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This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance…

Machine Learning · Computer Science 2025-11-17 Thomas Pethick , Kimon Antonakopoulos , Antonio Silveti-Falls , Leena Chennuru Vankadara , Volkan Cevher

Deep learning is pervasive in our daily life, including self-driving cars, virtual assistants, social network services, healthcare services, face recognition, etc. However, deep neural networks demand substantial compute resources during…

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

Learning an explainable classifier often results in low accuracy model or ends up with a huge rule set, while learning a deep model is usually more capable of handling noisy data at scale, but with the cost of hard to explain the result and…

Artificial Intelligence · Computer Science 2022-11-11 Yuanlong Li , Gaopan Huang , Min Zhou , Chuan Fu , Honglin Qiao , Yan He

In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 Piotr Dollár , Mannat Singh , Ross Girshick

Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…

Statistics Theory · Mathematics 2023-03-29 Mingyao Ai , Holger Dette , Zhengfu Liu , Jun Yu

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

While the scaling laws of large language models (LLMs) training have been extensively studied, optimal inference configurations of LLMs remain underexplored. We study inference scaling laws (aka test-time scaling laws) and compute-optimal…

Artificial Intelligence · Computer Science 2025-03-04 Yangzhen Wu , Zhiqing Sun , Shanda Li , Sean Welleck , Yiming Yang

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

The internal structure and operation mechanism of large-scale language models are analyzed theoretically, especially how Transformer and its derivative architectures can restrict computing efficiency while capturing long-term dependencies.…

Machine Learning · Computer Science 2024-05-21 Taiyuan Mei , Yun Zi , Xiaohan Cheng , Zijun Gao , Qi Wang , Haowei Yang

Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…

Machine Learning · Computer Science 2024-01-30 Jonas Pfeiffer , Sebastian Ruder , Ivan Vulić , Edoardo Maria Ponti

Deep neural networks (DNN) are the state of the art on many engineering problems such as computer vision and audition. A key factor in the success of the DNN is scalability - bigger networks work better. However, the reason for this…

Machine Learning · Computer Science 2015-02-13 Andrew J. R. Simpson

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is…

Machine Learning · Computer Science 2018-11-22 Bryan Wilder , Bistra Dilkina , Milind Tambe

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Machine Learning · Computer Science 2022-01-11 Calvin Murdock , George Cazenavette , Simon Lucey

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

In the last decade, motivated by the success of Deep Learning, the scientific community proposed several approaches to make the learning procedure of Neural Networks more effective. When focussing on the way in which the training data are…

Machine Learning · Computer Science 2021-06-22 Simone Marullo , Matteo Tiezzi , Marco Gori , Stefano Melacci

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing…

Machine Learning · Computer Science 2023-09-18 Elias Frantar , Carlos Riquelme , Neil Houlsby , Dan Alistarh , Utku Evci

While deep learning models have replaced hand-designed features across many domains, these models are still trained with hand-designed optimizers. In this work, we leverage the same scaling approach behind the success of deep learning to…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Machine Learning · Computer Science 2025-07-28 Mohd Halim Mohd Noor , Ayokunle Olalekan Ige

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that…

Machine Learning · Statistics 2026-02-27 Dechen Zhang , Xuan Tang , Yingyu Liang , Difan Zou