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How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows…

机器学习 · 计算机科学 2026-03-03 Tom Jacobs , Chao Zhou , Rebekka Burkholz

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…

机器学习 · 计算机科学 2022-08-31 Xiaoxia Wu , Edgar Dobriban , Tongzheng Ren , Shanshan Wu , Zhiyuan Li , Suriya Gunasekar , Rachel Ward , Qiang Liu

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…

机器学习 · 计算机科学 2024-08-21 Huixiu Jiang , Ling Yang , Yu Bao , Rutong Si , Sikun Yang

Adaptive optimizers like AdamW apply uniform hyperparameters across all parameter groups, ignoring heterogeneous optimization dynamics across layers and modules. We address this limitation by proposing MetaAdamW - a new optimizer that…

机器学习 · 计算机科学 2026-05-07 JiangBo Zhao , ZhaoXin Liu

Optimizers that further adjust the scale of gradient, such as Adam, Natural Gradient (NG), etc., despite widely concerned and used by the community, are often found poor generalization performance, compared with Stochastic Gradient Descent…

机器学习 · 计算机科学 2021-01-19 Zedong Tang , Fenlong Jiang , Junke Song , Maoguo Gong , Hao Li , Fan Yu , Zidong Wang , Min Wang

The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…

机器学习 · 计算机科学 2019-04-30 Dmitrii Marin , Meng Tang , Ismail Ben Ayed , Yuri Boykov

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

机器学习 · 计算机科学 2013-03-28 Tom Schaul , Yann LeCun

Stochastic gradient descent (SGD) has taken the stage as the primary workhorse for large-scale machine learning. It is often used with its adaptive variants such as AdaGrad, Adam, and AMSGrad. This paper proposes an adaptive stochastic…

机器学习 · 计算机科学 2021-01-01 Tianyi Chen , Ziye Guo , Yuejiao Sun , Wotao Yin

A number of recent adaptive optimizers improve the generalisation performance of Adam by essentially reducing the variance of adaptive stepsizes to get closer to SGD with momentum. Following the above motivation, we suppress the range of…

机器学习 · 计算机科学 2024-07-15 Guoqiang Zhang

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…

机器学习 · 计算机科学 2024-07-12 Steffen Dereich , Robin Graeber , Arnulf Jentzen

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

最优化与控制 · 数学 2025-10-03 Yufeng Yang , Erin Tripp , Yifan Sun , Shaofeng Zou , Yi Zhou

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter…

机器学习 · 计算机科学 2018-04-13 Noam Shazeer , Mitchell Stern

Gradient descent has been a central training principle for artificial neural networks from the early beginnings to today's deep learning networks. The most common implementation is the backpropagation algorithm for training feed-forward…

机器学习 · 计算机科学 2020-06-09 Stefan Jaeger

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…

机器学习 · 统计学 2018-05-09 Li He , Qi Meng , Wei Chen , Zhi-Ming Ma , Tie-Yan Liu

We propose a novel algorithm for the fitting of 3D human shape to images. Combining the accuracy and refinement capabilities of iterative gradient-based optimization techniques with the robustness of deep neural networks, we propose a…

计算机视觉与模式识别 · 计算机科学 2020-08-20 Jie Song , Xu Chen , Otmar Hilliges

The increasing size of deep learning models has made distributed training across multiple devices essential. However, current methods such as distributed data-parallel training suffer from large communication and synchronization overheads…

机器学习 · 计算机科学 2025-02-10 Cabrel Teguemne Fokam , Khaleelulla Khan Nazeer , Lukas König , David Kappel , Anand Subramoney

We classified the decoupled stochastic parallel gradient descent (SPGD) optimization model into two different types: software and hardware decoupling methods. A kind of software decoupling method is then proposed and a kind of hardware…

天体物理仪器与方法 · 物理学 2015-06-19 Qiang Fu , Jörg-Uwe Pott , Feng Shen , Changhui Rao , Xinyang Li

Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…

机器学习 · 计算机科学 2025-11-05 Xinghan Li , Haodong Wen , Kaifeng Lyu

Existing convergence analyses of Q-learning mostly focus on the vanilla stochastic gradient descent (SGD) type of updates. Despite the Adaptive Moment Estimation (Adam) has been commonly used for practical Q-learning algorithms, there has…

最优化与控制 · 数学 2020-07-16 Bowen Weng , Huaqing Xiong , Yingbin Liang , Wei Zhang

Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in…

机器学习 · 计算机科学 2022-10-20 Bozhou Chen , Hongzhi Wang , Chenmin Ba