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We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when…

Machine Learning · Statistics 2021-01-05 Aitor Lewkowycz , Guy Gur-Ari

Scale of data and scale of computation infrastructures together enable the current deep learning renaissance. However, training large-scale deep architectures demands both algorithmic improvement and careful system configuration. In this…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-21 Shang-Xuan Zou , Chun-Yen Chen , Jui-Lin Wu , Chun-Nan Chou , Chia-Chin Tsao , Kuan-Chieh Tung , Ting-Wei Lin , Cheng-Lung Sung , Edward Y. Chang

Why do neural networks trained with large learning rates for a longer time often lead to better generalization? In this paper, we delve into this question by examining the relation between training and testing loss in neural networks.…

Machine Learning · Computer Science 2024-01-23 Yinuo Ren , Chao Ma , Lexing Ying

The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely…

Computer Vision and Pattern Recognition · Computer Science 2015-10-16 Bharat Singh , Soham De , Yangmuzi Zhang , Thomas Goldstein , Gavin Taylor

The unprecedented growth of deep learning models has enabled remarkable advances but introduced substantial computational bottlenecks. A key factor contributing to training efficiency is batch-size and learning-rate scheduling in stochastic…

Machine Learning · Computer Science 2025-08-08 Hikaru Umeda , Hideaki Iiduka

The learning rate is one of the most important hyperparameters in deep learning, and how to control it is an active area within both AutoML and deep learning research. Approaches for learning rate control span from classic optimization to…

Machine Learning · Computer Science 2025-07-03 Micha Henheik , Theresa Eimer , Marius Lindauer

To understand how deep learning works, it is crucial to understand the training dynamics of neural networks. Several interesting hypotheses about these dynamics have been made based on empirically observed phenomena, but there exists a…

Machine Learning · Statistics 2021-11-16 Nikhil Ghosh , Song Mei , Bin Yu

Most theoretical studies explaining the regularization effect in deep learning have only focused on gradient descent with a sufficient small learning rate or even gradient flow (infinitesimal learning rate). Such researches, however, have…

Machine Learning · Computer Science 2020-12-17 Wei Huang , Weitao Du , Richard Yi Da Xu , Chunrui Liu

We propose a novel explanation method that explains the decisions of a deep neural network by investigating how the intermediate representations at each layer of the deep network were refined during the training process. This way we can a)…

Machine Learning · Computer Science 2021-09-14 Lukas Pfahler , Katharina Morik

Distributed machine learning is critical for training deep learning models on large datasets with numerous parameters. Current research primarily focuses on leveraging additional hardware resources and powerful computing units to accelerate…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-03 Kuan-Wei Lu , Ding-Yong Hong , Pangfeng Liu , Jan-Jan Wu

The learning rate is one of the most important hyper-parameters for model training and generalization. However, current hand-designed parametric learning rate schedules offer limited flexibility and the predefined schedule may not match the…

Machine Learning · Computer Science 2019-09-24 Zhen Xu , Andrew M. Dai , Jonas Kemp , Luke Metz

Modern deep neural network training is typically based on mini-batch stochastic gradient optimization. While the use of large mini-batches increases the available computational parallelism, small batch training has been shown to provide…

Machine Learning · Computer Science 2018-04-23 Dominic Masters , Carlo Luschi

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…

Machine Learning · Statistics 2025-10-30 Andrea Montanari , Pierfrancesco Urbani

Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and…

Machine Learning · Computer Science 2021-06-08 Rohitash Chandra , Shaurya Goyal , Rishabh Gupta

One very important hyperparameter for training deep neural networks is the learning rate schedule of the optimizer. The choice of learning rate schedule determines the computational cost of getting close to a minima, how close you actually…

Machine Learning · Computer Science 2021-06-01 Nikhil Iyer , V Thejas , Nipun Kwatra , Ramachandran Ramjee , Muthian Sivathanu

Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

Machine Learning · Computer Science 2022-12-20 Jean-Roch Vlimant , Junqi Yin

Curriculum Learning emphasizes the order of training instances in a computational learning setup. The core hypothesis is that simpler instances should be learned early as building blocks to learn more complex ones. Despite its usefulness,…

Computation and Language · Computer Science 2016-11-21 Volkan Cirik , Eduard Hovy , Louis-Philippe Morency

Generalization of deep neural networks remains one of the main open problems in machine learning. Previous theoretical works focused on deriving tight bounds of model complexity, while empirical works revealed that neural networks exhibit…

Machine Learning · Computer Science 2022-01-31 James Wang , Cheng-Lin Yang

Low precision training can significantly reduce the computational overhead of training deep neural networks (DNNs). Though many such techniques exist, cyclic precision training (CPT), which dynamically adjusts precision throughout training…

Machine Learning · Computer Science 2024-03-05 Cameron R. Wolfe , Anastasios Kyrillidis

It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates…

Computer Vision and Pattern Recognition · Computer Science 2017-04-05 Leslie N. Smith