Empirical evaluation of the Frank-Wolfe methods for constructing white-box adversarial attacks

2025/12/11 by Kristina Korotkova, Korotkova, Kristina, Aleksandr Katrutsa +1
Computer Science · #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2512.10936

openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

Abstract

The construction of adversarial attacks for neural networks appears to be a crucial challenge for their deployment in various services. To estimate the adversarial robustness of a neural network, a fast and efficient approach is needed to construct adversarial attacks. Since the formalization of adversarial attack construction involves solving a specific optimization problem, we consider the problem of constructing an efficient and effective adversarial attack from a numerical optimization perspective. Specifically, we suggest utilizing advanced projection-free methods, known as modified Frank-Wolfe methods, to construct white-box adversarial attacks on the given input data. We perform a theoretical and numerical evaluation of these methods and compare them with standard approaches based on projection operations or geometrical intuition. Numerical experiments are performed on the MNIST and CIFAR-10 datasets, utilizing a multiclass logistic regression model, the convolutional neural networks (CNNs), and the Vision Transformer (ViT).

Citations

• Adversarial Attacks of Vision Tasks in the Past 10 Years: A Survey
• Certification of Speaker Recognition Models to Additive Perturbations
• Sparse and Transferable Universal Singular Vectors Attack
• The Frank-Wolfe algorithm: a short introduction
• Learning Cuts via Enumeration Oracles
• Translate your gibberish: black-box adversarial attack on machine translation systems
• A Multistep Frank-Wolfe Method
• Frank-Wolfe and friends: a journey into projection-free first-order optimization methods
• Adversarial Attacks and Defenses for Speech Recognition Systems
• Understanding and Increasing Efficiency of Frank-Wolfe Adversarial Training
• An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale
• Universal Adversarial Attack on Attention and the Resulting Dataset DAmageNet
• Imperceptible, Robust, and Targeted Adversarial Examples for Automatic Speech Recognition
• A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks
• Art of singular vectors and universal adversarial perturbations
• Towards Deep Learning Models Resistant to Adversarial Attacks
• Simple Black-Box Adversarial Perturbations for Deep Networks
• Adversarial Machine Learning at Scale
• Universal adversarial perturbations
• Towards Evaluating the Robustness of Neural Networks
• On the Global Linear Convergence of Frank-Wolfe Optimization Variants
• DeepFool: a simple and accurate method to fool deep neural networks
• Explaining and Harnessing Adversarial Examples
• Intriguing properties of neural networks
• Solving Variational Inequalities with Monotone Operators on Domains Given by Linear Minimization Oracles
• The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle

Related

• A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks
• Understanding and Increasing Efficiency of Frank-Wolfe Adversarial Training
• Generalizable Adversarial Attacks with Latent Variable Perturbation\n Modelling
• Thundernna: a white box adversarial attack
• DI-AA: An Interpretable White-box Attack for Fooling Deep Neural Networks