相关论文: Muon Optimizer Accelerates Grokking

Mutation analysis has many applications, such as assessing the quality of test cases, fault localization, test input generation, security analysis, etc. Such applications involve running test suite against a large number of program mutants…

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…

Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data. Previous research has linked this delayed generalization to…

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…

Mechanistic interpretability typically relies on post-hoc analysis of trained networks. We instead adopt an interventional approach: testing hypotheses a priori by modifying architectural topology to observe training dynamics. We study…

Recent developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as $\sf Muon$ and $\sf Scion$. After over a decade of $\sf Adam$'s dominance, these…

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it…

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…

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a…

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…

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great…

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…

Modern optimizers, like Muon, impose matrix-wise geometry constraints on their updates. These matrix-wise constraints can be unified under Linear Minimization Oracle (LMO) theory. However, all current methods impose fixed LMO geometries for…

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…

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…

Optimization algorithms are core methods by which machine learning models iteratively minimize loss functions, update parameters, learn from data, and improve performance. Momentum SGD and AdamW represent two important optimization…

Large language models (LLMs) have demonstrated impressive generalization and emergent capabilities, yet their pre-training remains computationally expensive and sensitive to optimization dynamics. While Adam-based optimizers offer fast…

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…

As machine learning models grow increasingly complex and computationally demanding, understanding the environmental impact of training decisions becomes critical for sustainable AI development. This paper presents a comprehensive empirical…

Zeroth-order (ZO) optimization has become increasingly popular and important in fine-tuning large language models (LLMs), especially on edge devices due to its ability to adjust the model to local data without the need for memory-intensive…