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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…

Machine Learning · Computer Science 2025-10-07 Shuche Wang , Fengzhuo Zhang , Jiaxiang Li , Cunxiao Du , Chao Du , Tianyu Pang , Zhuoran Yang , Mingyi Hong , Vincent Y. F. Tan

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…

Machine Learning · Computer Science 2025-12-23 Yiheng Zhang , Shaowu Wu , Yuanzhuo Xu , Jiajun Wu , Shang Xu , Steve Drew , Xiaoguang Niu

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare…

Machine Learning · Computer Science 2025-06-04 Leshem Choshen , Yang Zhang , Jacob Andreas

Neural scaling laws have driven significant advancements in machine learning, particularly in domains like language modeling and computer vision. However, the exploration of neural scaling laws within robotics has remained relatively…

Robotics · Computer Science 2025-01-28 Sebastian Sartor , Neil Thompson

We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…

Machine Learning · Computer Science 2026-01-27 Javier Porras-Valenzuela , Samar Hadou , Alejandro Ribeiro

Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…

Machine Learning · Computer Science 2026-02-19 Akiyoshi Tomihari , Issei Sato

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…

The scaling laws for recommender systems have been increasingly validated, where MetaFormer-based architectures consistently benefit from increased model depth, hidden dimensionality, and user behavior sequence length. However, whether…

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…

Machine Learning · Computer Science 2026-05-11 Dingzhi Yu , Hongyi Tao , Yuanyu Wan , Luo Luo , Lijun Zhang

Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…

Machine Learning · Computer Science 2020-09-24 Luke Metz , Niru Maheswaranathan , C. Daniel Freeman , Ben Poole , Jascha Sohl-Dickstein

After their successful debut in natural language processing, Transformer architectures are now becoming the de-facto standard in many domains. An obstacle for their deployment over new modalities is the architectural configuration: the…

Machine Learning · Computer Science 2021-06-10 Noam Wies , Yoav Levine , Daniel Jannai , Amnon Shashua

Ad hoc networking specific challenges foster a strong research effort on efficient protocols design. Routing protocols based on a self-organized structure have been studied principally for the robustness and the scalability they provide. On…

Networking and Internet Architecture · Computer Science 2016-08-16 Hervé Rivano , Fabrice Theoleyre , Fabrice Valois

MLP is a heavily used backbone in modern deep learning (DL) architectures for supervised learning on tabular data, and AdamW is the go-to optimizer used to train tabular DL models. Unlike architecture design, however, the choice of…

Machine Learning · Computer Science 2026-04-20 Yury Gorishniy , Ivan Rubachev , Dmitrii Feoktistov , Artem Babenko

In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…

Machine Learning · Computer Science 2018-12-12 Prasad Cheema , Mehrisadat M. Alamdari , Gareth A. Vio

Improvements in language model capabilities are often attributed to increasing model size or training data, but in some cases smaller models trained on curated data or with different architectural decisions can outperform larger ones…

A data mixture refers to how different data sources are combined to train large language models, and selecting an effective mixture is crucial for optimal downstream performance. Existing methods either conduct costly searches directly on…

Machine Learning · Computer Science 2026-05-07 Jingwei Li , Xinran Gu , Jingzhao Zhang

AI systems are increasingly deployed in high-stakes contexts (medical diagnosis, legal research, financial analysis) under the assumption they can be governed by norms. This paper demonstrates that the assumption is formally invalid for…

Artificial Intelligence · Computer Science 2026-03-03 Radha Sarma

Conventional scaling of neural networks typically involves designing a base network and growing different dimensions like width, depth, etc. of the same by some predefined scaling factors. We introduce an automated scaling approach…

Machine Learning · Computer Science 2024-02-21 Akash Guna R. T , Arnav Chavan , Deepak Gupta

The choice of optimizer significantly impacts the training efficiency and computational costs of large language models (LLMs). Recently, the Muon optimizer has demonstrated promising results by orthogonalizing parameter updates, improving…

Machine Learning · Computer Science 2025-10-08 Zichong Li , Liming Liu , Chen Liang , Weizhu Chen , Tuo Zhao

We study the compute-optimal trade-off between model and training data set sizes for large neural networks. Our result suggests a linear relation similar to that supported by the empirical analysis of chinchilla. While that work studies…

Machine Learning · Computer Science 2023-10-20 Hong Jun Jeon , Benjamin Van Roy