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Deep ReLU networks trained with the square loss have been observed to perform well in classification tasks. We provide here a theoretical justification based on analysis of the associated gradient flow. We show that convergence to a…

Machine Learning · Computer Science 2021-01-05 Tomaso Poggio , Qianli Liao

We introduce a Normalized Convolutional Neural Layer, a novel approach to normalization in convolutional networks. Unlike conventional methods, this layer normalizes the rows of the im2col matrix during convolution, making it inherently…

Computer Vision and Pattern Recognition · Computer Science 2025-04-03 Dongsuk Kim , Geonhee Lee , Myungjae Lee , Shin Uk Kang , Dongmin Kim

Batch normalization (BN) is an important technique commonly incorporated into deep learning models to perform standardization within mini-batches. The merits of BN in improving a model's learning efficiency can be further amplified by…

Machine Learning · Computer Science 2021-04-07 Lei Huang , Yi Zhou , Li Liu , Fan Zhu , Ling Shao

As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However,…

Computer Vision and Pattern Recognition · Computer Science 2018-03-01 Guangrun Wang , Jiefeng Peng , Ping Luo , Xinjiang Wang , Liang Lin

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

Machine Learning · Computer Science 2021-08-26 Difan Zou , Yuan Cao , Yuanzhi Li , Quanquan Gu

Deep neural networks often suffer the data distribution shift between training and testing, and the batch statistics are observed to reflect the shift. In this paper, targeting of alleviating distribution shift in test time, we revisit the…

Machine Learning · Computer Science 2022-05-23 Tao Yang , Shenglong Zhou , Yuwang Wang , Yan Lu , Nanning Zheng

Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered…

Machine Learning · Computer Science 2020-06-25 Jary Pomponi , Simone Scardapane , Vincenzo Lomonaco , Aurelio Uncini

It is important to understand how dropout, a popular regularization method, aids in achieving a good generalization solution during neural network training. In this work, we present a theoretical derivation of an implicit regularization of…

Machine Learning · Computer Science 2023-04-11 Zhongwang Zhang , Zhi-Qin John Xu

In this paper, we study normalization methods for neural networks from the perspective of elimination singularity. Elimination singularities correspond to the points on the training trajectory where neurons become consistently deactivated.…

Computer Vision and Pattern Recognition · Computer Science 2020-08-10 Siyuan Qiao , Huiyu Wang , Chenxi Liu , Wei Shen , Alan Yuille

Batch Normalization (BatchNorm) is a technique that improves the training of deep neural networks, especially Convolutional Neural Networks (CNN). It has been empirically demonstrated that BatchNorm increases performance, stability, and…

Machine Learning · Computer Science 2023-03-24 Yashna Peerthum , Mark Stamp

Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of…

Machine Learning · Computer Science 2017-10-24 Chunjie Luo , Jianfeng Zhan , Lei Wang , Qiang Yang

Neural Network based models have been state-of-the-art models for various Natural Language Processing tasks, however, the input and output dimension problem in the networks has still not been fully resolved, especially in text generation…

Computation and Language · Computer Science 2020-01-27 Jinyang Liu , Yujia Zhai , Zizhong Chen

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize…

Standard convolutional neural networks(CNNs) require consistent image resolutions in both training and testing phase. However, in practice, testing with smaller image sizes is necessary for fast inference. We show that trivially evaluating…

Computer Vision and Pattern Recognition · Computer Science 2020-09-08 Zhuoran Yu , Aojun Zhou , Yukun Ma , Yudian Li , Xiaohan Zhang , Ping Luo

Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA)…

Computer Vision and Pattern Recognition · Computer Science 2023-01-30 Alexandre Ramé , Matthieu Kirchmeyer , Thibaud Rahier , Alain Rakotomamonjy , Patrick Gallinari , Matthieu Cord

Despite the significant success of deep learning in computer vision tasks, cross-domain tasks still present a challenge in which the model's performance will degrade when the training set and the test set follow different distributions.…

Computer Vision and Pattern Recognition · Computer Science 2024-09-17 Lei Qi , Dongjia Zhao , Yinghuan Shi , Xin Geng

A popular method to reduce the training time of deep neural networks is to normalize activations at each layer. Although various normalization schemes have been proposed, they all follow a common theme: normalize across spatial dimensions…

Computer Vision and Pattern Recognition · Computer Science 2019-12-20 Boyi Li , Felix Wu , Kilian Q. Weinberger , Serge Belongie

Despite the simplicity, stochastic gradient descent (SGD)-like algorithms are successful in training deep neural networks (DNNs). Among various attempts to improve SGD, weight averaging (WA), which averages the weights of multiple models,…

Machine Learning · Computer Science 2023-04-25 Xiaozhe Gu , Zixun Zhang , Yuncheng Jiang , Tao Luo , Ruimao Zhang , Shuguang Cui , Zhen Li

In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions,…

Machine Learning · Computer Science 2019-07-18 Simon Guiroy , Vikas Verma , Christopher Pal

Modern meta-learning approaches for image classification rely on increasingly deep networks to achieve state-of-the-art performance, making batch normalization an essential component of meta-learning pipelines. However, the hierarchical…

Machine Learning · Statistics 2020-07-14 John Bronskill , Jonathan Gordon , James Requeima , Sebastian Nowozin , Richard E. Turner