Related papers: Nesterov Method for Asynchronous Pipeline Parallel…

This paper studies the online convex optimization problem by using an Online Continuous-Time Nesterov Accelerated Gradient method (OCT-NAG). We show that the continuous-time dynamics generated by the online version of the Bregman Lagrangian…

A common problem in training neural networks is the vanishing and/or exploding gradient problem which is more prominently seen in training of Recurrent Neural Networks (RNNs). Thus several algorithms have been proposed for training RNNs.…

In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…

Large-scale language models have become increasingly challenging and expensive to train. Among various methods addressing this issue, Pipeline Parallelism has been widely employed to accommodate massive model weights within limited GPU…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

Under the multiplicative noise scaling (MNS) condition, original Nesterov acceleration is provably sensitive to noise and may diverge when gradient noise overwhelms the signal. In this paper, we develop two accelerated stochastic gradient…

Graph-structured data is ubiquitous in the real world, and Graph Neural Networks (GNNs) have become increasingly popular in various fields due to their ability to process such irregular data directly. However, as data scale, GNNs become…

Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…

In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…

Single-Program-Multiple-Data (SPMD) parallelism has recently been adopted to train large deep neural networks (DNNs). Few studies have explored its applicability on heterogeneous clusters, to fully exploit available resources for large…

Incorporating second order curvature information in gradient based methods have shown to improve convergence drastically despite its computational intensity. In this paper, we propose a stochastic (online) quasi-Newton method with…

For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…

Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve…

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

The ability to train large-scale neural networks has resulted in state-of-the-art performance in many areas of computer vision. These results have largely come from computational break throughs of two forms: model parallelism, e.g. GPU…

This paper describes the design and implementation of parallel neural networks (PNNs) with the novel programming language Golang. We follow in our approach the classical Single-Program Multiple-Data (SPMD) model where a PNN is composed of…

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

Neural-ODE parameterize a differential equation using continuous depth neural network and solve it using numerical ODE-integrator. These models offer a constant memory cost compared to models with discrete sequence of hidden layers in which…

While Graph Neural Networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve…