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We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps: $$L(s) = L_0 + A\cdot S_1^{-\alpha} - C\cdot S_2,$$ where $L(s)$ is the…

Computation and Language · Computer Science 2024-10-28 Howe Tissue , Venus Wang , Lu Wang

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal image$\leftrightarrow$text models, and mathematical problem solving. In all cases autoregressive…

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse…

Scaling laws for large language models (LLMs) have provided useful guidance in training ever larger models for predictable performance gains. Time series forecasting shares a similar sequential structure to language, and is amenable to…

Machine Learning · Computer Science 2025-01-09 Thomas D. P. Edwards , James Alvey , Justin Alsing , Nam H. Nguyen , Benjamin D. Wandelt

Recent work has shown that, in generative modeling, cross-entropy loss improves smoothly with model size and training compute, following a power law plus constant scaling law. One challenge in extending these results to reinforcement…

Machine Learning · Computer Science 2023-02-21 Jacob Hilton , Jie Tang , John Schulman

Neural scaling laws have driven significant advancements in machine learning, particularly in domains like language modeling and computer vision. However, the exploration of neural scaling laws within robotics has remained relatively…

Robotics · Computer Science 2025-01-28 Sebastian Sartor , Neil Thompson

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

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

When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…

Machine Learning · Computer Science 2020-04-24 Utkarsh Sharma , Jared Kaplan

Large language models (LLMs) have shown strong results on a range of applications, including regression and scoring tasks. Typically, one obtains outputs from an LLM via autoregressive sampling from the model's output distribution. We show…

Computation and Language · Computer Science 2024-11-04 Michal Lukasik , Harikrishna Narasimhan , Aditya Krishna Menon , Felix Yu , Sanjiv Kumar

Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…

Computation and Language · Computer Science 2026-04-08 Alexandros Christoforos

While large language models (LLMs) have emerged as powerful decision-makers across a wide range of single-agent and stationary environments, fewer efforts have been devoted to settings where LLMs must engage in \emph{repeated} and…

Multiagent Systems · Computer Science 2026-02-27 Xiangyu Liu , Di Wang , Zhe Feng , Aranyak Mehta

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

Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many…

Machine Learning · Computer Science 2024-05-16 Jinyeop Song , Ziming Liu , Max Tegmark , Jeff Gore

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

We introduce compression laws for language language models (LLMs). While recent scaling laws have sought to understand how LLMs scale with respect to model size, pre-training data, and computational resources, we focus on understanding how…

Computation and Language · Computer Science 2025-04-08 Ayan Sengupta , Siddhant Chaudhary , Tanmoy Chakraborty

The scaling law is becoming a fundamental law in many machine learning areas. That is, test error falls off with the power law when increasing training data, model size, and computing resource. However, whether this law is suitable for the…

Software Engineering · Computer Science 2024-02-21 Jiayi Lin , Hande Dong , Yutao Xie , Lei Zhang

Sequence models, such as Large Language Models (LLMs) and autoregressive image generators, have a tendency to memorize and inadvertently leak sensitive information. While this tendency has critical legal implications, existing tools are…

Cryptography and Security · Computer Science 2025-06-06 Lorenzo Rossi , Michael Aerni , Jie Zhang , Florian Tramèr

How does scaling the number of parameters in large language models (LLMs) affect their core capabilities? We study two natural scaling techniques -- weight pruning and simply training a smaller or larger model, which we refer to as dense…

Computation and Language · Computer Science 2023-10-10 Tian Jin , Nolan Clement , Xin Dong , Vaishnavh Nagarajan , Michael Carbin , Jonathan Ragan-Kelley , Gintare Karolina Dziugaite