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Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate $\eta$ and weight decay $\lambda$. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and…

Machine Learning · Computer Science 2025-11-25 Shane Bergsma , Nolan Dey , Gurpreet Gosal , Gavia Gray , Daria Soboleva , Joel Hestness

We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…

Optimization and Control · Mathematics 2024-12-23 Rajiv Sambharya , Bartolomeo Stellato

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern…

Machine Learning · Computer Science 2025-10-20 Zhiyuan Fan , Yifeng Liu , Qingyue Zhao , Angela Yuan , Quanquan Gu

In this work, we study optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps…

Machine Learning · Computer Science 2025-06-09 Thomas Pethick , Wanyun Xie , Kimon Antonakopoulos , Zhenyu Zhu , Antonio Silveti-Falls , Volkan Cevher

There is a recent trend in machine learning to increase model quality by growing models to sizes previously thought to be unreasonable. Recent work has shown that autoregressive generative models with cross-entropy objective functions…

Audio and Speech Processing · Electrical Eng. & Systems 2021-06-18 Jasha Droppo , Oguz Elibol

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation…

Machine Learning · Computer Science 2025-02-17 Lechao Xiao

Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when…

In order to improve reproducibility, deep reinforcement learning (RL) has been adopting better scientific practices such as standardized evaluation metrics and reporting. However, the process of hyperparameter optimization still varies…

Machine Learning · Computer Science 2023-06-05 Theresa Eimer , Marius Lindauer , Roberta Raileanu

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

Recent years have seen a growing interest and adoption of LLMs, with Mixture-of-Experts (MoE) emerging as a leading architecture in extremely large models. Currently, the largest open-source models reach over $1$T parameters. At such…

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

Machine Learning · Statistics 2024-06-25 Blake Bordelon , Alexander Atanasov , Cengiz Pehlevan

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…

Machine Learning · Computer Science 2025-05-30 Athanasios Glentis , Jiaxiang Li , Qiulin Shang , Andi Han , Ioannis Tsaknakis , Quan Wei , Mingyi Hong

Recently, Large Language Models (LLMs) have achieved remarkable success. A key factor behind this success is the scaling law observed by OpenAI. Specifically, for models with Transformer architecture, the test loss exhibits a power-law…

Machine Learning · Computer Science 2025-03-04 Yifang Chen , Xuyang Guo , Xiaoyu Li , Yingyu Liang , Zhenmei Shi , Zhao Song

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven…

Recent advances in large language models (LLMs) highlight a strong connection between intelligence and compression. Learned image compression, a fundamental task in modern data compression, has made significant progress in recent years.…

Computer Vision and Pattern Recognition · Computer Science 2025-08-13 Yuqi Li , Haotian Zhang , Li Li , Dong Liu , Feng Wu

Recent advances in large language models (LLMs) have been largely driven by scaling laws for individual models, which predict performance improvements as model parameters and data volume increase. However, the capabilities of any single LLM…

Machine Learning · Computer Science 2026-01-29 Dakuan Lu , Jiaqi Zhang , Cheng Yuan , Jiawei Shao , Xuelong Li

As we scale to more massive machine learning models, the frequent synchronization demands inherent in data-parallel approaches create significant slowdowns, posing a critical challenge to further scaling. Recent work develops an approach…

Machine Learning · Computer Science 2025-03-14 Zachary Charles , Gabriel Teston , Lucio Dery , Keith Rush , Nova Fallen , Zachary Garrett , Arthur Szlam , Arthur Douillard

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model…

Machine Learning · Computer Science 2025-06-03 Andrei Panferov , Alexandra Volkova , Ionut-Vlad Modoranu , Vage Egiazarian , Mher Safaryan , Dan Alistarh

Probabilistic Transformer (PT), a white-box probabilistic model for contextual word representation, has demonstrated substantial similarity to standard Transformers in both computational structure and downstream task performance on small…

Computation and Language · Computer Science 2026-04-29 Penghao Kuang , Haoyi Wu , Kewei Tu

Hyperparameter optimization (HPO) is critical for enhancing the performance of machine learning models, yet it often involves a computationally intensive search across a large parameter space. Traditional approaches such as Grid Search and…

Machine Learning · Computer Science 2024-12-24 Md. Tarek Hasan