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Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance…

Machine Learning · Computer Science 2025-07-16 Zhengyu Chen , Siqi Wang , Teng Xiao , Yudong Wang , Shiqi Chen , Xunliang Cai , Junxian He , Jingang Wang

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of…

Machine Learning · Computer Science 2024-04-08 Hui Su , Zhi Tian , Xiaoyu Shen , Xunliang Cai

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model…

Machine Learning · Computer Science 2025-06-03 Andrei Panferov , Alexandra Volkova , Ionut-Vlad Modoranu , Vage Egiazarian , Mher Safaryan , Dan Alistarh

The success of today's large language models (LLMs) depends on the observation that larger models perform better. However, the origin of this neural scaling law, that loss decreases as a power law with model size, remains unclear. We…

Machine Learning · Computer Science 2026-05-05 Yizhou Liu , Ziming Liu , Jeff Gore

The current trend of scaling language models involves increasing both parameter count and training dataset size. Extrapolating this trend suggests that training dataset size may soon be limited by the amount of text data available on the…

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

The end-to-end autonomous driving paradigm has recently attracted lots of attention due to its scalability. However, existing methods are constrained by the limited scale of real-world data, which hinders a comprehensive exploration of the…

The scaling exponent $\alpha$ in neural scaling laws $L(N) \propto N^{-\alpha}$ is commonly treated as a fixed constant set by architecture and data. We present evidence that $\alpha$ depends systematically on the optimizer. In controlled…

Machine Learning · Computer Science 2026-05-29 Vansh Ramani , Shourya Vir Jain

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

While data scaling laws of large language models (LLMs) have been widely examined in the one-pass regime with massive corpora, their form under limited data and repeated epochs remains largely unexplored. This paper presents a theoretical…

Machine Learning · Computer Science 2026-03-16 Tingkai Yan , Haodong Wen , Binghui Li , Kairong Luo , Wenguang Chen , Kaifeng Lyu

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

Machine Learning · Computer Science 2024-05-24 Sotiris Anagnostidis , Gregor Bachmann , Imanol Schlag , Thomas Hofmann

Kaplan et al. and Hoffmann et al. developed influential scaling laws for the optimal model size as a function of the compute budget, but these laws yield substantially different predictions. We explain the discrepancy by reproducing the…

Machine Learning · Computer Science 2025-01-22 Tomer Porian , Mitchell Wortsman , Jenia Jitsev , Ludwig Schmidt , Yair Carmon

Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed…

Machine Learning · Computer Science 2026-05-14 Joshua Shay Kricheli , Alexander Lawrence Reid , Soumajyoti Sarkar , Venkata Gandikota , Paulo Shakarian

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of…

Machine Learning · Computer Science 2025-09-19 Konwoo Kim , Suhas Kotha , Percy Liang , Tatsunori Hashimoto

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest…

Machine Learning · Computer Science 2023-07-25 Ethan Caballero , Kshitij Gupta , Irina Rish , David Krueger

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

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…

Neural scaling laws have become foundational for optimizing large language model (LLM) training, yet they typically assume a single dense model output. This limitation effectively overlooks "Familial models, a transformative paradigm…

Machine Learning · Computer Science 2026-01-26 Huan Song , Qingfei Zhao , Ting Long , Shuyu Tian , Hongjun An , Jiawei Shao , Xuelong Li

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

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to…

Machine Learning · Computer Science 2026-03-31 Eric Czech , Zhiwei Xu , Yael Elmatad , Yixin Wang , William Held