigorously defined privacy, which requires gradient clipping to bound the maximum norm of individual gradients and additive…

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…

The success of SGD in deep learning has been ascribed by prior works to the implicit bias induced by finite batch sizes ("SGD noise"). While prior works focused on offline learning (i.e., multiple-epoch training), we study the impact of SGD…

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well…

The Noisy-SGD algorithm is widely used for privately training machine learning models. Traditional privacy analyses of this algorithm assume that the internal state is publicly revealed, resulting in privacy loss bounds that increase…

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…

Mini-batch stochastic gradient methods (SGD) are state of the art for distributed training of deep neural networks. Drastic increases in the mini-batch sizes have lead to key efficiency and scalability gains in recent years. However,…

We study how the batch size affects the total gradient variance in differentially private stochastic gradient descent (DP-SGD), seeking a theoretical explanation for the usefulness of large batch sizes. As DP-SGD is the basis of modern DP…

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…

The noise in stochastic gradient descent (SGD), caused by minibatch sampling, is poorly understood despite its practical importance in deep learning. This work presents the first systematic study of the SGD noise and fluctuations close to a…

One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model…

Differential privacy (DP) has become a prevalent privacy model in a wide range of machine learning tasks, especially after the debut of DP-SGD. However, DP-SGD, which directly perturbs gradients in the training iterations, fails to mitigate…

Stochastic Gradient Descent (SGD) based training of neural networks with a large learning rate or a small batch-size typically ends in well-generalizing, flat regions of the weight space, as indicated by small eigenvalues of the Hessian of…

The stochastic gradient descent (SGD) method and its variants are algorithms of choice for many Deep Learning tasks. These methods operate in a small-batch regime wherein a fraction of the training data, say $32$-$512$ data points, is…

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…

What enables Stochastic Gradient Descent (SGD) to achieve better generalization than Gradient Descent (GD) in Neural Network training? This question has attracted much attention. In this paper, we study the distribution of the Stochastic…

Recent results in the literature suggest that the penultimate (second-to-last) layer representations of neural networks that are trained for classification exhibit a clustering property called neural collapse (NC). We study the implicit…

Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average…