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This paper demonstrates that in classification problems, fully connected neural networks (FCNs) and residual neural networks (ResNets) cannot be approximated by kernel logistic regression based on the Neural Tangent Kernel (NTK) under…

Machine Learning · Computer Science 2025-07-15 Zixiong Yu , Songtao Tian , Guhan Chen

Domain adaptation is widely used in learning problems lacking labels. Recent studies show that deep adversarial domain adaptation models can make markable improvements in performance, which include symmetric and asymmetric architectures.…

Computer Vision and Pattern Recognition · Computer Science 2019-09-19 Guanyu Cai , Yuqin Wang , Mengchu Zhou , Lianghua He

Multiple different approaches of generating adversarial examples have been proposed to attack deep neural networks. These approaches involve either directly computing gradients with respect to the image pixels, or directly solving an…

Neural and Evolutionary Computing · Computer Science 2017-03-29 Shumeet Baluja , Ian Fischer

Adversarial training (AT) is an effective defense for large language models (LLMs) against jailbreak attacks, but performing AT on LLMs is costly. To improve the efficiency of AT for LLMs, recent studies propose continuous AT (CAT) that…

Machine Learning · Computer Science 2026-04-15 Shaopeng Fu , Di Wang

Adversarial training (AT) is a powerful regularization method for neural networks, aiming to achieve robustness to input perturbations. Yet, the specific effects of the robustness obtained from AT are still unclear in the context of natural…

Computation and Language · Computer Science 2018-04-23 Michihiro Yasunaga , Jungo Kasai , Dragomir Radev

The Neural Tangent Kernel (NTK) framework has provided deep insights into the training dynamics of neural networks under gradient flow. However, it relies on the assumption that the network is differentiable with respect to its parameters,…

Machine Learning · Computer Science 2025-09-17 Sriram Nagaraj , Vishakh Hari

Lecture notes from the course given by Professor Julia Kempe at the summer school "Statistical physics of Machine Learning" in Les Houches. The notes discuss the so-called NTK approach to problems in machine learning, which consists of…

Machine Learning · Computer Science 2023-07-07 Francesco Cagnetta , Deborah Oliveira , Mahalakshmi Sabanayagam , Nikolaos Tsilivis , Julia Kempe

Deep networks are vulnerable to adversarial examples. Adversarial Training (AT) has been a standard foundation of modern adversarial defense approaches due to its remarkable effectiveness. However, AT is extremely time-consuming, refraining…

Machine Learning · Computer Science 2024-05-28 Shao-Yuan Lo , Vishal M. Patel

The vulnerability of deep neural networks (DNNs) to adversarial examples has attracted great attention in the machine learning community. The problem is related to non-flatness and non-smoothness of normally obtained loss landscapes.…

Machine Learning · Computer Science 2023-02-13 Qizhang Li , Yiwen Guo , Wangmeng Zuo , Hao Chen

Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not…

Machine Learning · Computer Science 2021-05-11 Greg Yang , Etai Littwin

We analyze the convergence of the averaged stochastic gradient descent for overparameterized two-layer neural networks for regression problems. It was recently found that a neural tangent kernel (NTK) plays an important role in showing the…

Machine Learning · Statistics 2021-06-14 Atsushi Nitanda , Taiji Suzuki

For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a…

Machine Learning · Computer Science 2021-10-14 Guillermo Ortiz-Jiménez , Seyed-Mohsen Moosavi-Dezfooli , Pascal Frossard

Neural networks are getting deeper and more computation-intensive nowadays. Quantization is a useful technique in deploying neural networks on hardware platforms and saving computation costs with negligible performance loss. However, recent…

Machine Learning · Computer Science 2021-01-26 Chang Song , Elias Fallon , Hai Li

While deep neural networks have achieved remarkable success in various computer vision tasks, they often fail to generalize to new domains and subtle variations of input images. Several defenses have been proposed to improve the robustness…

Computer Vision and Pattern Recognition · Computer Science 2021-09-08 Omid Poursaeed , Tianxing Jiang , Harry Yang , Serge Belongie , SerNam Lim

While existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real-world settings. In many such cases although test data might not be…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Tejas Gokhale , Rushil Anirudh , Bhavya Kailkhura , Jayaraman J. Thiagarajan , Chitta Baral , Yezhou Yang

Recently, unsupervised adversarial training (AT) has been highlighted as a means of achieving robustness in models without any label information. Previous studies in unsupervised AT have mostly focused on implementing self-supervised…

Machine Learning · Computer Science 2023-10-27 Minseon Kim , Hyeonjeong Ha , Sooel Son , Sung Ju Hwang

Raw deep neural network (DNN) performance is not enough; in real-world settings, computational load, training efficiency and adversarial security are just as or even more important. We propose to simultaneously tackle Performance,…

Computer Vision and Pattern Recognition · Computer Science 2022-04-15 Madan Ravi Ganesh , Salimeh Yasaei Sekeh , Jason J. Corso

Adversarial Training (AT) is one of the most effective methods for developing robust deep neural networks (DNNs). However, AT faces a trade-off problem between clean accuracy and adversarial robustness. In this work, we reveal a surprising…

Computer Vision and Pattern Recognition · Computer Science 2026-04-30 Yanyun Wang , Qingqing Ye , Li Liu , Zi Liang , Haibo Hu

In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed…

Numerical Analysis · Mathematics 2025-11-20 Max Hirsch , Federico Pichi

Adversarial training is a method for enhancing neural networks to improve the robustness against adversarial examples. Besides the security concerns of potential adversarial examples, adversarial training can also improve the generalization…

Machine Learning · Computer Science 2022-12-21 Zhiyuan Zhang , Wei Li , Ruihan Bao , Keiko Harimoto , Yunfang Wu , Xu Sun