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Large language models (LLMs) have made remarkable advances in recent years, with scaling laws playing a critical role in this rapid progress. In this paper, we empirically investigate how a critical hyper-parameter, i.e., the global batch…

Computation and Language · Computer Science 2024-12-03 Xian Shuai , Yiding Wang , Yimeng Wu , Xin Jiang , Xiaozhe Ren

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…

Artificial Intelligence · Computer Science 2026-01-09 Yunhua Zhou , Shuhao Xing , Junhao Huang , Xipeng Qiu , Qipeng Guo

State-of-the-art LLMs are powered by scaling -- scaling model size, dataset size and cluster size. It is economically infeasible to extensively tune hyperparameter for the largest runs. Instead, approximately optimal hyperparameters must be…

Machine Learning · Computer Science 2025-02-25 Johan Bjorck , Alon Benhaim , Vishrav Chaudhary , Furu Wei , Xia Song

Pretraining large language models is a costly process. To make this process more efficient, several methods have been proposed to optimize model architecture/parametrization and hardware use. On the parametrization side, $\mu P$ (Maximal…

Machine Learning · Computer Science 2025-06-19 Soufiane Hayou , Liyuan Liu

In recent years, Large Language Models (LLMs) have made significant strides towards Artificial General Intelligence. However, training these models from scratch requires substantial computational resources and vast amounts of text data. In…

Computation and Language · Computer Science 2024-10-03 Wenzhen Zheng , Wenbo Pan , Xu Xu , Libo Qin , Li Yue , Ming Zhou

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other…

Computation and Language · Computer Science 2024-09-13 Yikang Shen , Matthew Stallone , Mayank Mishra , Gaoyuan Zhang , Shawn Tan , Aditya Prasad , Adriana Meza Soria , David D. Cox , Rameswar Panda

Continual learning (CL) in large language models (LLMs) is an evolving domain that focuses on developing efficient and sustainable training strategies to adapt models to emerging knowledge and achieve robustness in dynamic environments. Our…

Computation and Language · Computer Science 2025-02-13 Çağatay Yıldız , Nishaanth Kanna Ravichandran , Nitin Sharma , Matthias Bethge , Beyza Ermis

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

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in…

Scaling laws guide the development of large language models (LLMs) by offering estimates for the optimal balance of model size, tokens, and compute. More recently, loss-to-loss scaling laws that relate losses across pretraining datasets and…

Machine Learning · Computer Science 2026-05-21 Prasanna Mayilvahanan , Thaddäus Wiedemer , Sayak Mallick , Matthias Bethge , Wieland Brendel

Despite recent progress in optimal hyperparameter transfer under model and dataset scaling, no unifying explanatory principle has been established. For Adam and Scion optimizers, we discover that joint optimal scaling across model and…

Machine Learning · Computer Science 2026-01-28 Oleg Filatov , Jiangtao Wang , Jan Ebert , Stefan Kesselheim

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold…

Machine Learning · Computer Science 2025-04-22 Hanlin Zhang , Depen Morwani , Nikhil Vyas , Jingfeng Wu , Difan Zou , Udaya Ghai , Dean Foster , Sham Kakade

While protein language models (pLMs) have transformed biological research, the scaling laws governing their improvement remain underexplored. By adapting methodologies from NLP scaling laws, we investigated the optimal ratio between model…

Biomolecules · Quantitative Biology 2024-06-27 Yaiza Serrano , Álvaro Ciudad , Alexis Molina

Hyperparameter transfer allows extrapolating optimal optimization hyperparameters from small to large scales, making it critical for training large language models (LLMs). This is done either by fitting a scaling law to the hyperparameters…

Machine Learning · Computer Science 2026-05-21 Dayal Singh Kalra , Maissam Barkeshli

Recent research has highlighted the importance of dataset size in scaling language models. However, large language models (LLMs) are notoriously token-hungry during pre-training, and high-quality text data on the web is approaching its…

Machine Learning · Computer Science 2023-10-10 Fuzhao Xue , Yao Fu , Wangchunshu Zhou , Zangwei Zheng , Yang You

Batch size scheduling (BSS) plays a critical role in large-scale deep learning training, influencing both optimization dynamics and computational efficiency. Yet, its theoretical foundations remain poorly understood. In this work, we show…

Machine Learning · Computer Science 2026-02-24 Jinbo Wang , Binghui Li , Zhanpeng Zhou , Mingze Wang , Yuxuan Sun , Jiaqi Zhang , Xunliang Cai , Lei Wu

While Large Language Models (LLMs) have exhibited remarkable emergent capabilities through extensive pre-training, they still face critical limitations in generalizing to specialized domains and handling diverse linguistic variations, known…

Computation and Language · Computer Science 2025-05-28 Jinwu Hu , Zhitian Zhang , Guohao Chen , Xutao Wen , Chao Shuai , Wei Luo , Bin Xiao , Yuanqing Li , Mingkui Tan

Transferring the optimal learning rate from small to large neural networks can enable efficient training at scales where hyperparameter tuning is otherwise prohibitively expensive. To this end, the Maximal Update Parameterization (muP)…

Machine Learning · Computer Science 2026-02-16 Atli Kosson , Jeremy Welborn , Yang Liu , Martin Jaggi , Xi Chen

Low-Rank Adaptation (LoRA) is a standard tool for parameter-efficient finetuning of large models. While it induces a small memory footprint, its training dynamics can be surprisingly complex as they depend on several hyperparameters such as…

Machine Learning · Computer Science 2026-02-09 Nan Chen , Soledad Villar , Soufiane Hayou

While large language models (LLMs) often adopt finetuning to unlock their capabilities for downstream applications, our understanding on the inductive biases (especially the scaling properties) of different finetuning methods is still…

Computation and Language · Computer Science 2024-02-28 Biao Zhang , Zhongtao Liu , Colin Cherry , Orhan Firat
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