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Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…

Machine Learning · Computer Science 2025-03-19 Dayal Singh Kalra , John Kirchenbauer , Maissam Barkeshli , Tom Goldstein

It is well known that we need to choose the hyper-parameters in Momentum, AdaGrad, AdaDelta, and other alternative stochastic optimizers. While in many cases, the hyper-parameters are tuned tediously based on experience becoming more of an…

Machine Learning · Computer Science 2022-04-05 Jun Lu

We present Amos, a stochastic gradient-based optimizer designed for training deep neural networks. It can be viewed as an Adam optimizer with theoretically supported, adaptive learning-rate decay and weight decay. A key insight behind Amos…

Machine Learning · Computer Science 2022-11-22 Ran Tian , Ankur P. Parikh

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient…

Machine Learning · Computer Science 2020-06-02 Liang Liu , Xiaopeng Luo

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often…

Machine Learning · Computer Science 2022-06-15 Zeke Xie , Xinrui Wang , Huishuai Zhang , Issei Sato , Masashi Sugiyama

Averaging, or smoothing, is a fundamental approach to obtain stable, de-noised estimates from noisy observations. In certain scenarios, observations made along trajectories of random dynamical systems are of particular interest. One popular…

Machine Learning · Statistics 2025-05-19 Frederik Köhne , Anton Schiela

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…

Machine Learning · Computer Science 2017-01-31 Diederik P. Kingma , Jimmy Ba

Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers…

Machine Learning · Computer Science 2025-02-03 Ouya Wang , Shenglong Zhou , Geoffrey Ye Li

When aligning large language models (LLMs), their performance on various tasks (such as being helpful, harmless, and honest) depends heavily on the composition of their training data. However, selecting a data mixture that achieves strong…

Machine Learning · Computer Science 2025-06-03 Nicholas E. Corrado , Julian Katz-Samuels , Adithya Devraj , Hyokun Yun , Chao Zhang , Yi Xu , Yi Pan , Bing Yin , Trishul Chilimbi

Efficiently exploring complex loss landscapes is key to the performance of deep neural networks. While momentum-based optimizers are widely used in state-of-the-art setups, classical momentum can still struggle with large, misaligned…

Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order…

Optimization and Control · Mathematics 2025-03-14 Yongqi Li , Xiaowei Zhang

We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.…

Machine Learning · Computer Science 2026-02-12 Francisco Patitucci , Aryan Mokhtari

We examine two different techniques for parameter averaging in GAN training. Moving Average (MA) computes the time-average of parameters, whereas Exponential Moving Average (EMA) computes an exponentially discounted sum. Whilst MA is known…

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Machine Learning · Computer Science 2020-11-25 Mingrui Liu , Wei Zhang , Francesco Orabona , Tianbao Yang

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Optimization and Control · Mathematics 2021-07-07 Junxiang Wang , Fuxun Yu , Xiang Chen , Liang Zhao

Selecting an optimizer is a central step in the contemporary deep learning pipeline. In this paper, we demonstrate the sensitivity of optimizer comparisons to the hyperparameter tuning protocol. Our findings suggest that the hyperparameter…

Machine Learning · Computer Science 2020-06-17 Dami Choi , Christopher J. Shallue , Zachary Nado , Jaehoon Lee , Chris J. Maddison , George E. Dahl

Adaptive learning rate methods have been successfully applied in many fields, especially in training deep neural networks. Recent results have shown that adaptive methods with exponential increasing weights on squared past gradients (i.e.,…

Machine Learning · Computer Science 2021-01-05 Hui Zhong , Zaiyi Chen , Chuan Qin , Zai Huang , Vincent W. Zheng , Tong Xu , Enhong Chen

In the training of large language models, momentum is widely used and often demonstrated to achieve significant acceleration. However, storing momentum typically presents memory challenges. In this paper, we propose AdaPM, an adaptive…

Machine Learning · Computer Science 2025-10-13 Yimu Zhang , Yuanshi Liu , Cong Fang

Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we…

Machine Learning · Computer Science 2019-02-26 Guoqiang Zhang , Kenta Niwa , W. Bastiaan Kleijn

Few-shot meta-learning presents a challenge for gradient descent optimization due to the limited number of training samples per task. To address this issue, we propose an episodic memory optimization for meta-learning, we call EMO, which is…

Machine Learning · Computer Science 2023-06-28 Yingjun Du , Jiayi Shen , Xiantong Zhen , Cees G. M. Snoek