Robustness Verification against Patch Attacks via Group-Lasso Semidefinite Relaxation

Robustness verification is essential for ensuring the safety and security of neural networks, but current methods focus heavily on norm-ball attacks, which do not adequately model typical real-world threats that present physical perturbations, known as patch attacks. A naive approach requires computationally prohibitive enumeration of all possible patch positions. To address the challenge, we propose a novel neural network verification method specialized to the patch-attack threat. Instead of enumerating patch locations, we first model the patch attack with group-wise sparsity and formulate its verification methods as a mixed-integer semidefinite program (MISDP) by applying SDP relaxation to the neural network. We then propose three relaxations, including Group-Lasso relaxation, that remove the integer variables while preserving the sparse, group-wise structure of the original attack, enabling substantially efficient verification. Our empirical analysis demonstrates that the proposed relaxations require less than 3% of the computation time of the original MISDP, while the Group-Lasso relaxation incurs only a 0.34\% average increase in the objective value over the original formulation. Furthermore, Group-Lasso achieves a verified rate of 91%, compared with under 70% for prior methods.