Title: Adversarial Attack on Tensor Ring Decomposition
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: High-dimensional Data, Tensor Ring Decomposition, Adversarial Attack, Tensor Completion

Abstract: Tensor ring (TR) decomposition, a powerful tool for handling high-dimensional data, has been widely applied in various fields such as computer vision and recommender systems. However, the vulnerability of TR decomposition to adversarial perturbations has not been systematically studied, and it remains unclear how adversarial perturbations affect its low-rank approximation performance. To tackle this problem, we introduce a novel adversarial attack approach on tensor ring decomposition (AdaTR), formulated as an asymmetric max–min objective. Specifically, we aim to find the optimal perturbation that maximizes the reconstruction error of the low-TR-rank approximation. Furthermore, to alleviate the memory and computational overhead caused by iterative dependency during attacks, we propose a novel faster approximate gradient attack model (FAG-AdaTR) that avoids step-by-step perturbation tensor tracking while maintaining high attack effectiveness. Subsequently, we develop a gradient descent algorithm with numerical convergence guarantees. Numerical experiments on tensor decomposition, completion, and recommender systems using color images and videos validate the attack effectiveness of the proposed methods.