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Normalization techniques are essential for accelerating the training and improving the generalization of deep neural networks (DNNs), and have successfully been used in various applications. This paper reviews and comments on the past,…

Machine Learning · Computer Science 2020-09-29 Lei Huang , Jie Qin , Yi Zhou , Fan Zhu , Li Liu , Ling Shao

Neural networks can be powerful function approximators, which are able to model high-dimensional feature distributions from a subset of examples drawn from the target distribution. Naturally, they perform well at generalizing within the…

Machine Learning · Computer Science 2021-08-06 Aaron Eisermann , Jae Hee Lee , Cornelius Weber , Stefan Wermter

Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard…

Computer Vision and Pattern Recognition · Computer Science 2022-04-25 Xiaotong Li , Yongxing Dai , Yixiao Ge , Jun Liu , Ying Shan , Ling-Yu Duan

In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However,…

Machine Learning · Computer Science 2020-06-17 Jiacheng Sun , Xiangyong Cao , Hanwen Liang , Weiran Huang , Zewei Chen , Zhenguo Li

The performance of neural networks has been significantly improved by increasing the number of channels in convolutional layers. However, this increase in performance comes with a higher computational cost, resulting in numerous studies…

Machine Learning · Computer Science 2025-09-01 Youngkyu Lee , Jongho Park , Chang-Ock Lee

Re-initializing a neural network during training has been observed to improve generalization in recent works. Yet it is neither widely adopted in deep learning practice nor is it often used in state-of-the-art training protocols. This…

Machine Learning · Computer Science 2023-04-04 Sheheryar Zaidi , Tudor Berariu , Hyunjik Kim , Jörg Bornschein , Claudia Clopath , Yee Whye Teh , Razvan Pascanu

A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. To date, only limited progress has been made understanding…

Machine Learning · Computer Science 2022-09-30 Randall Balestriero , Richard G. Baraniuk

We perform an extensive empirical study of the statistical properties of Batch Norm and other common normalizers. This includes an examination of the correlation between representations of minibatches, gradient norms, and Hessian spectra…

Machine Learning · Computer Science 2020-10-22 Vinay Rao , Jascha Sohl-Dickstein

Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al.…

Machine Learning · Statistics 2019-06-10 Waldyn Martinez , J. Brian Gray

We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…

Machine Learning · Computer Science 2020-06-22 Thomas Steinke , Lydia Zakynthinou

While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch…

Machine Learning · Statistics 2016-06-21 Devansh Arpit , Yingbo Zhou , Hung Ngo , Venu Govindaraju

Ensemble methods are known for enhancing the accuracy and robustness of machine learning models by combining multiple base learners. However, standard approaches like greedy or random ensembling often fall short, as they assume a constant…

Machine Learning · Computer Science 2025-06-24 Sebastian Pineda Arango , Maciej Janowski , Lennart Purucker , Arber Zela , Frank Hutter , Josif Grabocka

Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization…

Machine Learning · Computer Science 2017-06-19 Twan van Laarhoven

In this paper, we analyze batch normalization from the perspective of discriminability and find the disadvantages ignored by previous studies: the difference in $l_2$ norms of sample features can hinder batch normalization from obtaining…

Computer Vision and Pattern Recognition · Computer Science 2023-03-22 Zhennan Wang , Kehan Li , Runyi Yu , Yian Zhao , Pengchong Qiao , Chang Liu , Fan Xu , Xiangyang Ji , Guoli Song , Jie Chen

Batch normalization (BatchNorm) is an effective yet poorly understood technique for neural network optimization. It is often assumed that the degradation in BatchNorm performance to smaller batch sizes stems from it having to estimate layer…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Neofytos Dimitriou , Ognjen Arandjelovic

While neural networks have shown remarkable success on classification tasks in terms of average-case performance, they often fail to perform well on certain groups of the data. Such group information may be expensive to obtain; thus, recent…

Machine Learning · Computer Science 2022-04-12 Nimit S. Sohoni , Maziar Sanjabi , Nicolas Ballas , Aditya Grover , Shaoliang Nie , Hamed Firooz , Christopher Ré

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

Machine Learning · Computer Science 2021-02-09 Taejong Joo , Uijung Chung

Real-world image recognition is often challenged by the variability of visual styles including object textures, lighting conditions, filter effects, etc. Although these variations have been deemed to be implicitly handled by more training…

Computer Vision and Pattern Recognition · Computer Science 2019-04-26 Hyeonseob Nam , Hyo-Eun Kim

Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…

Machine Learning · Computer Science 2022-02-22 Ming-Chang Chiu , Xuezhe Ma

Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…

Statistical Mechanics · Physics 2007-05-23 S. N. Coppersmith
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