Variance-Adaptive Muon: Accelerating LLM Pretraining with NSR-Modulated and Variance-Scaled Momentum
Large Language Models (LLMs) achieve competitive performance across diverse natural language processing (NLP) tasks, yet pretraining is computationally demanding, making optimizer efficiency an important practical consideration. Muon accelerates LLM pretraining via orthogonal momentum updates that serve as a matrix analogue of the element-wise sign operator. Motivated by the recent perspective that Adam is a variance-adaptive sign update algorithm, we propose two variants of Muon, Muon-NSR and Muon-VS, which apply variance-adaptive normalization to momentum before orthogonalization. Muon-NSR applies noise-to-signal ratio (NSR) modulation, while Muon-VS performs variance-based scaling without introducing additional hyperparameters. Experiments on GPT-2 and LLaMA pretraining demonstrate that our proposed methods accelerate convergence and consistently achieve lower validation loss than both competitive, well-tuned AdamW and Muon baselines. For example, on the LLaMA-1.2B model, Muon-NSR and Muon-VS reduce the iterations required to reach the target validation loss by $1.36\times$ relative to the well-tuned Muon following the recent benchmark.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
MARS-M: When Variance Reduction Meets Matrices
Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent be…
Sign-Based Optimizers Are Effective Under Heavy-Tailed Noise
While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training larg…
NorMuon: Making Muon more efficient and scalable
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 …
HTMuon: Improving Muon via Heavy-Tailed Spectral Correction
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 o…
Image ClassificationOptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality
Orthogonalized momentum updates, as used in Muon-style optimizers, have recently shown strong empirical stability in large-scale deep learning. However, most current orthogonalized methods are still paired with fixed, ex…
Stochastic Optimization