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Projected Gradient Descent (PGD) is a strong and widely used first-order adversarial attack, yet its computational cost scales poorly, as all training samples undergo identical iterative inner-loop optimization despite contributing…

Machine Learning · Computer Science 2025-12-29 Youran Ye , Dejin Wang , Ajinkya Bhandare

Adversarial attacks on deep neural network models have seen rapid development and are extensively used to study the stability of these networks. Among various adversarial strategies, Projected Gradient Descent (PGD) is a widely adopted…

Machine Learning · Computer Science 2024-10-17 Dayana Savostianova , Emanuele Zangrando , Francesco Tudisco

Adversarial training, especially projected gradient descent (PGD), has proven to be a successful approach for improving robustness against adversarial attacks. After adversarial training, gradients of models with respect to their inputs…

Machine Learning · Statistics 2023-04-21 Ricardo Bigolin Lanfredi , Joyce D. Schroeder , Tolga Tasdizen

In recent years, deep neural networks have demonstrated outstanding performance in many machine learning tasks. However, researchers have discovered that these state-of-the-art models are vulnerable to adversarial examples: legitimate…

Machine Learning · Computer Science 2018-10-10 Ting-Jui Chang , Yukun He , Peng Li

Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberately mislead the models. While they can be easily generated using gradient-based techniques in digital and physical…

Computer Vision and Pattern Recognition · Computer Science 2024-01-18 Haotian Xue , Alexandre Araujo , Bin Hu , Yongxin Chen

High cost of training time caused by multi-step adversarial example generation is a major challenge in adversarial training. Previous methods try to reduce the computational burden of adversarial training using single-step adversarial…

Machine Learning · Computer Science 2021-02-09 Lehui Xie , Yaopeng Wang , Jia-Li Yin , Ximeng Liu

Adversarial training is the most successful empirical method for increasing the robustness of neural networks against adversarial attacks. However, the most effective approaches, like training with Projected Gradient Descent (PGD) are…

Machine Learning · Computer Science 2020-03-18 Leo Schwinn , René Raab , Björn Eskofier

Deep learning achieves state-of-the-art performance in many tasks but exposes to the underlying vulnerability against adversarial examples. Across existing defense techniques, adversarial training with the projected gradient decent attack…

Cryptography and Security · Computer Science 2022-10-04 Tianjin Huang , Vlado Menkovski , Yulong Pei , Mykola Pechenizkiy

Generating high-quality and interpretable adversarial examples in the text domain is a much more daunting task than it is in the image domain. This is due partly to the discrete nature of text, partly to the problem of ensuring that the…

Machine Learning · Computer Science 2019-05-31 Samuel Barham , Soheil Feizi

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

Projected Gradient Descent (PGD) under the $L_\infty$ ball has become one of the defacto methods used in adversarial robustness evaluation for computer vision (CV) due to its reliability and efficacy, making a strong and easy-to-implement…

Computer Vision and Pattern Recognition · Computer Science 2025-03-26 Philip Doldo , Derek Everett , Amol Khanna , Andre T Nguyen , Edward Raff

Projected Gradient Descent (PGD) based adversarial training has become one of the most prominent methods for building robust deep neural network models. However, the computational complexity associated with this approach, due to the…

Machine Learning · Computer Science 2020-05-01 Sidharth Gupta , Parijat Dube , Ashish Verma

Adversarial Training (AT) with Projected Gradient Descent (PGD) is an effective approach for improving the robustness of the deep neural networks. However, PGD AT has been shown to suffer from two main limitations: i) high computational…

Computer Vision and Pattern Recognition · Computer Science 2020-12-29 Ahmadreza Jeddi , Mohammad Javad Shafiee , Alexander Wong

Recent work on adversarial attack and defense suggests that PGD is a universal $l_\infty$ first-order attack, and PGD adversarial training can significantly improve network robustness against a wide range of first-order $l_\infty$-bounded…

Machine Learning · Computer Science 2018-10-22 Tianhang Zheng , Changyou Chen , Kui Ren

Deep learning models have achieved state-of-the-art performances in various domains, while they are vulnerable to the inputs with well-crafted but small perturbations, which are named after adversarial examples (AEs). Among many strategies…

Computer Vision and Pattern Recognition · Computer Science 2023-10-11 Huihui Gong

Adversarial attacks against deep learning models represent a major threat to the security and reliability of natural language processing (NLP) systems. In this paper, we propose a modification to the BERT-Attack framework, integrating…

Machine Learning · Computer Science 2024-08-01 Hetvi Waghela , Jaydip Sen , Sneha Rakshit

Making deep neural networks robust to small adversarial noises has recently been sought in many applications. Adversarial training through iterative projected gradient descent (PGD) has been established as one of the mainstream ideas to…

Machine Learning · Computer Science 2021-03-30 Zeinab Golgooni , Mehrdad Saberi , Masih Eskandar , Mohammad Hossein Rohban

Deep neural network-based image classifications are vulnerable to adversarial perturbations. The image classifications can be easily fooled by adding artificial small and imperceptible perturbations to input images. As one of the most…

Computer Vision and Pattern Recognition · Computer Science 2023-08-16 Jindong Gu , Hengshuang Zhao , Volker Tresp , Philip Torr

Diffusion models have shown remarkable promise for image restoration by leveraging powerful priors. Prominent methods typically frame the restoration problem within a Bayesian inference framework, which iteratively combines a denoising step…

Computer Vision and Pattern Recognition · Computer Science 2025-09-04 Hongjie Wu , Mingqin Zhang , Linchao He , Ji-Zhe Zhou , Jiancheng Lv

Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that…

Statistics Theory · Mathematics 2024-11-27 Niklas Dexheimer , Johannes Schmidt-Hieber
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