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Current state-of-the-art optimizers are adaptive gradient-based optimization methods such as Adam. Recently, there has been an increasing interest in formulating gradient-based optimizers in a probabilistic framework for better modeling the…

NLP research has explored different neural model architectures and sizes, datasets, training objectives, and transfer learning techniques. However, the choice of optimizer during training has not been explored as extensively. Typically,…

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…

It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as,…

Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g. Adam) and accelerated schemes (e.g. stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks…

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

The stochastic gradient descent (SGD) optimizers are generally used to train the convolutional neural networks (CNNs). In recent years, several adaptive momentum based SGD optimizers have been introduced, such as Adam, diffGrad, Radam and…

It is widely believed that stochastic gradient descent (SGD) performs significantly worse than adaptive optimizers such as Adam in pre-training Large Language Models (LLMs). Yet the underlying reason for this gap remains unclear. In this…

Deep learning algorithms - typically consisting of a class of deep neural networks trained by a stochastic gradient descent (SGD) optimization method - are nowadays the key ingredients in many artificial intelligence (AI) systems and have…

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…

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

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,…

Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…

Adam is known to perform significantly better than Stochastic Gradient Descent (SGD) in language models, a phenomenon for which a number of explanations have been proposed. In this work, we revisit this "optimizer gap" through a series of…

Convolutional neural networks (CNNs) are trained using stochastic gradient descent (SGD)-based optimizers. Recently, the adaptive moment estimation (Adam) optimizer has become very popular due to its adaptive momentum, which tackles the…

Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights…

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable…

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…