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We define the local complexity of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn…

Machine Learning · Computer Science 2025-07-15 Niket Patel , Guido Montufar

Adversarial robustness is essential for security and reliability of machine learning systems. However, adversarial robustness enhanced by defense algorithms is easily erased as the neural network's weights update to learn new tasks. To…

Machine Learning · Computer Science 2024-08-14 Xiaolei Ru , Xiaowei Cao , Zijia Liu , Jack Murdoch Moore , Xin-Ya Zhang , Xia Zhu , Wenjia Wei , Gang Yan

Adversarial training is a widely-applied approach to training deep neural networks to be robust against adversarial perturbation. However, although adversarial training has achieved empirical success in practice, it still remains unclear…

Machine Learning · Computer Science 2025-02-10 Binghui Li , Yuanzhi Li

Deep Neural Networks (DNN) have been shown to be vulnerable to adversarial examples. Adversarial training (AT) is a popular and effective strategy to defend against adversarial attacks. Recent works (Benz et al., 2020; Xu et al., 2021; Tian…

Machine Learning · Computer Science 2023-02-09 Boqi Li , Weiwei Liu

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial…

Machine Learning · Computer Science 2018-11-27 Seyed-Mohsen Moosavi-Dezfooli , Alhussein Fawzi , Jonathan Uesato , Pascal Frossard

We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks…

Machine Learning · Computer Science 2022-02-01 Chandresh Pravin , Ivan Martino , Giuseppe Nicosia , Varun Ojha

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

Machine Learning · Computer Science 2021-05-27 Yatong Bai , Tanmay Gautam , Yu Gai , Somayeh Sojoudi

Artificial neural networks in general and deep learning networks in particular established themselves as popular and powerful machine learning algorithms. While the often tremendous sizes of these networks are beneficial when solving…

Machine Learning · Computer Science 2020-05-28 Moritz Seiler , Heike Trautmann , Pascal Kerschke

Deep networks are well-known to be fragile to adversarial attacks. We conduct an empirical analysis of deep representations under the state-of-the-art attack method called PGD, and find that the attack causes the internal representation to…

Machine Learning · Computer Science 2019-10-29 Chengzhi Mao , Ziyuan Zhong , Junfeng Yang , Carl Vondrick , Baishakhi Ray

The new wave of adversarial attacks that utilize gradient-related vulnerabilities in neural network-based classifiers makes Network Intrusion Detection Systems more open to such threats. Although state-of-the-art adversarial training…

Cryptography and Security · Computer Science 2026-05-12 Hira Nasir , Eiman Javed , Balawal Shabir , Zunera Jalil , Ahmad Mohsin

While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…

Machine Learning · Computer Science 2019-12-05 Varun Chandrasekaran , Brian Tang , Nicolas Papernot , Kassem Fawaz , Somesh Jha , Xi Wu

In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to…

Machine Learning · Computer Science 2025-06-27 Silas Dobler , Florian Lemmerich

In recent years, neural networks have demonstrated outstanding effectiveness in a large amount of applications.However, recent works have shown that neural networks are susceptible to adversarial examples, indicating possible flaws…

Machine Learning · Computer Science 2018-06-08 Fuxun Yu , Zirui Xu , Yanzhi Wang , Chenchen Liu , Xiang Chen

The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization…

Machine Learning · Computer Science 2020-06-15 Yonatan Dukler , Quanquan Gu , Guido Montúfar

We propose ReDense as a simple and low complexity way to improve the performance of trained neural networks. We use a combination of random weights and rectified linear unit (ReLU) activation function to add a ReLU dense (ReDense) layer to…

Machine Learning · Computer Science 2020-10-27 Alireza M. Javid , Sandipan Das , Mikael Skoglund , Saikat Chatterjee

Adversarial attacks add perturbations to the input features with the intent of changing the classification produced by a machine learning system. Small perturbations can yield adversarial examples which are misclassified despite being…

Machine Learning · Computer Science 2019-02-05 Rakshit Agrawal , Luca de Alfaro , David Helmbold

Many existing deep learning models are vulnerable to adversarial examples that are imperceptible to humans. To address this issue, various methods have been proposed to design network architectures that are robust to one particular type of…

Machine Learning · Computer Science 2021-01-19 Jia Liu , Yaochu Jin

Deep Neural Networks are vulnerable to adversarial attacks. Among many defense strategies, adversarial training with untargeted attacks is one of the most effective methods. Theoretically, adversarial perturbation in untargeted attacks can…

Computer Vision and Pattern Recognition · Computer Science 2022-12-01 Pengyue Hou , Jie Han , Xingyu Li

In recent years, it has been found that neural networks can be easily fooled by adversarial examples, which is a potential safety hazard in some safety-critical applications. Many researchers have proposed various method to make neural…

Machine Learning · Computer Science 2018-04-24 Shuangtao Li , Yuanke Chen , Yanlin Peng , Lin Bai

In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a…

Machine Learning · Computer Science 2025-11-05 Jingchao Gao , Ziqing Lu , Raghu Mudumbai , Xiaodong Wu , Jirong Yi , Myung Cho , Catherine Xu , Hui Xie , Weiyu Xu