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Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful…

Machine Learning · Computer Science 2025-02-03 Philipp Misof , Pan Kessel , Jan E. Gerken

Neural networks are vulnerable to adversarial examples, i.e. inputs that are imperceptibly perturbed from natural data and yet incorrectly classified by the network. Adversarial training, a heuristic form of robust optimization that…

Machine Learning · Computer Science 2019-11-12 Ruiqi Gao , Tianle Cai , Haochuan Li , Liwei Wang , Cho-Jui Hsieh , Jason D. Lee

Sequential training from task to task is becoming one of the major objects in deep learning applications such as continual learning and transfer learning. Nevertheless, it remains unclear under what conditions the trained model's…

Machine Learning · Statistics 2022-03-21 Ryo Karakida , Shotaro Akaho

The performance of the data-dependent neural tangent kernel (NTK; Jacot et al. (2018)) associated with a trained deep neural network (DNN) often matches or exceeds that of the full network. This implies that DNN training via gradient…

Machine Learning · Computer Science 2025-05-22 Johannes Schwab , Bryan Kelly , Semyon Malamud , Teng Andrea Xu

A recent breakthrough in deep learning theory shows that the training of over-parameterized deep neural networks can be characterized by a kernel function called \textit{neural tangent kernel} (NTK). However, it is known that this type of…

Machine Learning · Computer Science 2020-10-07 Zixiang Chen , Yuan Cao , Quanquan Gu , Tong Zhang

The Neural Tangent Kernel (NTK) has recently attracted intense study, as it describes the evolution of an over-parameterized Neural Network (NN) trained by gradient descent. However, it is now well-known that gradient descent is not always…

Machine Learning · Computer Science 2021-03-23 Lei Tan , Shutong Wu , Xiaolin Huang

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

Machine Learning · Statistics 2025-10-27 Antônio H. Ribeiro , David Vävinggren , Dave Zachariah , Thomas B. Schön , Francis Bach

Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples,…

Machine Learning · Computer Science 2020-11-20 Yinpeng Dong , Zhijie Deng , Tianyu Pang , Hang Su , Jun Zhu

Training data privacy is a fundamental problem in modern Artificial Intelligence (AI) applications, such as face recognition, recommendation systems, language generation, and many others, as it may contain sensitive user information related…

Machine Learning · Computer Science 2024-11-05 Jiuxiang Gu , Yingyu Liang , Zhizhou Sha , Zhenmei Shi , Zhao Song

Adversarial training (AT) has proven to be one of the most effective ways to defend Deep Neural Networks (DNNs) against adversarial attacks. However, the phenomenon of robust overfitting, i.e., the robustness will drop sharply at a certain…

Machine Learning · Computer Science 2022-05-25 Shudong Zhang , Haichang Gao , Tianwei Zhang , Yunyi Zhou , Zihui Wu

This paper investigates the Neural Tangent Kernel (NTK) to search vision transformers without training. In contrast with the previous observation that NTK-based metrics can effectively predict CNNs performance at initialization, we…

Computer Vision and Pattern Recognition · Computer Science 2024-05-09 Qiqi Zhou , Yichen Zhu

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

Adversarial training (AT) is a regularization method that can be used to improve the robustness of neural network methods by adding small perturbations in the training data. We show how to use AT for the tasks of entity recognition and…

Computation and Language · Computer Science 2019-01-15 Giannis Bekoulis , Johannes Deleu , Thomas Demeester , Chris Develder

Neural Tangent Kernel (NTK) is widely used to analyze overparametrized neural networks due to the famous result by Jacot et al. (2018): in the infinite-width limit, the NTK is deterministic and constant during training. However, this result…

Machine Learning · Computer Science 2022-07-22 Mariia Seleznova , Gitta Kutyniok

A counter-intuitive property of convolutional neural networks (CNNs) is their inherent susceptibility to adversarial examples, which severely hinders the application of CNNs in security-critical fields. Adversarial examples are similar to…

Machine Learning · Computer Science 2022-07-27 Jiebao Zhang , Wenhua Qian , Rencan Nie , Jinde Cao , Dan Xu

The Neural Tangent Kernel (NTK) has discovered connections between deep neural networks and kernel methods with insights of optimization and generalization. Motivated by this, recent works report that NTK can achieve better performances…

Machine Learning · Computer Science 2021-04-06 Insu Han , Haim Avron , Neta Shoham , Chaewon Kim , Jinwoo Shin

Deep Neural Network (DNN) are vulnerable to adversarial attacks. As a countermeasure, adversarial training aims to achieve robustness based on the min-max optimization problem and it has shown to be one of the most effective defense…

Computer Vision and Pattern Recognition · Computer Science 2022-05-03 Yaxin Li , Xiaorui Liu , Han Xu , Wentao Wang , Jiliang Tang

The Neural Tangent Kernel (NTK) is an important milestone in the ongoing effort to build a theory for deep learning. Its prediction that sufficiently wide neural networks behave as kernel methods, or equivalently as random feature models,…

Machine Learning · Computer Science 2020-06-25 Maxim Samarin , Volker Roth , David Belius

Deep neural networks are susceptible to adversarial attacks and common corruptions, which undermine their robustness. In order to enhance model resilience against such challenges, Adversarial Training (AT) has emerged as a prominent…

Machine Learning · Computer Science 2025-06-17 Tejaswini Medi , Steffen Jung , Margret Keuper

Adversarial training is exploited to develop a robust Deep Neural Network (DNN) model against the malicious altered data. These attacks may have catastrophic effects on DNN models but are indistinguishable for a human being. For example, an…

Machine Learning · Computer Science 2022-10-14 Farzad Nikfam , Alberto Marchisio , Maurizio Martina , Muhammad Shafique