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Standard mixed-precision training of neural networks requires many bytes of accelerator memory for each model parameter. These bytes reflect not just the parameter itself, but also its gradient and one or more optimizer state variables.…

Machine Learning · Computer Science 2026-03-13 Jose Javier Gonzalez Ortiz , Abhay Gupta , Christopher Rinard , Davis Blalock

Second-order optimization methods offer notable advantages in training deep neural networks by utilizing curvature information to achieve faster convergence. However, traditional second-order techniques are computationally prohibitive,…

Machine Learning · Computer Science 2024-10-04 James Vo

Optimization methods (optimizers) get special attention for the efficient training of neural networks in the field of deep learning. In literature there are many papers that compare neural models trained with the use of different…

Machine Learning · Computer Science 2020-11-17 Nicola Landro , Ignazio Gallo , Riccardo La Grassa

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…

Machine Learning · Computer Science 2024-07-12 Steffen Dereich , Robin Graeber , Arnulf Jentzen

Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion…

Machine Learning · Computer Science 2017-12-21 Nitish Shirish Keskar , Richard Socher

Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce…

Machine Learning · Computer Science 2024-06-18 Kaan Ozkara , Can Karakus , Parameswaran Raman , Mingyi Hong , Shoham Sabach , Branislav Kveton , Volkan Cevher

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

We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…

Machine Learning · Computer Science 2026-02-03 Aikaterini Karoni , Rajit Rajpal , Benedict Leimkuhler , Gabriel Stoltz

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Machine Learning · Computer Science 2017-11-23 Haiping Huang , Taro Toyoizumi

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…

Optimization and Control · Mathematics 2026-05-11 Yunlang Zhu , Lingjun Guo , Zahra Khatti , Xiaoyi Qu , Chia-Yuan Wu , Lara Zebiane , Frank E. Curtis

Large language models (LLMs) have demonstrated impressive generalization and emergent capabilities, yet their pre-training remains computationally expensive and sensitive to optimization dynamics. While Adam-based optimizers offer fast…

Machine Learning · Computer Science 2025-10-01 Junjie Wang , Pan Zhou , Yiming Dong , Huan Li , Jia Li , Xun Zhou , Qicheng Lao , Cong Fang , Zhouchen Lin

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

Machine Learning · Computer Science 2026-05-22 Saurabh Saini , Kapil Ahuja , Thomas Wick , Saurav Kumar

With the increasing practicality of deep learning applications, practitioners are inevitably faced with datasets corrupted by noise from various sources such as measurement errors, mislabeling, and estimated surrogate inputs/outputs that…

Machine Learning · Computer Science 2023-08-30 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Takamitsu Matsubara

Fine-tuning LLMs is necessary for various dedicated downstream tasks, but classic backpropagation-based fine-tuning methods require substantial GPU memory. To this end, a recent work, MeZO, which relies solely on forward passes to fine-tune…

Machine Learning · Computer Science 2026-05-04 Zhijie Cai , Haolong Chen , Guangxu Zhu

This paper proposes a new optimizer for deep learning, named d-AmsGrad. In the real-world data, noise and outliers cannot be excluded from dataset to be used for learning robot skills. This problem is especially striking for robots that…

Machine Learning · Computer Science 2021-04-02 Taisuke Kobayashi

The concept of learning to optimize involves utilizing a trainable optimization strategy rather than relying on manually defined full gradient estimations such as ADAM. We present a framework that jointly trains the full gradient estimator…

Machine Learning · Computer Science 2026-01-30 Ruiqi Wang , Diego Klabjan

Continual learning, an important aspect of artificial intelligence and machine learning research, focuses on developing models that learn and adapt to new tasks while retaining previously acquired knowledge. Existing continual learning…

Machine Learning · Computer Science 2024-04-04 Liwei Kang , Wee Sun Lee

Descent methods for deep networks are notoriously capricious: they require careful tuning of step size, momentum and weight decay, and which method will work best on a new benchmark is a priori unclear. To address this problem, this paper…

Neural and Evolutionary Computing · Computer Science 2021-09-21 Yang Liu , Jeremy Bernstein , Markus Meister , Yisong Yue

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared…

Machine Learning · Computer Science 2019-04-22 Liangchen Luo , Yuanhao Xiong , Yan Liu , Xu Sun

We propose NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay. In our experiments on neural networks for image classification, speech recognition, machine translation,…