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Ever since Reddi et al. 2018 pointed out the divergence issue of Adam, many new variants have been designed to obtain convergence. However, vanilla Adam remains exceptionally popular and it works well in practice. Why is there a gap between…

Adam is one of the most influential adaptive stochastic algorithms for training deep neural networks, which has been pointed out to be divergent even in the simple convex setting via a few simple counterexamples. Many attempts, such as…

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…

While Adam is one of the most effective optimizer for training large-scale machine learning models, a theoretical understanding of how to optimally set its momentum factors, $\beta_1$ and $\beta_2$, remains largely incomplete. Prior works…

Adam has been at the core of large-scale training for almost a decade, yet a simple empirical fact remains unaccounted for: both validation scores and the qualitative behaviour of the training runs improve when the momentum parameters…

We present a theory for the previously unexplained divergent behavior noticed in the training of large language models. We argue that the phenomenon is an artifact of the dominant optimization algorithm used for training, called Adam. We…

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property…

One of the most popular training algorithms for deep neural networks is the Adaptive Moment Estimation (Adam) introduced by Kingma and Ba. Despite its success in many applications there is no satisfactory convergence analysis: only local…

Here I present a small update to the bias-correction term in the Adam optimizer that has the advantage of making smaller gradient updates in the first several steps of training. With the default bias-correction, Adam may actually make…

Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as…

Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near…

Adaptive optimization algorithms, particularly Adam and its variant AdamW, are fundamental components of modern deep learning. However, their training dynamics lack comprehensive theoretical understanding, with limited insight into why…

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples. Many attempts, such…

The adaptive optimizer for training neural networks has continually evolved to overcome the limitations of the previously proposed adaptive methods. Recent studies have found the rare counterexamples that Adam cannot converge to the optimal…

Scalable training of large models (like BERT and GPT-3) requires careful optimization rooted in model design, architecture, and system capabilities. From a system standpoint, communication has become a major bottleneck, especially on…

Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…

Recent evidence suggests that Adam performs robustly when its momentum parameters are tied, $\beta_1=\beta_2$, reducing the optimizer to a single remaining parameter. However, how this parameter should be set remains poorly understood. We…

With limited high-quality data and growing compute, multi-epoch training is gaining back its importance across sub-areas of deep learning. Adam(W), versions of which are go-to optimizers for many tasks such as next token prediction, has two…

Convergence and convergence rate analyses of adaptive methods, such as Adaptive Moment Estimation (Adam) and its variants, have been widely studied for nonconvex optimization. The analyses are based on assumptions that the expected or…