arXiv AI
Jul 28
Scale Weight Decay and Train Better
arXiv:2607. 23777v1 Announce Type: cross Abstract: The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data.
Convergence Bound and Critical Batch Size of Muon Optimizer
arXiv:2507. 01598v5 Announce Type: replace Abstract: 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.
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arXiv Machine Learning
Jun 30
To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters
arXiv:2603. 00742v2 Announce Type: replace Abstract: While Adam has long been the ubiquitous default optimizer for deep neural networks, Muon has recently seen rapid adoption due to its superior training speed.
arXiv AI
Jul 24
SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales
arXiv:2607. 20548v1 Announce Type: cross Abstract: Higher-order optimizers such as Muon and SOAP offer faster convergence than AdamW, but their computational cost and numerical stability challenges have limited adoption at scale.
arXiv Machine Learning
Aug 6
On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations
arXiv:2608. 04607v1 Announce Type: cross Abstract: Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs).
arXiv Machine Learning
1d ago
On the Principles Behind Neural Network Optimizers
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv Machine Learning
Jun 4
Muon in Associative Memory Learning: Training Dynamics and Scaling Laws
arXiv:2602. 05725v3 Announce Type: replace Abstract: Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory.
arXiv Machine Learning
Jun 26
DMuon: Efficient Distributed Muon Training with Near-Adam Overhead
arXiv:2606. 27153v1 Announce Type: cross Abstract: Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads.
arXiv AI
Jul 16
Reassessing Muon for Matrix Factorization
arXiv:2607. 13246v1 Announce Type: cross Abstract: Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training.
arXiv Machine Learning
Jun 3
MuLoCo: Muon is a practical inner optimizer for DiLoCo
arXiv:2505. 23725v3 Announce Type: replace Abstract: DiLoCo is a powerful framework for training large language models (LLMs), enabling larger optimal batch sizes and increased accelerator utilization under networking constraints.
arXiv Machine Learning
Jun 25
Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
arXiv:2606. 25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models.
arXiv Machine Learning
Jun 9
LiMuon: Light and Fast Muon Optimizer for Large Models
arXiv:2509. 14562v4 Announce Type: replace Abstract: Large models recently are widely applied in machine learning, so efficient training of large models has received widespread attention.
arXiv Machine Learning
Jun 17
The Implicit Bias of Steepest Descent with Mini-batch Stochastic Gradient
arXiv:2602. 11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries.