Related papers: MARS-M: When Variance Reduction Meets Matrices

Masked Language Modeling (MLM) has proven to be an essential component of Vision-Language (VL) pretraining. To implement MLM, the researcher must make two design choices: the masking strategy, which determines which tokens to mask, and the…

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…

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by…

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 large language models…

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even…

Fine-tuning Large Language Models (LLMs) is essential for adapting pre-trained models to downstream tasks. Yet traditional first-order optimizers such as Stochastic Gradient Descent (SGD) and Adam incur prohibitive memory and computational…

The Muon optimizer is consistently faster than Adam in training Large Language Models (LLMs), yet the mechanism underlying its success remains unclear. This paper demystifies this mechanism through the lens of associative memory. By…

Large language models (LLMs) deployed on edge servers are increasingly used in latency-sensitive applications such as personalized assistants, recommendation, and content moderation. However, the non-stationary nature of user data…

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…

Large Reasoning Models (LRMs) face two fundamental limitations: excessive token consumption when overanalyzing simple information processing tasks, and inability to access up-to-date knowledge beyond their training data. We introduce MARS…

Optimizers are crucial for the efficient training of Large Language Models (LLMs). While AdamW is the de facto standard, recent structure-aware optimizers like Muon have emerged, which regularize gradient updates by operating on entire…

With increasing size of large language models (LLMs), full-parameter fine-tuning imposes substantial memory demands. To alleviate this, we propose a novel memory-efficient training paradigm called Momentum Low-rank compression (MLorc). The…

Orthogonalized-momentum optimizers such as Muon improve transformer training by approximately whitening/orthogonalizing matrix-valued momentum updates via a short polar-decomposition iteration. However, polar-factor approximations typically…

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…

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods…

Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances…

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 developments have shown that Muon-type optimizers based on linear minimization oracles (LMOs) over non-Euclidean norm balls have the potential to get superior practical performance than Adam-type methods in the training of large…

Gradient orthogonalization is a simple strategy that shows great utility in speeding up gradient descent. The Muon optimizer (Jordan, Jin, et al., 2024) combines gradient orthogonalization with first-order momentum and achieves significant…

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…