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For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…

Machine Learning · Computer Science 2021-11-10 Preetum Nakkiran

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

Statistics Theory · Mathematics 2012-05-14 Peter M. Robinson

Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…

Machine Learning · Statistics 2024-10-14 Roman Worschech , Bernd Rosenow

Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on…

Artificial Intelligence · Computer Science 2025-11-04 Aske Plaat , Annie Wong , Suzan Verberne , Joost Broekens , Niki van Stein , Thomas Back

Does continued scaling of large language models (LLMs) yield diminishing returns? In this work, we show that short-task benchmarks may give an illusion of slowing progress, as even marginal gains in single-step accuracy can compound into…

Artificial Intelligence · Computer Science 2026-03-16 Akshit Sinha , Arvindh Arun , Shashwat Goel , Steffen Staab , Jonas Geiping

Scaling laws have played a major role in the modern AI revolution, providing practitioners predictive power over how the model performance will improve with increasing data, compute, and number of model parameters. This has spurred an…

Machine Learning · Computer Science 2026-01-16 Maissam Barkeshli , Alberto Alfarano , Andrey Gromov

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

Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using…

Computation and Language · Computer Science 2025-09-19 Yu Wang , Nan Yang , Liang Wang , Furu Wei , Fuli Feng

Larger models learn tasks smaller models do not. What drives this phenomenon? We develop a simple phenomenological argument that power-law scaling already suggests that a larger model will be able to learn a part of the data distribution…

Understanding how and why large language models (LLMs) fail is becoming a central challenge as models rapidly evolve and static evaluations fall behind. While automated probing has been enabled by dynamic test generation, existing…

Computation and Language · Computer Science 2026-02-16 Yue Huang , Zhengzhe Jiang , Yuchen Ma , Yu Jiang , Xiangqi Wang , Yujun Zhou , Yuexing Hao , Kehan Guo , Pin-Yu Chen , Stefan Feuerriegel , Xiangliang Zhang

Large language models (LLMs) demonstrate exceptional instruct-following ability to complete various downstream tasks. Although this impressive ability makes LLMs flexible task solvers, their performance in solving tasks also heavily relies…

Computation and Language · Computer Science 2024-06-03 Pengwei Zhan , Zhen Xu , Qian Tan , Jie Song , Ru Xie

As children acquire the knowledge of their language's morphology, they invariably discover the productive processes that can generalize to new words. Morphological learning is made challenging by the fact that even fully productive rules…

Computation and Language · Computer Science 2021-05-13 Caleb Belth , Sarah Payne , Deniz Beser , Jordan Kodner , Charles Yang

Previous work has shown that there exists a scaling law between the size of Language Models (LMs) and their zero-shot performance on different downstream NLP tasks. In this work, we show that this phenomenon does not hold when evaluating…

Computation and Language · Computer Science 2022-09-27 Joel Jang , Seonghyeon Ye , Minjoon Seo

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

Machine Learning · Computer Science 2024-11-12 Alex Havrilla , Wenjing Liao

Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet…

Machine Learning · Computer Science 2025-03-03 Kechen Li , Wenqi Zhu , Coralia Cartis , Tianbo Ji , Shiwei Liu

Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…

Artificial Intelligence · Computer Science 2025-09-17 Marylou Fauchard , Florian Carichon , Margarida Carvalho , Golnoosh Farnadi

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…

Machine Learning · Computer Science 2025-10-24 Baoqing Yue , Jinyuan Zhou , Zixi Wei , Jingtao Zhan , Qingyao Ai , Yiqun Liu

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

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

The scaling of large language models (LLMs) is a critical research area for the efficiency and effectiveness of model training and deployment. Our work investigates the transferability and discrepancies of scaling laws between Dense Models…

Machine Learning · Computer Science 2024-10-10 Siqi Wang , Zhengyu Chen , Bei Li , Keqing He , Min Zhang , Jingang Wang
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