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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

Many deep architectures and self-supervised pre-training techniques have been proposed for human activity recognition (HAR) from wearable multimodal sensors. Scaling laws have the potential to help move towards more principled design by…

Machine Learning · Computer Science 2025-05-22 Tom Hoddes , Alex Bijamov , Saket Joshi , Daniel Roggen , Ali Etemad , Robert Harle , David Racz

Neural scaling laws predict how language model performance improves with increased training inputs. While aggregate metrics like validation loss can follow smooth power-law curves, individual downstream tasks exhibit diverse scaling…

Machine Learning · Computer Science 2026-05-11 Michael Y. Hu , Jane Pan , Ayush Rajesh Jhaveri , Nicholas Lourie , Kyunghyun Cho

In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…

Machine Learning · Computer Science 2025-02-14 Shihong Ding , Haihan Zhang , Hanzhen Zhao , Cong Fang

Recent empirical studies show three phenomena with increasing size of language models: compute-optimal size scaling, emergent capabilities, and performance plateauing. We present a simple unified mathematical framework to explain all of…

Information Theory · Computer Science 2024-10-17 Anuj K. Nayak , Lav R. Varshney

How close are neural networks to the best they could possibly do? Standard benchmarks cannot answer this because they lack access to the true posterior p(y|x). We use class-conditional normalizing flows as oracles that make exact posteriors…

Machine Learning · Computer Science 2026-02-13 Arian Khorasani , Nathaniel Chen , Yug D Oswal , Akshat Santhana Gopalan , Egemen Kolemen , Ravid Shwartz-Ziv

Large language models have demonstrated predictable scaling behaviors with respect to model parameters and training data. This study investigates whether a similar scaling relationship exist for vision-language models with respect to the…

Artificial Intelligence · Computer Science 2025-12-30 Tenghui Li , Guoxu Zhou , Xuyang Zhao , Qibin Zhao

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

As agent systems scale, skills accumulate into large reusable libraries, yet their scaling laws remain poorly understood. Across 15 frontier LLMs, 1,141 real-world skills, and over 3M routing or execution decisions, we identify two coupled…

Continual Pre-training (CPT) serves as a fundamental approach for adapting foundation models to domain-specific applications. Scaling laws for pre-training define a power-law relationship between dataset size and the test loss of an LLM.…

Machine Learning · Computer Science 2025-12-29 Lei Liu , Hao Zhu , Yue Shen , Zhixuan Chu , Jian Wang , Jinjie Gu , Kui Ren

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…

Machine Learning · Statistics 2024-10-14 Roman Worschech , Bernd Rosenow

The cross-entropy scaling law has long served as a key tool for guiding the development of large language models. It shows that cross-entropy loss decreases in a predictable power-law rate as the model size increases. However, recent…

Machine Learning · Computer Science 2026-03-03 Junxi Yan , Zixi Wei , Qingyao Ai , Yiqun Liu , Jingtao Zhan

We explore optimally training protein language models, an area of significant interest in biological research where guidance on best practices is limited. Most models are trained with extensive compute resources until performance gains…

Machine Learning · Computer Science 2024-11-05 Xingyi Cheng , Bo Chen , Pan Li , Jing Gong , Jie Tang , Le Song

Conventional optical character recognition (OCR) techniques segmented each character and then recognized. This made them prone to error in character segmentation, and devoid of context to exploit language models. Advances in sequence to…

Computer Vision and Pattern Recognition · Computer Science 2025-09-01 Shashank Vempati , Nishit Anand , Gaurav Talebailkar , Arpan Garai , Chetan Arora

In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data-…

Materials Science · Physics 2026-02-06 Max Großmann , Malte Grunert , Erich Runge

While scaling laws guide compute allocation for LLM pre-training, analogous prescriptions for reinforcement learning (RL) post-training of large language models (LLMs) remain poorly understood. We study the compute-optimal allocation of…

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

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…

Machine Learning · Computer Science 2024-06-28 Yasaman Bahri , Ethan Dyer , Jared Kaplan , Jaehoon Lee , Utkarsh Sharma

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i)…

Machine Learning · Computer Science 2021-09-17 Behrooz Ghorbani , Orhan Firat , Markus Freitag , Ankur Bapna , Maxim Krikun , Xavier Garcia , Ciprian Chelba , Colin Cherry

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a…

High Energy Physics - Phenomenology · Physics 2023-12-06 Joshua Batson , Yonatan Kahn