Related papers: Muon Outperforms Adam in Tail-End Associative Memo…

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…

Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…

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…

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…

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…

With the rapid development of natural language processing technology, large-scale language models (LLM) have achieved remarkable results in a variety of tasks. However, how to effectively train these huge models and improve their…

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…

Large Language Models (LLMs) are typically fine-tuned for reasoning tasks through a two-stage pipeline of Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL), a process fraught with catastrophic forgetting and suboptimal…

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

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…

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…

Reinforcement learning (RL), particularly RL from verifiable reward (RLVR), has become a crucial phase of training large language models (LLMs) and a key focus of current scaling efforts. However, optimization practices in RL largely follow…

Muon is a recently proposed optimizer that enforces orthogonality in parameter updates by projecting gradients onto the Stiefel manifold, leading to stable and efficient training in large-scale deep neural networks. Meanwhile, the…

Large language models (LLMs) are still struggling in aligning with human preference in complex tasks and scenarios. They are prone to overfit into the unexpected patterns or superficial styles in the training data. We conduct an empirical…

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…

Adaptive optimization methods (such as Adam) play a major role in LLM pretraining, significantly outperforming Gradient Descent (GD). Recent studies have proposed new smoothness assumptions on the loss function to explain the advantages of…

Orthogonal momentum gradient updates have emerged to overcome the limitations of vector-based optimizers like Adam. The vector-based optimizer Adam suffers from high memory costs and ill-conditioned momentum gradient updates. However,…

The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to…

Adam has been shown to outperform gradient descent on large language models by a larger margin than on other tasks, but it is unclear why. We show that a key factor in this performance gap is the heavy-tailed class imbalance found in…

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of…