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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

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ''best-of-$N$'' (BoN) strategy has already demonstrated significant improvements in…

Machine Learning · Computer Science 2026-02-03 Muheng Li , Jian Qian , Wenlong Mou

The guidance of scaling laws has increased the resource demands of modern large language models (LLMs), yet it remains questionable whether these models utilize resources effectively under a fixed budget. Previous research has proved…

Machine Learning · Computer Science 2026-05-28 Wenjie Sun , Jinning Yang , Shuai Zhang , Mengnan Du

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

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the Random…

Machine Learning · Computer Science 2025-05-13 Francesco Cagnetta , Alessandro Favero , Antonio Sclocchi , Matthieu Wyart

Scaling-law has guided the language model designing for past years, however, it is worth noting that the scaling laws of NLP cannot be directly applied to RecSys due to the following reasons: (1) The amount of training samples and model…

Information Retrieval · Computer Science 2025-08-26 Xiao Lv , Jiangxia Cao , Shijie Guan , Xiaoyou Zhou , Zhiguang Qi , Yaqiang Zang , Ming Li , Ben Wang , Kun Gai , Guorui Zhou

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…

Machine Learning · Computer Science 2026-03-27 Shashank Subramanian , Alexander Kiefer , Arnur Nigmetov , Amir Gholami , Dmitriy Morozov , Michael W. Mahoney

Long-sequence decision-making, which is usually addressed through reinforcement learning (RL), is a critical component for optimizing strategic operations in dynamic environments, such as real-time bidding in computational advertising. The…

Artificial Intelligence · Computer Science 2026-01-16 Xiaowei Lv , Zhilin Zhang , Yijun Li , Yusen Huo , Siyuan Ju , Xuyan Li , Chunxiang Hong , Tianyu Wang , Yongcai Wang , Peng Sun , Chuan Yu , Jian Xu , Bo Zheng

Precise estimation of downstream performance in large language models (LLMs) prior to training is essential for guiding their development process. Scaling laws analysis utilizes the statistics of a series of significantly smaller sampling…

Computation and Language · Computer Science 2025-04-09 Yangyi Chen , Binxuan Huang , Yifan Gao , Zhengyang Wang , Jingfeng Yang , Heng Ji

This paper derives `Scaling Laws for Economic Impacts' -- empirical relationships between the training compute of Large Language Models (LLMs) and professional productivity. In a preregistered experiment, over 500 consultants, data…

General Economics · Economics 2025-12-25 Ali Merali

We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first…

Computation and Language · Computer Science 2025-10-29 Yanxi Chen , Xuchen Pan , Yaliang Li , Bolin Ding , Jingren Zhou

Symbolic regression (SR) aims to discover the underlying mathematical expressions that explain observed data. This holds promise for both gaining scientific insight and for producing inherently interpretable and generalizable models for…

Machine Learning · Computer Science 2026-02-05 David Otte , Jörg K. H. Franke , Arbër Zela , Fábio Ferreira , Frank Hutter

This paper derives "scaling laws"--empirical relationships between the training compute of Large Language Models (LLMs) and their performance--for economic outcomes. In a preregistered online experiment, 300 professional translators…

General Economics · Economics 2024-12-10 Ali Merali

We introduce a framework for optimizing domain-specific dataset construction in foundation model training. Specifically, we seek a cost-efficient way to estimate the quality of data sources (e.g. synthetically generated or filtered web…

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

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation…

Computation and Language · Computer Science 2024-06-25 Xuyang Shen , Dong Li , Ruitao Leng , Zhen Qin , Weigao Sun , Yiran Zhong

Deep graph models (e.g., graph neural networks and graph transformers) have become important techniques for leveraging knowledge across various types of graphs. Yet, the neural scaling laws on graphs, i.e., how the performance of deep graph…

Machine Learning · Computer Science 2024-12-03 Jingzhe Liu , Haitao Mao , Zhikai Chen , Tong Zhao , Neil Shah , Jiliang Tang

Large language models (LLMs) with long-context processing are still challenging because of their implementation complexity, training efficiency and data sparsity. To address this issue, a new paradigm named Online Long-context Processing…

Artificial Intelligence · Computer Science 2024-09-27 Lewei He , Tianyu Shi , Pengran Huang , Bingzhi Chen , Qianglong Chen , Jiahui Pan

Robustness and Effectiveness are critical aspects of developing dense retrieval models for real-world applications. It is known that there is a trade-off between the two. Recent work has addressed scaling laws of effectiveness in dense…

Information Retrieval · Computer Science 2025-06-02 Yu-An Liu , Ruqing Zhang , Jiafeng Guo , Maarten de Rijke , Yixing Fan , Xueqi Cheng

The remarkable progress in deep learning in recent years is largely driven by improvements in scale, where bigger models are trained on larger datasets for longer schedules. To predict the benefit of scale empirically, we argue for a more…

Machine Learning · Computer Science 2022-11-02 Ibrahim Alabdulmohsin , Behnam Neyshabur , Xiaohua Zhai