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This paper aims to clearly distinguish between Stochastic Gradient Descent with Momentum (SGDM) and Adam in terms of their convergence rates. We demonstrate that Adam achieves a faster convergence compared to SGDM under the condition of…

Machine Learning · Computer Science 2024-03-25 Bohan Wang , Huishuai Zhang , Qi Meng , Ruoyu Sun , Zhi-Ming Ma , Wei Chen

In this work, we question the necessity of adaptive gradient methods for training deep neural networks. SGD-SaI is a simple yet effective enhancement to stochastic gradient descent with momentum (SGDM). SGD-SaI performs learning rate…

Machine Learning · Computer Science 2024-12-18 Minghao Xu , Lichuan Xiang , Xu Cai , Hongkai Wen

Adaptive gradient methods have achieved remarkable success in training deep neural networks on a wide variety of tasks. However, not much is known about the mathematical and statistical properties of this family of methods. This work aims…

Machine Learning · Computer Science 2021-05-18 Zhang Zhiyi , Liu Ziyin

The Shapley value has been proposed as a solution to many applications in machine learning, including for equitable valuation of data. Shapley values are computationally expensive and involve the entire dataset. The query for a point's…

Machine Learning · Computer Science 2022-06-02 Lauren Watson , Rayna Andreeva , Hao-Tsung Yang , Rik Sarkar

As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been…

Machine Learning · Statistics 2019-06-11 Amirata Ghorbani , James Zou

In this paper, we provide a rigorous proof of convergence of the Adaptive Moment Estimate (Adam) algorithm for a wide class of optimization objectives. Despite the popularity and efficiency of the Adam algorithm in training deep neural…

Optimization and Control · Mathematics 2023-11-08 Haochuan Li , Alexander Rakhlin , Ali Jadbabaie

Despite the omnipresent use of stochastic gradient descent (SGD) optimization methods in the training of deep neural networks (DNNs), it remains, in basically all practically relevant scenarios, a fundamental open problem to provide a…

Machine Learning · Computer Science 2025-03-04 Thang Do , Arnulf Jentzen , Adrian Riekert

Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be…

Machine Learning · Computer Science 2024-05-22 Juhan Bae , Wu Lin , Jonathan Lorraine , Roger Grosse

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by…

Machine Learning · Computer Science 2024-05-31 Kwangjun Ahn , Zhiyu Zhang , Yunbum Kook , Yan Dai

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

We implement the adaptive step size scheme from the optimization methods AdaGrad and Adam in a novel variant of the Proximal Gradient Method (PGM). Our algorithm, dubbed AdaProx, avoids the need for explicit computation of the Lipschitz…

Optimization and Control · Mathematics 2020-07-06 Peter Melchior , Rémy Joseph , Fred Moolekamp

Adaptive optimization algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in some scenarios. However, recent studies show that they often lead to worse generalization…

Machine Learning · Computer Science 2018-09-19 Zijun Zhang , Lin Ma , Zongpeng Li , Chuan Wu

Time-series forecasting often faces challenges from non-stationarity, particularly distributional drift, where the data distribution evolves over time. This dynamic behavior can undermine the effectiveness of adaptive optimizers, such as…

Machine Learning · Computer Science 2026-03-12 Yuze Dong , Jinsong Wu

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property…

Machine Learning · Computer Science 2021-12-08 Zhishuai Guo , Yi Xu , Wotao Yin , Rong Jin , Tianbao Yang

Annotating the right set of data amongst all available data points is a key challenge in many machine learning applications. Batch active learning is a popular approach to address this, in which batches of unlabeled data points are selected…

Machine Learning · Statistics 2021-04-20 Amirata Ghorbani , James Zou , Andre Esteva

Running out of GPU memory has become a main bottleneck for large-scale DNN training. How to reduce the memory footprint during training has received intensive research attention. We find that previous gradient accumulation reduces…

Machine Learning · Computer Science 2023-06-01 Yijia Zhang , Yibo Han , Shijie Cao , Guohao Dai , Youshan Miao , Ting Cao , Fan Yang , Ningyi Xu

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…

Machine Learning · Computer Science 2024-07-15 Guoqiang Zhang

Deep learning has become the standard approach for most machine learning tasks. While its impact is undeniable, interpreting the predictions of deep learning models from a human perspective remains a challenge. In contrast to model…

Machine Learning · Computer Science 2023-11-13 Kyriakos Axiotis , Sami Abu-al-haija , Lin Chen , Matthew Fahrbach , Gang Fu

We introduce a new method inspired by Adam that enhances convergence speed and achieves better loss function minima. Traditional optimizers, including Adam, apply uniform or globally adjusted learning rates across neural networks without…

Machine Learning · Computer Science 2024-11-01 Remi Genet , Hugo Inzirillo

Adaptive optimizers such as Adam (Kingma & Ba, 2015) have been central to the success of large language models. However, they often require to maintain optimizer states throughout training, which can result in memory requirements several…

Machine Learning · Computer Science 2025-02-24 Chao Ma , Wenbo Gong , Meyer Scetbon , Edward Meeds
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