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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…

机器学习 · 计算机科学 2017-01-31 Diederik P. Kingma , Jimmy Ba

Training Artificial Neural Networks poses a challenging and critical problem in machine learning. Despite the effectiveness of gradient-based learning methods, such as Stochastic Gradient Descent (SGD), in training neural networks, they do…

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension…

机器学习 · 计算机科学 2019-10-16 Zhanhong Jiang , Aditya Balu , Sin Yong Tan , Young M Lee , Chinmay Hegde , Soumik Sarkar

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…

机器学习 · 计算机科学 2025-02-12 Abulikemu Abuduweili , Changliu Liu

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…

机器学习 · 计算机科学 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

Currently, widely used first-order deep learning optimizers include non-adaptive learning rate optimizers and adaptive learning rate optimizers. The former is represented by SGDM (Stochastic Gradient Descent with Momentum), while the latter…

机器学习 · 计算机科学 2024-09-25 Honglin Qin , Hongye Zheng , Bingxing Wang , Zhizhong Wu , Bingyao Liu , Yuanfang Yang

The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the…

机器学习 · 计算机科学 2020-12-15 Lukas Balles , Philipp Hennig

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…

机器学习 · 计算机科学 2016-04-06 Wei Zhang , Suyog Gupta , Xiangru Lian , Ji Liu

Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…

机器学习 · 计算机科学 2021-03-30 Loris Nanni , Gianluca Maguolo , Alessandra Lumini

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…

Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term…

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…

机器学习 · 计算机科学 2015-11-03 Caglar Gulcehre , Marcin Moczulski , Yoshua Bengio

Adam has proven remarkable successful in training deep neural networks, but the mechanisms underlying its empirical successes and limitations remain underexplored. In this study, we demonstrate that the effectiveness of Adam stems largely…

机器学习 · 计算机科学 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Wen Gao

Training a neural network (NN) typically relies on some type of curve-following method, such as gradient descent (GD) (and stochastic gradient descent (SGD)), ADADELTA, ADAM or limited memory algorithms. Convergence for these algorithms…

机器学习 · 计算机科学 2023-05-08 Michael A Kouritzin , Stephen Styles , Beatrice-Helen Vritsiou

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…

机器学习 · 计算机科学 2017-03-03 Caglar Gulcehre , Jose Sotelo , Marcin Moczulski , Yoshua Bengio

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…

最优化与控制 · 数学 2022-05-13 Feihu Huang , Junyi Li , Heng Huang

Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…

机器学习 · 计算机科学 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Zhouchen Lin

The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…

机器学习 · 计算机科学 2024-06-18 Thomas Flynn

Adaptive gradient algorithm (AdaGrad) and its variants, such as RMSProp, Adam, AMSGrad, etc, have been widely used in deep learning. Although these algorithms are faster in the early phase of training, their generalization performance is…

机器学习 · 计算机科学 2021-09-14 Kun Zeng , Jinlan Liu , Zhixia Jiang , Dongpo Xu

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each…

机器学习 · 计算机科学 2018-08-09 Jeremy Bernstein , Yu-Xiang Wang , Kamyar Azizzadenesheli , Anima Anandkumar