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Distributed training is an effective way to accelerate the training process of large-scale deep learning models. However, the parameter exchange and synchronization of distributed stochastic gradient descent introduce a large amount of…
Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
The increasing size of deep learning models has made distributed training across multiple devices essential. However, current methods such as distributed data-parallel training suffer from large communication and synchronization overheads…
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…
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…
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 consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or…
Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for…
Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…
Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data. Here we study the generalisation dynamics of two-layer neural networks in a…
The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…
Stochastic gradient descent (SGD) is an estimation tool for large data employed in machine learning and statistics. Due to the Markovian nature of the SGD process, inference is a challenging problem. An underlying asymptotic normality of…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…
Distributed machine learning has been widely studied in the literature to scale up machine learning model training in the presence of an ever-increasing amount of data. We study distributed machine learning from another perspective, where…
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
Distributed stochastic gradient descent (SGD) is essential for scaling the machine learning algorithms to a large number of computing nodes. However, the infrastructures variability such as high communication delay or random node slowdown…
Decentralized stochastic gradient descent (D-SGD) is an efficient method for large-scale distributed learning. Existing generalization studies mainly address expected results, achieving rates limited to $\mathcal{O}\left(\frac{1}{\delta…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…