Related papers: When Muon Optimizer Meets Adversarial Training: A …

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…

Muon is a recently developed matrix-aware optimizer that has shown strong results in transformer training, but its behavior in vision transformers (ViTs) is not yet well understood. We study Muon for ViT training, largely on ImageNet-100…

We present a comprehensive theoretical and empirical study of the Muon optimizer for training transformers only with a small to medium decoder (30M - 200M parameters), with an emphasis on its mathematical foundations, convergence properties…

The Muon optimizer has rapidly emerged as a powerful, geometry-aware alternative to AdamW, demonstrating strong performance in large-scale training of neural networks. However, a critical theory-practice disconnect exists: Muon's efficiency…

Neural network (NN) training is inherently a large-scale matrix optimization problem, yet the matrix structure of NN parameters has long been overlooked. Recently, the optimizer Muon \citep{jordanmuon}, which explicitly exploits this…

The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it remains unclear how to determine the learning rates for…

Despite the fundamental distinction between adversarial and natural training (AT and NT), AT methods generally adopt momentum SGD (MSGD) for the outer optimization. This paper aims to analyze this choice by investigating the overlooked role…

Adversarial training (AT) and its variants have spearheaded progress in improving neural network robustness to adversarial perturbations and common corruptions in the last few years. Algorithm design of AT and its variants are focused on…

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…

The Muon optimizer, based on matrix orthogonalization, has recently shown faster convergence and better computational efficiency over AdamW in LLM pre-training. However, the memory overhead of maintaining high-precision optimizer states…

Modern optimizers, like Muon, impose matrix-wise geometry constraints on their updates. These matrix-wise constraints can be unified under Linear Minimization Oracle (LMO) theory. However, all current methods impose fixed LMO geometries for…

Adversarial training (AT) is a simple yet effective defense against adversarial attacks to image classification systems, which is based on augmenting the training set with attacks that maximize the loss. However, the effectiveness of AT as…

Adversarial Training (AT) has been demonstrated to improve the robustness of deep neural networks (DNNs) against adversarial attacks. AT is a min-max optimization procedure where in adversarial examples are generated to train a more robust…

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,…

Adversarial Training (AT) with Projected Gradient Descent (PGD) is an effective approach for improving the robustness of the deep neural networks. However, PGD AT has been shown to suffer from two main limitations: i) high computational…

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…

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce…

Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization. However, its practical efficiency is limited by the…

The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap remains between its practical performance and theoretical understanding.…