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Existing scaling laws for Large Language Models (LLMs), predominantly monotonic power laws, fail to explain emerging non-monotonic phenomena such as catastrophic overtraining and quantization-induced degradation, where performance…

Machine Learning · Computer Science 2026-05-25 Xu Ouyang , Deyi Liu , Yuhang Cai , Jing Liu , Yuan Yang , Chen Zheng , Thomas Hartvigsen , Yiyuan Ma

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…

High Energy Physics - Phenomenology · Physics 2026-05-29 Oz Amram , Darius A. Faroughy , Tjarko Gerdes , Anna Hallin , Gregor Kasieczka , Michael Krämer , Humberto Reyes-Gonzalez , David Shih

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

The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…

Machine Learning · Computer Science 2022-04-13 Sungyeop Lee , Junghyo Jo

Scaling laws have emerged as a unifying lens for understanding and guiding the training of large language models (LLMs). However, existing studies predominantly focus on the final-step loss, leaving open whether the entire loss dynamics…

Machine Learning · Computer Science 2026-02-17 Binghui Li , Fengling Chen , Zixun Huang , Lean Wang , Lei Wu

Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…

Systems and Control · Electrical Eng. & Systems 2025-03-18 Matteo Scandella , Michelangelo Bin , Thomas Parisini

Researchers build scaling laws to forecast the training performance of expensive large-scale runs with larger model size N and data size D. These laws assume that other training hyperparameters are optimally chosen, which can require…

Machine Learning · Computer Science 2026-02-12 Huaqing Zhang , Kaiyue Wen , Tengyu Ma

Modern retrieval systems are often driven by an underlying machine learning model. The goal of such systems is to identify and possibly rank the few most relevant items for a given query or context. Thus, such systems are typically…

Machine Learning · Statistics 2017-03-02 Elad ET. Eban , Mariano Schain , Alan Mackey , Ariel Gordon , Rif A. Saurous , Gal Elidan

Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the…

Computational Physics · Physics 2020-09-03 N. Saraceni , S. Cantori , S. Pilati

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

Speech Language Models (SLMs) aim to learn language from raw audio, without textual resources. Despite significant advances, our current models exhibit weak syntax and semantic abilities. However, if the scaling properties of neural…

Audio and Speech Processing · Electrical Eng. & Systems 2024-12-13 Santiago Cuervo , Ricard Marxer

What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…

Machine Learning · Computer Science 2025-07-08 Shikai Qiu , Lechao Xiao , Andrew Gordon Wilson , Jeffrey Pennington , Atish Agarwala

Large Language Models (LLMs) have shown remarkable reasoning performance but struggle with multi-step deductive reasoning involving a series of rule application steps, especially when rules are presented non-sequentially. Our preliminary…

Computation and Language · Computer Science 2024-08-27 Siyuan Wang , Zhongyu Wei , Yejin Choi , Xiang Ren

Large language models (LLMs) have demonstrated remarkable performance across a wide range of industrial applications, from search and recommendation systems to generative tasks. Although scaling laws indicate that larger models generally…

This paper investigates the scaling properties of Recurrent Neural Network Language Models (RNNLMs). We discuss how to train very large RNNs on GPUs and address the questions of how RNNLMs scale with respect to model size, training-set…

Computation and Language · Computer Science 2015-02-03 Will Williams , Niranjani Prasad , David Mrva , Tom Ash , Tony Robinson

Large Language Models (LLMs) are unable to reliably reason about specific physical systems. Attempts to imbue LLMs with knowledge of the necessary physics concepts have shown great promise, but explainability and validation remain open…

Artificial Intelligence · Computer Science 2026-05-22 Sean Memery , Kartic Subr

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…

$\textbf{Formal version available at}$ https://cell.com/patterns/fulltext/S2666-3899(23)00200-3 Networks of spiking neurons underpin the extraordinary information-processing capabilities of the brain and have become pillar models in…

Neural and Evolutionary Computing · Computer Science 2023-09-18 Gehua Ma , Rui Yan , Huajin Tang

This paper investigates the classification capability of small-scale spiking neural networks based on the Leaky Integrate-and-Fire (LIF) neuron model. We analyze the relationship between classification accuracy and three factors: the number…

Neurons and Cognition · Quantitative Biology 2026-01-22 Zhengdi Zhang , Cong Han , Wenjun Xia

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
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