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A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…

Machine Learning · Computer Science 2022-06-28 Yang Zhao , Hao Zhang , Xiuyuan Hu

Adversarial training (AT) with samples generated by Fast Gradient Sign Method (FGSM), also known as FGSM-AT, is a computationally simple method to train robust networks. However, during its training procedure, an unstable mode of…

Computer Vision and Pattern Recognition · Computer Science 2022-09-07 Zichao Li , Li Liu , Zeyu Wang , Yuyin Zhou , Cihang Xie

Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other…

Machine Learning · Computer Science 2020-10-06 Wei Hu , Zhiyuan Li , Dingli Yu

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

Machine Learning · Statistics 2017-11-07 Jason Xu , Eric C. Chi , Kenneth Lange

Adversarial examples are augmented data points generated by imperceptible perturbation of input samples. They have recently drawn much attention with the machine learning and data mining community. Being difficult to distinguish from real…

Machine Learning · Computer Science 2016-03-03 Chunchuan Lyu , Kaizhu Huang , Hai-Ning Liang

We study the generalization properties of stochastic gradient methods for learning with convex loss functions and linearly parameterized functions. We show that, in the absence of penalizations or constraints, the stability and…

Machine Learning · Computer Science 2016-05-27 Junhong Lin , Raffaello Camoriano , Lorenzo Rosasco

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

Computation and Language · Computer Science 2018-11-05 Deren Lei , Zichen Sun , Yijun Xiao , William Yang Wang

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Machine Learning · Computer Science 2021-02-24 Shengchao Liu , Dimitris Papailiopoulos , Dimitris Achlioptas

The nature of deep neural networks has given rise to a variety of attacks, but little work has been done to address the effect of adversarial attacks on segmentation models trained on MRI datasets. In light of the grave consequences that…

Image and Video Processing · Electrical Eng. & Systems 2024-01-23 Zhongxuan Wang , Leo Xu

Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs).…

Machine Learning · Computer Science 2021-06-14 Tianle Cai , Shengjie Luo , Keyulu Xu , Di He , Tie-Yan Liu , Liwei Wang

Adversarial training, a method for learning robust deep networks, is typically assumed to be more expensive than traditional training due to the necessity of constructing adversarial examples via a first-order method like projected gradient…

Machine Learning · Computer Science 2020-01-14 Eric Wong , Leslie Rice , J. Zico Kolter

Adversarial training (AT) has been demonstrated to be effective in improving model robustness by leveraging adversarial examples for training. However, most AT methods are in face of expensive time and computational cost for calculating…

Computer Vision and Pattern Recognition · Computer Science 2022-07-13 Xiaojun Jia , Yong Zhang , Baoyuan Wu , Jue Wang , Xiaochun Cao

Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…

Artificial Intelligence · Computer Science 2011-04-19 Salah Rifai , Xavier Glorot , Yoshua Bengio , Pascal Vincent

Transfer learning is often used to decrease the computational cost of model training, as fine-tuning a model allows a downstream task to leverage the features learned from the pre-training dataset and quickly adapt them to a new task. This…

Machine Learning · Computer Science 2025-07-01 Joshua C. Zhao , Saurabh Bagchi

Deep neural networks are vulnerable to adversarial examples, which are crafted by adding small, human-imperceptible perturbations to the original images, but make the model output inaccurate predictions. Before deep neural networks are…

Computer Vision and Pattern Recognition · Computer Science 2021-01-13 Bo Yang , Kaiyong Xu , Hengjun Wang , Hengwei Zhang

The notion of adversarial attacks on image classification models based on convolutional neural networks (CNN) is introduced in this work. To classify images, deep learning models called CNNs are frequently used. However, when the networks…

Computer Vision and Pattern Recognition · Computer Science 2023-12-29 Jaydip Sen , Abhiraj Sen , Ananda Chatterjee

Recently, Neural networks have seen a huge surge in its adoption due to their ability to provide high accuracy on various tasks. On the other hand, the existence of adversarial examples have raised suspicions regarding the generalization…

Machine Learning · Computer Science 2018-01-04 Mayank Singh , Abhishek Sinha , Balaji Krishnamurthy

Most machine learning models are vulnerable to adversarial examples, which poses security concerns on these models. Adversarial examples are crafted by applying subtle but intentionally worst-case modifications to examples from the dataset,…

Machine Learning · Computer Science 2025-10-23 Xingyang Nie , Guojie Xiao , Su Pan , Biao Wang , Huilin Ge , Tao Fang

Deep neural networks have shown to be very vulnerable to adversarial examples crafted by adding human-imperceptible perturbations to benign inputs. After achieving impressive attack success rates in the white-box setting, more focus is…

Computer Vision and Pattern Recognition · Computer Science 2022-04-26 Xu Han , Anmin Liu , Yifeng Xiong , Yanbo Fan , Kun He