Related papers: Muon Optimizes Under Spectral Norm Constraints

In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent method where the update direction is the minimizer of the…

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of…

In this article, we explore the use of various matrix norms for optimizing functions of weight matrices, a crucial problem in training large language models. Moving beyond the spectral norm underlying the Muon update, we leverage duals of…

The majority of parameters in neural networks are naturally represented as matrices. However, most commonly used optimizers treat these matrix parameters as flattened vectors during optimization, potentially overlooking their inherent…

Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW. This…

The recently introduced optimizer, Muon, has gained increasing attention due to its superior performance across a wide range of applications. However, its effectiveness in federated learning remains unexplored. To address this gap, this…

Large models recently are widely applied in artificial intelligence, so efficient training of large models has received widespread attention. More recently, a useful Muon optimizer is specifically designed for matrix-structured parameters…

The Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such…

Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight…

Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It performs comparably or favorably to AdamW but with greater memory efficiency. As we can expect from…

Matrix-structured parameters frequently appear in many artificial intelligence models such as large language models. More recently, an efficient Muon optimizer is designed for matrix parameters of large-scale models, and shows markedly…

The choice of optimizer significantly impacts the training efficiency and computational costs of large language models (LLMs). Recently, the Muon optimizer has demonstrated promising results by orthogonalizing parameter updates, improving…

Muon has recently shown promising results in LLM training. In this work, we study how to further improve Muon. We argue that Muon's orthogonalized update rule suppresses the emergence of heavy-tailed weight spectra and over-emphasizes the…

For a long period of time, Adam has served as the ubiquitous default choice for training deep neural networks. Recently, many new optimizers have been introduced, out of which Muon has perhaps gained the highest popularity due to its…

The rapid progress of large language models (LLMs) is increasingly constrained by memory and deployment costs, motivating compression methods for practical deployment. Many state-of-the-art compression pipelines leverage the low-rank…

Muon has recently emerged as a strong optimizer for large language model pre-training, orthogonalizing the momentum matrix via Newton--Schulz polar iterations. A natural intuition is that polar iterations, by flattening the singular…

Recent empirical research has demonstrated that deep learning optimizers based on the linear minimization oracle (LMO) over specifically chosen Non-Euclidean norm balls, such as Muon and Scion, outperform Adam-type methods in the training…

Recently, the Muon optimizer based on matrix orthogonalization has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling…

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to…

Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work,…