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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

Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which…

Machine Learning · Statistics 2024-02-22 Vivien Cabannes , Elvis Dohmatob , Alberto Bietti

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

Recent studies have found that model performance has a smooth power-law relationship, or scaling laws, with training data and model size, for a wide range of problems. These scaling laws allow one to choose nearly optimal data and model…

Audio and Speech Processing · Electrical Eng. & Systems 2023-06-29 Yile Gu , Prashanth Gurunath Shivakumar , Jari Kolehmainen , Ankur Gandhe , Ariya Rastrow , Ivan Bulyko

Generative language models define distributions over sequences of tokens that can represent essentially any combination of data modalities (e.g., any permutation of image tokens from VQ-VAEs, speech tokens from HuBERT, BPE tokens for…

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

Data scaling has revolutionized research fields like natural language processing, computer vision, and robotics control, providing foundation models with remarkable multi-task and generalization capabilities. In this paper, we investigate…

Systems and Control · Electrical Eng. & Systems 2025-03-27 Shaohuai Liu , Lin Dong , Chao Tian , Le Xie

Molecular generative models, often employing GPT-style language modeling on molecular string representations, have shown promising capabilities when scaled to large datasets and model sizes. However, it remains unclear and subject to debate…

Machine Learning · Computer Science 2026-02-02 Dong Xu , Qihua Pan , Sisi Yuan , Jianqiang Li , Zexuan Zhu , Junkai Ji

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model…

Machine Learning · Statistics 2021-09-27 Amélie Chatelain , Amine Djeghri , Daniel Hesslow , Julien Launay , Iacopo Poli

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

In recent years, pretraining models have made significant advancements in the fields of natural language processing (NLP), computer vision (CV), and life sciences. The significant advancements in NLP and CV are predominantly driven by the…

Machine Learning · Computer Science 2024-07-02 Xiaohong Ji , Zhen Wang , Zhifeng Gao , Hang Zheng , Linfeng Zhang , Guolin Ke , Weinan E

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law…

Machine Learning · Computer Science 2026-05-05 Justin Lovelace , Christian Belardi , Srivatsa Kundurthy , Shriya Sudhakar , Kilian Q. Weinberger

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

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their…

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

In this work, we provide a large-scale empirical study of the scaling properties of multilingual neural machine translation models. We examine how increases in the model size affect the model performance and investigate the role of the…

Computation and Language · Computer Science 2023-02-21 Patrick Fernandes , Behrooz Ghorbani , Xavier Garcia , Markus Freitag , Orhan Firat

Neural scaling laws aim to characterize how out-of-sample error behaves as a function of model and training dataset size. Such scaling laws guide allocation of a computational resources between model and data processing to minimize error.…

Machine Learning · Computer Science 2024-07-02 Hong Jun Jeon , Benjamin Van Roy

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly…

Machine Learning · Computer Science 2025-09-17 Oliver Knitter , Dan Zhao , Stefan Leichenauer , Shravan Veerapaneni

In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws…

Machine Learning · Statistics 2026-02-06 Leonardo Defilippis , Florent Krzakala , Bruno Loureiro , Antoine Maillard

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM…

Machine Learning · Computer Science 2026-02-13 Francesco Cagnetta , Allan Raventós , Surya Ganguli , Matthieu Wyart