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Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how…

Machine Learning · Computer Science 2025-03-18 Kairong Luo , Haodong Wen , Shengding Hu , Zhenbo Sun , Zhiyuan Liu , Maosong Sun , Kaifeng Lyu , Wenguang Chen

Large Language Models have driven significant AI advancements, yet their training is resource-intensive and highly sensitive to hyper-parameter selection. While scaling laws provide valuable guidance on model size and data requirements,…

Machine Learning · Computer Science 2026-05-21 Xingyu Xie , Kuangyu Ding , Shuicheng Yan , Kim-Chuan Toh , Tianwen Wei

We investigate the role of learning rate scheduling in the large-scale pre-training of large language models, focusing on its influence on downstream performance after supervised fine-tuning (SFT). Decay-based learning rate schedulers are…

Computation and Language · Computer Science 2026-03-18 Kazuki Yano , Shun Kiyono , Sosuke Kobayashi , Sho Takase , Jun Suzuki

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…

Machine Learning · Computer Science 2012-07-02 Yuhong Guo , Dale Schuurmans

Neural network structures have a critical impact on the accuracy and stability of forecasting. Neural architecture search procedures help design an optimal neural network according to some loss function, which represents a set of quality…

Machine Learning · Computer Science 2024-06-21 Mark Potanin , Kirill Vayser , Vadim Strijov

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

Deep neural networks have excelled on a wide range of problems, from vision to language and game playing. Neural networks very gradually incorporate information into weights as they process data, requiring very low learning rates. If the…

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

Machine Learning · Statistics 2024-06-25 Blake Bordelon , Alexander Atanasov , Cengiz Pehlevan

Dropout is a very effective way of regularizing neural networks. Stochastically "dropping out" units with a certain probability discourages over-specific co-adaptations of feature detectors, preventing overfitting and improving network…

Neural and Evolutionary Computing · Computer Science 2017-08-04 Pietro Morerio , Jacopo Cavazza , Riccardo Volpi , Rene Vidal , Vittorio Murino

Learning rate decay (lrDecay) is a \emph{de facto} technique for training modern neural networks. It starts with a large learning rate and then decays it multiple times. It is empirically observed to help both optimization and…

Machine Learning · Computer Science 2019-09-27 Kaichao You , Mingsheng Long , Jianmin Wang , Michael I. Jordan

If we want to train a neural network using any of the most popular optimization algorithms, we are immediately faced with a dilemma: how to set the various optimization and regularization hyperparameters? When computational resources are…

Machine Learning · Computer Science 2025-03-07 Sourabh Medapati , Priya Kasimbeg , Shankar Krishnan , Naman Agarwal , George Dahl

The optimal scheduling of interfering links in a dense wireless network with full frequency reuse is a challenging task. The traditional method involves first estimating all the interfering channel strengths then optimizing the scheduling…

Signal Processing · Electrical Eng. & Systems 2021-02-05 Wei Cui , Kaiming Shen , Wei Yu

Long training times of deep neural networks are a bottleneck in machine learning research. The major impediment to fast training is the quadratic growth of both memory and compute requirements of dense and convolutional layers with respect…

Machine Learning · Computer Science 2020-02-20 Mihailo Isakov , Michel A. Kinsy

Learning rate schedulers have been widely adopted in training deep neural networks. Despite their practical importance, there is a discrepancy between its practice and its theoretical analysis. For instance, it is not known what schedules…

Machine Learning · Computer Science 2022-06-15 Rui Pan , Haishan Ye , Tong Zhang

Momentum is a widely used technique for gradient-based optimizers in deep learning. In this paper, we propose a decaying momentum (\textsc{Demon}) rule. We conduct the first large-scale empirical analysis of momentum decay methods for…

Machine Learning · Computer Science 2021-07-02 John Chen , Cameron Wolfe , Zhao Li , Anastasios Kyrillidis

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal…

Artificial Intelligence · Computer Science 2026-01-09 Yunhua Zhou , Shuhao Xing , Junhao Huang , Xipeng Qiu , Qipeng Guo

We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple…

Machine Learning · Computer Science 2023-06-23 Xin Yuan , Pedro Savarese , Michael Maire

Large language models are increasingly trained in continual or open-ended settings, where the total training horizon is not known in advance. Despite this, most existing pretraining recipes are not anytime: they rely on horizon-dependent…

Machine Learning · Computer Science 2026-02-04 Alexandru Meterez , Pranav Ajit Nair , Depen Morwani , Cengiz Pehlevan , Sham Kakade

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of…

Machine Learning · Computer Science 2024-10-18 Alexander Hägele , Elie Bakouch , Atli Kosson , Loubna Ben Allal , Leandro Von Werra , Martin Jaggi

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on…

Machine Learning · Computer Science 2023-03-22 Brian R. Bartoldson , Bhavya Kailkhura , Davis Blalock