Related papers: Stochastic gradient descent performs variational i…

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new…

Neural networks trained with stochastic gradient descent (SGD) starting from different random initialisations typically find functionally very similar solutions, raising the question of whether there are meaningful differences between…

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…

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses…

Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization,…

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Recent empirical work on stochastic gradient descent (SGD) applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of…

When training deep neural networks, it is typically assumed that the training examples are uniformly difficult to learn. Or, to restate, it is assumed that the training error will be uniformly distributed across the training examples. Based…

Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training deep networks in practice. SGD is known to find a flat minimum that often generalizes well. However, it is mathematically unclear how deep learning can…

Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based…

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…

We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD…

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…

We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution. This distribution is implicitly defined as the transformation of an…

Understanding the implicit bias of Stochastic Gradient Descent (SGD) is one of the key challenges in deep learning, especially for overparametrized models, where the local minimizers of the loss function $L$ can form a manifold.…

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…