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Spectral optimizers such as Muon have recently shown strong empirical performance in large-scale language model training, but the source and extent of their advantage remain poorly understood. We study this question through the linear…

Machine Learning · Computer Science 2026-04-29 Juno Kim , Eshaan Nichani , Denny Wu , Alberto Bietti , Jason D. Lee

Recent developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as $\sf Muon$ and $\sf Scion$. After over a decade of $\sf Adam$'s dominance, these…

Machine Learning · Computer Science 2025-05-20 Artem Riabinin , Egor Shulgin , Kaja Gruntkowska , Peter Richtárik

Built upon the decision tree (DT) classification and regression idea, the subspace learning machine (SLM) has been recently proposed to offer higher performance in general classification and regression tasks. Its performance improvement is…

Machine Learning · Computer Science 2022-08-16 Hongyu Fu , Yijing Yang , Yuhuai Liu , Joseph Lin , Ethan Harrison , Vinod K. Mishra , C. -C. Jay Kuo

Sample efficiency in Reinforcement Learning (RL) has traditionally been driven by algorithmic enhancements. In this work, we demonstrate that scaling can also lead to substantial improvements. We conduct a thorough investigation into the…

Machine Learning · Computer Science 2024-12-04 Michal Nauman , Mateusz Ostaszewski , Krzysztof Jankowski , Piotr Miłoś , Marek Cygan

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants…

Optimization and Control · Mathematics 2026-05-27 Tim Tsz-Kit Lau , Weijie Su

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel…

Machine Learning · Computer Science 2022-04-19 Soumyajit Gupta , Gurpreet Singh , Raghu Bollapragada , Matthew Lease

This article introduces an enhanced particle swarm optimizer (PSO), termed Orthogonal PSO with Mutation (OPSO-m). Initially, it proposes an orthogonal array-based learning approach to cultivate an improved initial swarm for PSO,…

Neural and Evolutionary Computing · Computer Science 2024-05-22 Indu Bala , Dikshit Chauhan , Lewis Mitchell

Drones are effective for reducing human activity and interactions by performing tasks such as exploring and inspecting new environments, monitoring resources and delivering packages. Drones need a controller to maintain stability and to…

Systems and Control · Electrical Eng. & Systems 2021-05-19 Azin Shamshirgaran , Hamed Javidi , Dan Simon

Massive MIMO systems are seen by many researchers as a paramount technology toward next generation networks. This technology consists of hundreds of antennas that are capable of sending and receiving simultaneously a huge amount of data.…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-25 A. Dabah , H. Ltaief , Z. Rezki , M. -A. Arfaoui , M. -S. Alouini , D. Keyes

Electronic computers have evolved drastically over the past years with an ever-growing demand for improved performance. However, the transfer of information from memory and high energy consumption have emerged as issues that require…

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental…

Machine Learning · Computer Science 2026-02-10 Wenbo Gong , Javier Zazo , Qijun Luo , Puqian Wang , James Hensman , Chao Ma

In recent years, Large Language Models (LLMs) have exhibited remarkable capabilities, driving advancements in real-world applications. However, training LLMs on increasingly long input sequences imposes significant challenges due to high…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-14 Qiaoling Chen , Shenggui Li , Wei Gao , Peng Sun , Yonggang Wen , Tianwei Zhang

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

As Large Language Models (LLMs) are increasingly deployed in real-world applications, it is important to ensure their behaviors align with human values, societal norms, and ethical principles. However, safety alignment under Reinforcement…

Machine Learning · Computer Science 2026-02-02 Yifan Niu , Han Xiao , Dongyi Liu , Nuo Chen , Jia Li

Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…

Machine Learning · Computer Science 2024-03-18 James Kotary , Ferdinando Fioretto

In this paper, we introduce Dynamic Layer Operations (DLO), a novel approach for vertically scaling transformer-based Large Language Models (LLMs) by dynamically expanding, activating, or skipping layers using a sophisticated routing policy…

Machine Learning · Computer Science 2024-07-17 Zhen Tan , Daize Dong , Xinyu Zhao , Jie Peng , Yu Cheng , Tianlong Chen

Large language models (LLMs) have recently been used for sequential decision making in interactive environments. However, leveraging environment reward signals for continual LLM actor improvement is not straightforward. We propose Skill Set…

Machine Learning · Computer Science 2024-06-25 Kolby Nottingham , Bodhisattwa Prasad Majumder , Bhavana Dalvi Mishra , Sameer Singh , Peter Clark , Roy Fox

In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix…

Machine Learning · Computer Science 2026-05-25 Fangzhou Wu , Rikhav Shah , Sandeep Silwal , Qiuyi Zhang

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these…

Machine Learning · Computer Science 2025-10-28 Yehonathan Refael , Guy Smorodinsky , Tom Tirer , Ofir Lindenbaum

Power grid operators face increasing difficulties in the control room as the increase in energy demand and the shift to renewable energy introduce new complexities in managing congestion and maintaining a stable supply. Effective grid…