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Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…

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…

Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is…

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 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…

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity…

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance.…

Neural networks exhibit good generalization behavior in the over-parameterized regime, where the number of network parameters exceeds the number of observations. Nonetheless, current generalization bounds for neural networks fail to explain…

Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying…

Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…

This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic structure and…

Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an…

Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…

Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…