Related papers: MUON+: Towards More Effective Muon via One Additio…

The Muon optimizer enjoys strong empirical performance and theoretical grounding. However, the super-linear cost of its orthonormalization step introduces increasing overhead with scale. To alleviate this cost, several works have attempted…

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…

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. We study Muon in a linear associative memory model with softmax…

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 pursuit of faster optimization algorithms remains an active and important research direction in deep learning. Recently, the Muon optimizer [JJB+24] has demonstrated promising empirical performance, but its theoretical foundation…

We demonstrate that Muon, the simplest instantiation of a second-order optimizer, explicitly expands the Pareto frontier over AdamW on the compute-time tradeoff. We find that Muon is more effective than AdamW in retaining data efficiency at…

The ever-growing scale of deep learning models and training data underscores the critical importance of efficient optimization methods. While preconditioned gradient methods such as Adam and AdamW are the de facto optimizers for training…

Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware…

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…

Recently, decomposing complex problems into simple subtasks--a crucial part of human-like natural planning--to solve the given problem has significantly boosted the performance of large language models (LLMs). However, leveraging such…

The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay…

Multi-Task Learning (MTL) is a foundational machine learning problem that has seen extensive development over the past decade. Recently, various optimization-based MTL approaches have been proposed to learn multiple tasks simultaneously by…

Matrix-based optimizers have demonstrated immense potential in training Large Language Models (LLMs), however, designing an ideal optimizer remains a formidable challenge. A superior optimizer must satisfy three core desiderata: efficiency,…

Orthonormalized updates accelerate training, improve stability, and enable robust hyperparameter transfer, but existing methods like Muon rely on dense matrix operations that clash with sharded weights in large-scale LLM training, causing…

Optimizers play an important role in both pretraining and finetuning stages when training large language models (LLMs). In this paper, we present an observation that full finetuning with the same optimizer as in pretraining achieves a…

The Muon optimizer has recently attracted attention due to its orthogonalized first-order updates, and a deeper theoretical understanding of its convergence behavior is essential for guiding practical applications; however, existing…

Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training…

Fine-tuning pretrained language models (PLMs) on downstream tasks has become common practice in natural language processing. However, most of the PLMs are vulnerable, e.g., they are brittle under adversarial attacks or imbalanced data,…

Recent state-of-the-art language models utilize a two-phase training procedure comprised of (i) unsupervised pre-training on unlabeled text, and (ii) fine-tuning for a specific supervised task. More recently, many studies have been focused…

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…