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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

Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum…

Chemical Physics · Physics 2025-10-01 Siwoo Lee , Adji Bousso Dieng

Post-Training Quantization (PTQ) is a critical strategy for efficient Large Language Models (LLMs) deployment. However, existing scaling laws primarily focus on general performance, overlooking crucial fine-grained factors and how…

Computation and Language · Computer Science 2026-04-23 Chenxi Zhou , Pengfei Cao , Jiang Li , Bohan Yu , Jinyu Ye , Jun Zhao , Kang Liu

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

Classicalization is a phenomenon of redistribution of energy - initially stored in few hard quanta - into the high occupation numbers of the soft modes, described by a final state that is approximately classical. Using an effective…

High Energy Physics - Theory · Physics 2018-04-18 Gia Dvali

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

Quantization Aware Training (QAT) is a neural network quantization technique that compresses model size and improves operational efficiency while effectively maintaining model performance. The paradigm of QAT is to introduce fake…

Computer Vision and Pattern Recognition · Computer Science 2025-04-25 Wenqiang Zhou , Zhendong Yu , Xinyu Liu , Jiaming Yang , Rong Xiao , Tao Wang , Chenwei Tang , Jiancheng Lv

Training large language models (LLMs) is computationally expensive, partly because the loss exhibits slow power-law convergence whose origin remains debatable. Through systematic analysis of toy models and empirical evaluation of LLMs, we…

Machine Learning · Computer Science 2026-02-04 Yizhou Liu , Ziming Liu , Cengiz Pehlevan , Jeff Gore

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

The prediction of learning curves for Natural Language Processing (NLP) models enables informed decision-making to meet specific performance objectives, while reducing computational overhead and lowering the costs associated with dataset…

Machine Learning · Computer Science 2025-10-21 Viktoria Schram , Markus Hiller , Daniel Beck , Trevor Cohn

Neural scaling laws and double-descent phenomena suggest that deep-network training obeys a simple macroscopic structure despite highly nonlinear optimization dynamics. We derive such structure directly from gradient descent in function…

Machine Learning · Computer Science 2026-01-09 Yizhou Zhang

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

Quantization is an essential step in the efficient deployment of deep learning models and as such is an increasingly popular research topic. An important practical aspect that is not addressed in the current literature is how to analyze and…

Machine Learning · Computer Science 2020-12-16 Shachar Gluska , Mark Grobman

Large language models (LLMs) have shown remarkable proficiency in generating text, benefiting from extensive training on vast textual corpora. However, LLMs may also acquire unwanted behaviors from the diverse and sensitive nature of their…

Computation and Language · Computer Science 2025-03-24 Zhiwei Zhang , Fali Wang , Xiaomin Li , Zongyu Wu , Xianfeng Tang , Hui Liu , Qi He , Wenpeng Yin , Suhang Wang

Deep learning models can exhibit what appears to be a sudden ability to solve a new problem as training time, training data, or model size increases, a phenomenon known as emergence. In this paper, we present a framework where each new…

Machine Learning · Computer Science 2025-04-30 Yoonsoo Nam , Nayara Fonseca , Seok Hyeong Lee , Chris Mingard , Ard A. Louis

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

Recently, 1-bit Large Language Models (LLMs) have emerged, showcasing an impressive combination of efficiency and performance that rivals traditional LLMs. Research by Wang et al. (2023); Ma et al. (2024) indicates that the performance of…

Machine Learning · Computer Science 2024-11-05 Majid Daliri , Zhao Song , Chiwun Yang

This paper provides a comprehensive overview of the principles, challenges, and methodologies associated with quantizing large-scale neural network models. As neural networks have evolved towards larger and more complex architectures to…

Machine Learning · Computer Science 2024-09-19 Yanshu Wang , Tong Yang , Xiyan Liang , Guoan Wang , Hanning Lu , Xu Zhe , Yaoming Li , Li Weitao

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

Fine-tuned transformer models have shown superior performances in many natural language tasks. However, the large model size prohibits deploying high-performance transformer models on resource-constrained devices. This paper proposes a…

Computation and Language · Computer Science 2024-10-01 Zi Yang , Samridhi Choudhary , Siegfried Kunzmann , Zheng Zhang