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Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers…

Machine Learning · Computer Science 2025-10-31 Steffen Schotthöfer , Timon Klein , Jonas Kusch

Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. While Adam uses adaptive moment estimates to promote stability,…

Machine Learning · Computer Science 2026-02-23 Minxin Zhang , Yuxuan Liu , Hayden Schaeffer

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Systems and Control · Computer Science 2015-09-09 Adams Wei Yu , Wanli Ma , Yaoliang Yu , Jaime G. Carbonell , Suvrit Sra

To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…

Computer Vision and Pattern Recognition · Computer Science 2020-01-27 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Wenrui Dai , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

Muon has recently emerged as a competitive alternative to AdamW for large-scale pre-training, with orthogonalization via Newton-Schulz (NS) iterations as its core operation. Existing Muon variants apply a uniform NS schedule to all…

Machine Learning · Computer Science 2026-05-19 Xinlin Zhuang , Panyi Ouyang , Yichen Li , Jiangming Shi , Yizhang Chen , Shuman Liu , Ying Qian , Weiyang Liu , Haibo Zhang , Imran Razzak

In this paper, an orthogonal stochastic gradient descent (O-SGD) based learning approach is proposed to tackle the wireless channel over-training problem inherent in artificial neural network (ANN)-assisted MIMO signal detection. Our basic…

Signal Processing · Electrical Eng. & Systems 2020-02-26 Songyan Xue , Yi Ma , Rahim Tafazolli

Matrix-based optimizers have demonstrated immense potential in training Large Language Models (LLMs), however, designing an ideal optimizer remains a formidable challenge. A superior optimizer must satisfy three core desiderata: efficiency,…

Machine Learning · Computer Science 2026-05-06 Jinghui Yuan , Jiaxuan Zou , Shuo Wang , Yong Liu , Feiping Nie

We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural…

Machine Learning · Computer Science 2023-08-17 Adam N. McCaughan , Bakhrom G. Oripov , Natesh Ganesh , Sae Woo Nam , Andrew Dienstfrey , Sonia M. Buckley

Several recent empirical studies demonstrate that important machine learning tasks, e.g., training deep neural networks, exhibit low-rank structure, where the loss function varies significantly in only a few directions of the input space.…

Machine Learning · Computer Science 2022-06-17 Romain Cosson , Ali Jadbabaie , Anuran Makur , Amirhossein Reisizadeh , Devavrat Shah

Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training…

Machine Learning · Computer Science 2026-03-10 Peng Cheng , Jiucheng Zang , Qingnan Li , Liheng Ma , Yufei Cui , Yingxue Zhang , Boxing Chen , Ming Jian , Wen Tong

Training machine learning models on mobile devices has the potential of improving both privacy and accuracy of the models. However, one of the major obstacles to achieving this goal is the memory limitation of mobile devices. Reducing…

Audio and Speech Processing · Electrical Eng. & Systems 2020-01-27 Mary Gooneratne , Khe Chai Sim , Petr Zadrazil , Andreas Kabel , Françoise Beaufays , Giovanni Motta

The Muon optimizer enjoys strong empirical performance and theoretical grounding. However, the super-linear cost of its orthonormalization step introduces increasing overhead with scale. To alleviate this cost, several works have attempted…

Machine Learning · Computer Science 2025-12-22 Kwangjun Ahn , Noah Amsel , John Langford

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…

Machine Learning · Computer Science 2024-06-17 Mikhail Gorbunov , Nikolay Yudin , Vera Soboleva , Aibek Alanov , Alexey Naumov , Maxim Rakhuba

Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances…

Machine Learning · Computer Science 2026-05-20 Chongyu Fan , Gaowen Liu , Mingyi Hong , Ramana Rao Kompella , Sijia Liu

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

Machine Learning · Computer Science 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. Our investigation reveals that an orthogonal basis within each multidimensional weight's…

Machine Learning · Computer Science 2024-11-12 Daniel Coquelin , Katharina Flügel , Marie Weiel , Nicholas Kiefer , Charlotte Debus , Achim Streit , Markus Götz

We investigate the inherent bias of Stochastic Gradient Descent (SGD) toward learning low-rank weight matrices during the training of deep neural networks. Our results demonstrate that training with mini-batch SGD and weight decay induces a…

Machine Learning · Computer Science 2024-10-22 Tomer Galanti , Zachary S. Siegel , Aparna Gupte , Tomaso Poggio

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

Machine Learning · Computer Science 2014-04-17 Zheng Wang , Ming-Jun Lai , Zhaosong Lu , Wei Fan , Hasan Davulcu , Jieping Ye

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Numerical Analysis · Computer Science 2016-05-09 Yuan Lu , Jie Yang

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

Machine Learning · Computer Science 2020-11-11 Frithjof Gressmann , Zach Eaton-Rosen , Carlo Luschi