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Shampoo with Adam in the Preconditioner's eigenbasis (SOAP) has recently emerged as a promising optimization algorithm for neural network training, achieving superior training efficiency over both Adam and Shampoo in language modeling…

Machine Learning · Computer Science 2025-09-30 Yanqing Lu , Letao Wang , Jinbo Liu

Second-order methods offer an attractive path toward more sample-efficient LLM training, but their practical use is often blocked by the systems cost of maintaining and updating large matrix-based optimizer states. We introduce…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-18 Yishun Lu , Junhao Zhang , Zeyu Yang , Wes Armour

Shampoo and its efficient variant, SOAP, employ structured second-moment estimations and have shown strong performance for training neural networks (NNs). In practice, however, Shampoo typically requires step-size grafting with Adam to be…

Machine Learning · Statistics 2026-04-01 Wu Lin , Scott C. Lowe , Felix Dangel , Runa Eschenhagen , Zikun Xu , Roger B. Grosse

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific…

Machine Learning · Computer Science 2024-06-11 Satoki Ishikawa , Ryo Karakida

First order methods, which solely rely on gradient information, are commonly used in diverse machine learning (ML) and data analysis (DA) applications. This is attributed to the simplicity of their implementations, as well as low…

Machine Learning · Computer Science 2018-03-06 Sudhir B. Kylasa , Farbod Roosta-Khorasani , Michael W. Mahoney , Ananth Grama

First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…

Machine Learning · Computer Science 2020-02-05 Chih-Hao Fang , Sudhir B Kylasa , Fred Roosta , Michael W. Mahoney , Ananth Grama

Unstructured pruning reduces the memory footprint in deep neural networks (DNNs). Recently, researchers proposed different types of structural pruning intending to reduce also the computation complexity. In this work, we first suggest a new…

Artificial Intelligence · Computer Science 2021-10-22 Itay Hubara , Brian Chmiel , Moshe Island , Ron Banner , Seffi Naor , Daniel Soudry

We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive algorithms challenging. The best-known adaptive regret bounds…

Optimization and Control · Mathematics 2026-02-10 Ruichen Jiang , Zakaria Mhammedi , Mehryar Mohri , Aryan Mokhtari

Despite their better convergence properties compared to first-order optimizers, second-order optimizers for deep learning have been less popular due to their significant computational costs. The primary efficiency bottleneck in such…

Machine Learning · Computer Science 2023-10-30 Siddharth Singh , Zachary Sating , Abhinav Bhatele

The adoption of machine learning solutions is rapidly increasing across all parts of society. As the models grow larger, both training and inference of machine learning models is increasingly outsourced, e.g. to cloud service providers.…

Cryptography and Security · Computer Science 2024-10-16 Jonas Sander , Sebastian Berndt , Ida Bruhns , Thomas Eisenbarth

Scaling deep neural network (DNN) training to more devices can reduce time-to-solution. However, it is impractical for users with limited computing resources. FOSI, as a hybrid order optimizer, converges faster than conventional optimizers…

Machine Learning · Computer Science 2025-08-05 Shunxian Gu , Chaoqun You , Bangbang Ren , Lailong Luo , Junxu Xia , Deke Guo

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…

Optimization and Control · Mathematics 2022-01-20 Pham Duy Khanh , Boris Mordukhovich , Vo Thanh Phat , Dat Ba Tran

With increasing data and model complexities, the time required to train neural networks has become prohibitively large. To address the exponential rise in training time, users are turning to data parallel neural networks (DPNN) to utilize…

Machine Learning · Computer Science 2022-02-09 Daniel Coquelin , Charlotte Debus , Markus Götz , Fabrice von der Lehr , James Kahn , Martin Siggel , Achim Streit

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

Optimization and Control · Mathematics 2022-11-08 Zhaonan Qu , Wenzhi Gao , Oliver Hinder , Yinyu Ye , Zhengyuan Zhou

We present DASH (Deep Automated Supernova and Host classifier), a novel software package that automates the classification of the type, age, redshift, and host galaxy of supernova spectra. DASH makes use of a new approach that does not rely…

Instrumentation and Methods for Astrophysics · Physics 2019-12-06 Daniel Muthukrishna , David Parkinson , Brad Tucker

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic…

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…

Machine Learning · Statistics 2016-12-13 Shen-Yi Zhao , Ru Xiang , Ying-Hao Shi , Peng Gao , Wu-Jun Li

We study distributed (strongly convex) optimization problems over a network of agents, with no centralized nodes. The loss functions of the agents are assumed to be \textit{similar}, due to statistical data similarity or otherwise. In order…

Optimization and Control · Mathematics 2022-04-12 Ye Tian , Gesualdo Scutari , Tianyu Cao , Alexander Gasnikov

We introduce AdaSub, a stochastic optimization algorithm that computes a search direction based on second-order information in a low-dimensional subspace that is defined adaptively based on available current and past information. Compared…

Optimization and Control · Mathematics 2023-11-08 João Victor Galvão da Mata , Martin S. Andersen

Training massive-scale deep learning models on datasets spanning tens of terabytes presents critical challenges in hardware utilization and training reproducibility. In this paper, we identify and resolve profound data-loading bottlenecks…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-24 Kashish Mittal , Di Yu , Roozbeh Ketabi , Arushi Arora , Brendon Lapp , Peng Zhang