Related papers: Hyperparameter Transfer Enables Consistent Gains o…

Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight…

A central question in modern deep learning is how to design optimizers whose behavior remains stable as the network width $w$ increases. We address this question by interpreting several widely used neural-network optimizers, including…

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…

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 benchmark studies of…

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable…

Optimization lies at the core of modern deep learning, yet existing methods often face a fundamental trade-off between adapting to problem geometry and leveraging curvature utilization. Steepest descent algorithms adapt to different…

The rapid scaling of large language models (LLMs) has made low-precision training essential for reducing memory, improving efficiency, and enabling larger models and datasets. Existing convergence theories for adaptive optimizers, however,…

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal…

Adaptive optimizers like AdamW apply uniform hyperparameters across all parameter groups, ignoring heterogeneous optimization dynamics across layers and modules. We address this limitation by proposing MetaAdamW - a new optimizer that…

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…

One of the main challenges in optimal scaling of large language models (LLMs) is the prohibitive cost of hyperparameter tuning, particularly learning rate $\eta$ and batch size $B$. While techniques like $\mu$P (Yang et al., 2022) provide…

The Maximal Update Parametrization ($\mu$P) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new…

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models…

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…

Despite its popularity, several recent works question the effectiveness of MAML when test tasks are different from training tasks, thus suggesting various task-conditioned methodology to improve the initialization. Instead of searching for…

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…

Hyperparameter transfer across model architectures dramatically reduces the amount of compute necessary for tuning large language models (LLMs). The maximal update parameterization ({\mu}P) ensures transfer through principled mathematical…

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Pretrained language models (PLMs) are trained on massive corpora, but often need to specialize to specific domains. A parameter-efficient adaptation method suggests training an adapter for each domain on the task of language modeling. This…

Pre-training Large Language Models requires immense computational resources, making optimizer efficiency essential. The optimization landscape is highly anisotropic, with loss reduction driven predominantly by progress along flat…