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The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data…

Machine Learning · Computer Science 2026-02-25 Alexandra Volkova , Mher Safaryan , Christoph H. Lampert , Dan Alistarh

Pretraining large language models (LLMs) is resource-intensive, often requiring months of training time even with high-end GPU clusters. There are two approaches of mitigating such computational demands: reusing smaller models to train…

Machine Learning · Computer Science 2025-06-17 Seng Pei Liew , Takuya Kato , Sho Takase

The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…

Machine Learning · Computer Science 2026-02-03 Chiwun Yang

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…

Scaling laws play a central role in the success of Large Language Models (LLMs), enabling the prediction of model performance relative to compute budgets prior to training. While Transformers have been the dominant architecture, recent…

Machine Learning · Computer Science 2026-02-23 Maximilian Beck , Kajetan Schweighofer , Sebastian Böck , Sebastian Lehner , Sepp Hochreiter

Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the…

Machine Learning · Computer Science 2025-07-04 Samira Abnar , Harshay Shah , Dan Busbridge , Alaaeldin Mohamed Elnouby Ali , Josh Susskind , Vimal Thilak

Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…

Artificial Intelligence · Computer Science 2025-09-30 Xinyi Wang , Shawn Tan , Shenbo Xu , Mingyu Jin , William Yang Wang , Rameswar Panda , Yikang Shen

Code Large Language Models (LLMs) are revolutionizing software engineering. However, scaling laws that guide the efficient training are predominantly analyzed on Natural Language (NL). Given the fundamental differences like strict syntax…

Computation and Language · Computer Science 2026-05-19 Xianzhen Luo , Wenzhen Zheng , Qingfu Zhu , Rongyi Zhang , Houyi Li , Siming Huang , YuanTao Fan , Wanxiang Che

Guided by the belief of the scaling law, large language models (LLMs) have achieved impressive performance in recent years. However, scaling law only gives a qualitative estimation of loss, which is influenced by various factors such as…

Computation and Language · Computer Science 2024-09-16 Chuhan Wu , Ruiming Tang

We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training…

Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…

Computation and Language · Computer Science 2025-05-28 Ayan Sengupta , Yash Goel , Tanmoy Chakraborty

Modern large language models (LLMs) represent a paradigm shift in what can plausibly be expected of machine learning models. The fact that LLMs can effectively generate sensible answers to a diverse range of queries suggests that they would…

Computation and Language · Computer Science 2024-05-27 Dean Wyatte , Fatemeh Tahmasbi , Ming Li , Thomas Markovich

Recently, Large Language Models (LLMs) have been widely adopted in a wide range of tasks, leading to increasing attention towards the research on how scaling LLMs affects their performance. Existing works, termed Scaling Laws, have…

Computation and Language · Computer Science 2025-09-23 Yizhe Xiong , Xiansheng Chen , Xin Ye , Hui Chen , Zijia Lin , Haoran Lian , Zhenpeng Su , Wei Huang , Jianwei Niu , Jungong Han , Guiguang Ding

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different…

Machine Learning · Computer Science 2024-10-03 Yangjun Ruan , Chris J. Maddison , Tatsunori Hashimoto

The current standard architecture of Large Language Models (LLMs) with QKV self-attention is briefly summarized, including the architecture of a typical Transformer. Scaling laws for compute (flops) and memory (parameters plus data) are…

General Literature · Computer Science 2025-11-18 William H. Press

Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are…

Code large language models (Code LLMs) are powerful but costly to train, with scaling laws predicting performance from model size, data, and compute. However, different programming languages (PLs) have varying impacts during pre-training…

Computation and Language · Computer Science 2025-12-16 Jian Yang , Shawn Guo , Lin Jing , Wei Zhang , Aishan Liu , Chuan Hao , Zhoujun Li , Wayne Xin Zhao , Xianglong Liu , Weifeng Lv , Bryan Dai

Research on scaling large language models (LLMs) has primarily focused on model parameters and training data size, overlooking the role of vocabulary size. We investigate how vocabulary size impacts LLM scaling laws by training models…

Computation and Language · Computer Science 2024-11-04 Chaofan Tao , Qian Liu , Longxu Dou , Niklas Muennighoff , Zhongwei Wan , Ping Luo , Min Lin , Ngai Wong

Modern LLM pre-training consumes vast amounts of compute and training data, making the scaling behavior, or scaling laws, of different models a key distinguishing factor. Discrete diffusion language models (DLMs) have been proposed as an…

Machine Learning · Computer Science 2026-02-17 Dimitri von Rütte , Janis Fluri , Omead Pooladzandi , Bernhard Schölkopf , Thomas Hofmann , Antonio Orvieto

Generalization abilities of well-trained large language models (LLMs) are known to scale predictably as a function of model size. In contrast to the existence of practical scaling laws governing pre-training, the quality of LLMs after…

Machine Learning · Computer Science 2024-12-09 Zifei Xu , Alexander Lan , Wanzin Yazar , Tristan Webb , Sayeh Sharify , Xin Wang