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Deep neural networks are traditionally trained using human-designed stochastic optimization algorithms, such as SGD and Adam. Recently, the approach of learning to optimize network parameters has emerged as a promising research topic.…

Machine Learning · Computer Science 2018-11-26 Shipeng Wang , Jian Sun , Zongben Xu

Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators. In such…

Machine Learning · Computer Science 2026-05-29 Ruoran Xu , Borong She , Xiaobo Jin , Qiufeng Wang

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Numerical Analysis · Mathematics 2024-02-08 Davide Evangelista , James Nagy , Elena Morotti , Elena Loli Piccolomini

It is known that training deep neural networks, in particular, deep convolutional networks, with aggressively reduced numerical precision is challenging. The stochastic gradient descent algorithm becomes unstable in the presence of noisy…

Machine Learning · Computer Science 2016-07-11 Darryl D. Lin , Sachin S. Talathi

Training modern neural networks is increasingly fragile, with rare but severe destabilizing updates often causing irreversible divergence or silent performance degradation. Existing optimization methods primarily rely on preventive…

Machine Learning · Computer Science 2026-01-27 Barak Or

This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary…

Optimization and Control · Mathematics 2020-11-24 Hideaki Iiduka

A growing number of applications in particle physics and beyond use neural networks as unbinned likelihood ratio estimators applied to real or simulated data. Precision requirements on the inference tasks demand a high-level of stability…

High Energy Physics - Phenomenology · Physics 2025-03-04 G. Bruno De Luca , Benjamin Nachman , Eva Silverstein , Henry Zheng

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…

Machine Learning · Computer Science 2019-02-19 Eldad Haber , Lars Ruthotto

Scalable training of large models (like BERT and GPT-3) requires careful optimization rooted in model design, architecture, and system capabilities. From a system standpoint, communication has become a major bottleneck, especially on…

Machine Learning · Computer Science 2021-07-01 Hanlin Tang , Shaoduo Gan , Ammar Ahmad Awan , Samyam Rajbhandari , Conglong Li , Xiangru Lian , Ji Liu , Ce Zhang , Yuxiong He

This work examines the challenges of training neural networks using vector quantization using straight-through estimation. We find that a primary cause of training instability is the discrepancy between the model embedding and the…

Machine Learning · Computer Science 2023-05-16 Minyoung Huh , Brian Cheung , Pulkit Agrawal , Phillip Isola

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Machine Learning · Computer Science 2019-12-04 Michael R. Zhang , James Lucas , Geoffrey Hinton , Jimmy Ba

Background: Recent developments have made it possible to accelerate neural networks training significantly using large batch sizes and data parallelism. Training in an asynchronous fashion, where delay occurs, can make training even more…

Machine Learning · Computer Science 2020-02-14 Niv Giladi , Mor Shpigel Nacson , Elad Hoffer , Daniel Soudry

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning…

Training large-scale machine learning models poses distinct system challenges, given both the size and complexity of today's workloads. Recently, many organizations training state-of-the-art Generative AI models have reported cases of…

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

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…

Machine Learning · Computer Science 2018-02-12 Abhay Yadav , Sohil Shah , Zheng Xu , David Jacobs , Tom Goldstein

The Adam optimizer is the standard choice in deep learning applications. I propose a simple explanation of Adam's success: it makes each parameter's step size independent of the norms of the other parameters. Based on this principle I…

Machine Learning · Computer Science 2023-07-25 Jacob Jackson

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

Machine Learning · Computer Science 2021-03-03 Yasaman Esfandiari , Aditya Balu , Keivan Ebrahimi , Umesh Vaidya , Nicola Elia , Soumik Sarkar

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…

Machine Learning · Computer Science 2024-02-14 Xingjian Li , Pengkun Yang , Yangcheng Gu , Xueying Zhan , Tianyang Wang , Min Xu , Chengzhong Xu

Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent in data-driven learning problems as well as in scientific…

Optimization and Control · Mathematics 2025-01-13 Steffen Dereich , Arnulf Jentzen , Adrian Riekert