Adversarial Frontiers: Minimum-Norm Attack Ensembles for Robustness Evaluation

arXiv:2607.19855v1 Announce Type: new Abstract: Adversarial robustness is commonly evaluated with predefined attack ensembles, such as AutoAttack, at a single perturbation budget arepsilon and on a selective choice of perturbation norms. We argue this formulation is fundamentally limited. First, robustness--perturbation curves may intersect or decay at different rates across models, making single-arepsilon rankings unstable. Second, current ensembles provide no evidence of optimality, leaving an unknown gap to worst-case performance. Third, fixed attack configurations provide no systematic control over the trade-off between attack strength and evaluation cost. To address these limitations, we introduce a unified evaluation framework based on a comprehensive pool of minimum-norm attacks and robustness--perturbation curves across ell_0, ell_1, ell_2 and ell_infty norms. We define the attack frontier as the worst-case robustness estimate the attack pool produces against a model. We then formalize evaluation as a frontier-approximation problem, constructing minimum-norm attack ensembles, optimized subsets of the comprehensive pool, that approach the frontier under a controllable query budget, with larger budgets monotonically tightening the estimate. Furthermore, we define the defense frontier as the maximum robustness across the model set at each perturbation size. We finally propose the Defense Optimality Index to rank defenses by their gap to the defense frontier, providing a ranking without selecting a reference arepsilon. On CIFAR-10 and ImageNet, our ensembles match or exceed AutoAttack on most defenses at every budget tier, at fixed and controllable query cost, offering practitioners a query-controlled, curve-based alternative to fixed-arepsilon evaluation.

Source: arXiv cs.LG | 2026-07-23