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Convolutional neural networks have outperformed humans in image recognition tasks, but they remain vulnerable to attacks from adversarial examples. Since these data are crafted by adding imperceptible noise to normal images, their existence…

Computer Vision and Pattern Recognition · Computer Science 2021-06-10 Heng Yin , Hengwei Zhang , Jindong Wang , Ruiyu Dou

Adaptive gradient-based optimizers such as Adagrad and Adam are crucial for achieving state-of-the-art performance in machine translation and language modeling. However, these methods maintain second-order statistics for each parameter,…

Machine Learning · Computer Science 2019-09-13 Rohan Anil , Vineet Gupta , Tomer Koren , Yoram Singer

Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an…

Machine Learning · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Machine Learning · Computer Science 2025-02-12 Son Nguyen , Bo Liu , Lizhang Chen , Qiang Liu

Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control…

Machine Learning · Computer Science 2020-10-22 Jie Liu , Chen Lin , Chuming Li , Lu Sheng , Ming Sun , Junjie Yan , Wanli Ouyang

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…

Optimization and Control · Mathematics 2022-03-24 Hailiang Liu , Xuping Tian

Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs…

Machine Learning · Computer Science 2025-10-14 Xuan Tang , Han Zhang , Yuan Cao , Difan Zou

Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD…

Machine Learning · Computer Science 2016-04-06 Wei Zhang , Suyog Gupta , Xiangru Lian , Ji Liu

In the context of stochastic gradient descent(SGD) and adaptive moment estimation (Adam),researchers have recently proposed optimization techniques that transition from Adam to SGD with the goal of improving both convergence and…

Machine Learning · Computer Science 2020-07-01 Jiaxuan Wang , Jenna Wiens

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

Machine Learning · Computer Science 2016-03-16 Guillaume Bouchard , Théo Trouillon , Julien Perez , Adrien Gaidon

Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…

Machine Learning · Computer Science 2025-10-30 Zhifeng Wang , Longlong Li , Chunyan Zeng

In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

Machine Learning · Computer Science 2019-03-12 Jiawei Zhang

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

Machine Learning · Computer Science 2016-01-14 Yadong Mu , Wei Liu , Wei Fan

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

Machine Learning · Computer Science 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…

Optimization and Control · Mathematics 2020-12-29 Mingrui Liu , Youssef Mroueh , Jerret Ross , Wei Zhang , Xiaodong Cui , Payel Das , Tianbao Yang

We introduce AlphaGrad, a memory-efficient, conditionally stateless optimizer addressing the memory overhead and hyperparameter complexity of adaptive methods like Adam. AlphaGrad enforces scale invariance via tensor-wise L2 gradient…

Machine Learning · Computer Science 2025-04-24 Soham Sane

Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…

Machine Learning · Computer Science 2015-11-03 Caglar Gulcehre , Marcin Moczulski , Yoshua Bengio

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…

Machine Learning · Computer Science 2021-06-08 Jun-Kun Wang , Chi-Heng Lin , Jacob Abernethy

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed…

Machine Learning · Computer Science 2024-11-06 Ionut-Vlad Modoranu , Mher Safaryan , Grigory Malinovsky , Eldar Kurtic , Thomas Robert , Peter Richtarik , Dan Alistarh

Stochastic gradient descent (SGD) is a premium optimization method for training neural networks, especially for learning objectively defined labels such as image objects and events. When a neural network is instead faced with subjectively…

Neural and Evolutionary Computing · Computer Science 2022-04-15 Kosmas Pinitas , Konstantinos Makantasis , Antonios Liapis , Georgios N. Yannakakis
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