Related papers: A Rod Flow Model for Adam at the Edge of Stability

How can we understand gradient-based training over non-convex landscapes? The edge of stability phenomenon, introduced in Cohen et al. (2021), indicates that the answer is not so simple: namely, gradient descent (GD) with large step sizes…

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial…

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

Gradient descent (GD) based optimization methods are these days the standard tools to train deep neural networks in artificial intelligence systems. In optimization procedures in deep learning the employed optimizer is often not the…

Adaptive gradient optimization methods, such as Adam, are prevalent in training deep neural networks across diverse machine learning tasks due to their ability to achieve faster convergence. However, these methods often suffer from…

The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared…

Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…

The four-roll mill, wherein four identical cylinders undergo rotation of identical magnitude but alternate signs, was originally proposed by GI Taylor to create local extensional flows and study their ability to deform small liquid drops.…

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally,…

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

Training deep reinforcement learning (RL) agents necessitates overcoming the highly unstable nonconvex stochastic optimization inherent in the trial-and-error mechanism. To tackle this challenge, we propose a physics-inspired optimization…

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first…

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous…

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been…